Aerodynamic shape optimization using control theory
NASA Technical Reports Server (NTRS)
Reuther, James
1996-01-01
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Optimal control theory for unitary transformations
Palao, Jose P.; Kosloff, Ronnie
2003-12-01
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time-dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory is used to solve the inversion problem irrespective of the initial input state. A unified formalism based on the Krotov method is developed leading to a different scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the X {sup 1}{sigma}{sub g}{sup +} electronic state of Na{sub 2}. Raman-like transitions through the A {sup 1}{sigma}{sub u}{sup +} electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Of the schemes studied, the square modulus scheme converges fastest. A study of the implementation of the Q qubit Fourier transform in the Na{sub 2} molecule was carried out for up to five qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.
Helicopter trajectory planning using optimal control theory
NASA Technical Reports Server (NTRS)
Menon, P. K. A.; Cheng, V. H. L.; Kim, E.
1988-01-01
A methodology for optimal trajectory planning, useful in the nap-of-the-earth guidance of helicopters, is presented. This approach uses an adjoint-control transformation along with a one-dimensional search scheme for generating the optimal trajectories. In addition to being useful for helicopter nap-of-the-earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and the threat envelopes are incorporated in the equations of motion. Second-order necessary conditions are examined.
Robust control systems design by H-infinity optimization theory
NASA Technical Reports Server (NTRS)
Chang, B. C.; Li, X. P.; Banda, S. S.; Yeh, H. H.
1991-01-01
In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.
OPTIMAL CONTROL THEORY FOR SUSTAINABLE ENVIRONMENTAL MANAGEMENT
Sustainable management of the human and natural systems, taking into account their interactions, has become paramount. To achieve this complex multidisciplinary objective, systems theory based techniques prove useful. The proposed work is a step in that direction. Taking a food w...
A Control Theory Solution to Optimal Faculty Staffing.
ERIC Educational Resources Information Center
Rowe, Stephen M.; And Others
This study investigates the resource allocation problem of faculty hiring and promotion patterns using the techniques of optimal control theory. The mathematical structure of an academic faculty is described by a linear dynamic model whose parameters were estimated from actual data by two different techniques. The principal characteristics of the…
Optimal preview game theory approach to vehicle stability controller design
NASA Astrophysics Data System (ADS)
Tamaddoni, Seyed Hossein; Taheri, Saied; Ahmadian, Mehdi
2011-12-01
Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.
Quantum optimal control theory in the linear response formalism
Castro, Alberto; Tokatly, I. V.
2011-09-15
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice, this normally means optimizing the value of some observable, a so-called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization: the unperturbed Hamiltonian is allowed to be time dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in terms of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for nonequilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems.
Optimal guidance law for cooperative attack of multiple missiles based on optimal control theory
NASA Astrophysics Data System (ADS)
Sun, Xiao; Xia, Yuanqing
2012-08-01
This article considers the problem of optimal guidance laws for cooperative attack of multiple missiles based on the optimal control theory. New guidance laws are presented such that multiple missiles attack a single target simultaneously. Simulation results show the effectiveness of the proposed algorithms.
Stabilization of ultracold molecules using optimal control theory
Koch, Christiane P.; Palao, Jose P.; Kosloff, Ronnie; Masnou-Seeuws, Francoise
2004-07-01
In recent experiments on ultracold matter, molecules have been produced from ultracold atoms by photoassociation, Feshbach resonances, and three-body recombination. The created molecules are translationally cold, but vibrationally highly excited. This will eventually lead them to be lost from the trap due to collisions. We propose shaped laser pulses to transfer these highly excited molecules to their ground vibrational level. Optimal control theory is employed to find the light field that will carry out this task with minimum intensity. We present results for the sodium dimer. The final target can be reached to within 99% provided the initial guess field is physically motivated. We find that the optimal fields contain the transition frequencies required by a good Franck-Condon pumping scheme. The analysis identifies the ranges of intensity and pulse duration which are able to achieve this task before any other competing processes take place. Such a scheme could produce stable ultracold molecular samples or even stable molecular Bose-Einstein condensates.
Analysis of modern optimal control theory applied to plasma position and current control in TFTR
Firestone, M.A.
1981-09-01
The strong compression TFTR discharge has been segmented into regions where linear dynamics can approximate the plasma's interaction with the OH and EF power supply systems. The dynamic equations for these regions are utilized within the linear optimal control theory framework to provide active feedback gains to control the plasma position and current. Methods are developed to analyze and quantitatively evaluate the quality of control in a nonlinear, more realistic simulation. Tests are made of optimal control theory's assumptions and requirements, and the feasibility of this method for TFTR is assessed.
NASA Technical Reports Server (NTRS)
Newson, J. R.
1979-01-01
The results of optimal control theory are used to synthesize a feedback filter. The feedback filter is used to force the output of the filtered frequency response to match that of a desired optimal frequency response over a finite frequency range. This matching is accomplished by employing a nonlinear programing algorithm to search for the coefficients of the feedback filter that minimize the error between the optimal frequency response and the filtered frequency response. The method is applied to the synthesis of an active flutter-suppression control law for an aeroelastic wind-tunnel model. It is shown that the resulting control law suppresses flutter over a wide range of subsonic Mach numbers. This is a promising method for synthesizing practical control laws using the results of optimal control theory.
NASA Technical Reports Server (NTRS)
Armand, J. P.
1972-01-01
An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.
Reduced state feedback gain computation. [optimization and control theory for aircraft control
NASA Technical Reports Server (NTRS)
Kaufman, H.
1976-01-01
Because application of conventional optimal linear regulator theory to flight controller design requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. Therefore, a stochastic linear model that was developed is presented which accounts for aircraft parameter and initial uncertainty, measurement noise, turbulence, pilot command and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.
Optimal control theory for optical waveguide design: application to Y-branch structures.
Pant, D K; Coalson, R D; Hernández, M I; Campos-Martínez, J
1999-06-20
A recently introduced optimal control theory method for optical waveguide design is applied to Y-branch waveguides and Mach-Zehnder modulators. The method simultaneously optimizes many parameters in a chosen design scheme; computational effort scales mildly with the number of parameters considered. Significant improvement in guiding efficiency relative to intuitively reasonable initial parameter choices is obtained in all cases.
Aerodynamic shape optimization of wing and wing-body configurations using control theory
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony
1995-01-01
This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. Recently, the method has been implemented for both potential flows and flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can more easily be extended to treat general configurations. Here results are presented both for the optimization of a swept wing using an analytic mapping, and for the optimization of wing and wing-body configurations using a general mesh.
Asplund, Erik; Kluener, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ({Dirac_h}/2{pi})=m{sub e}=e=a{sub 0}= 1, have been used unless otherwise stated.
Asplund, Erik; Klüner, Thorsten
2012-03-28
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated. PMID:22462846
NASA Astrophysics Data System (ADS)
Asplund, Erik; Klüner, Thorsten
2012-03-01
In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)], 10.1063/1.473950. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998), 10.1063/1.475576; Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)], 10.1063/1.1650297. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.
A comparison of design variables for control theory based airfoil optimization
NASA Technical Reports Server (NTRS)
Reuther, James; Jameson, Antony
1995-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work in the area it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using either the potential flow or the Euler equations with either a conformal mapping or a general coordinate system. We have also explored three-dimensional extensions of these formulations recently. The goal of our present work is to demonstrate the versatility of the control theory approach by designing airfoils using both Hicks-Henne functions and B-spline control points as design variables. The research also demonstrates that the parameterization of the design space is an open question in aerodynamic design.
Optimal planning of LEO active debris removal based on hybrid optimal control theory
NASA Astrophysics Data System (ADS)
Yu, Jing; Chen, Xiao-qian; Chen, Li-hu
2015-06-01
The mission planning of Low Earth Orbit (LEO) active debris removal problem is studied in this paper. Specifically, the Servicing Spacecraft (SSc) and several debris exist on near-circular near-coplanar LEOs. The SSc should repeatedly rendezvous with the debris, and de-orbit them until all debris are removed. Considering the long-duration effect of J2 perturbation, a linear dynamics model is used for each rendezvous. The purpose of this paper is to find the optimal service sequence and rendezvous path with minimum total rendezvous cost (Δv) for the whole mission, and some complex constraints (communication time window constraint, terminal state constraint, and time distribution constraint) should be satisfied meanwhile. Considering this mission as a hybrid optimal control problem, a mathematical model is proposed, as well as the solution method. The proposed approach is demonstrated by a typical active debris removal problem. Numerical experiments show that (1) the model and solution method proposed in this paper can effectively address the planning problem of LEO debris removal; (2) the communication time window constraint and the J2 perturbation have considerable influences on the optimization results; and (3) under the same configuration, some suboptimal sequences are equivalent to the optimal one since their difference in Δv cost is very small.
Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Adamian, A.
1988-01-01
An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.
Goodwin, D. L.; Kuprov, Ilya
2015-08-28
Auxiliary matrix exponential method is used to derive simple and numerically efficient general expressions for the following, historically rather cumbersome, and hard to compute, theoretical methods: (1) average Hamiltonian theory following interaction representation transformations; (2) Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3) gradient ascent pulse engineering version of quantum optimal control theory. In the context of spin dynamics, the auxiliary matrix exponential method is more efficient than methods based on matrix factorizations and also exhibits more favourable complexity scaling with the dimension of the Hamiltonian matrix.
NASA Technical Reports Server (NTRS)
Armstrong, E. S.
1975-01-01
A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
Credibility theory based dynamic control bound optimization for reservoir flood limited water level
NASA Astrophysics Data System (ADS)
Jiang, Zhiqiang; Sun, Ping; Ji, Changming; Zhou, Jianzhong
2015-10-01
The dynamic control operation of reservoir flood limited water level (FLWL) can solve the contradictions between reservoir flood control and beneficial operation well, and it is an important measure to make sure the security of flood control and realize the flood utilization. The dynamic control bound of FLWL is a fundamental key element for implementing reservoir dynamic control operation. In order to optimize the dynamic control bound of FLWL by considering flood forecasting error, this paper took the forecasting error as a fuzzy variable, and described it with the emerging credibility theory in recent years. By combining the flood forecasting error quantitative model, a credibility-based fuzzy chance constrained model used to optimize the dynamic control bound was proposed in this paper, and fuzzy simulation technology was used to solve the model. The FENGTAN reservoir in China was selected as a case study, and the results show that, compared with the original operation water level, the initial operation water level (IOWL) of FENGTAN reservoir can be raised 4 m, 2 m and 5.5 m respectively in the three division stages of flood season, and without increasing flood control risk. In addition, the rationality and feasibility of the proposed forecasting error quantitative model and credibility-based dynamic control bound optimization model are verified by the calculation results of extreme risk theory.
NASA Astrophysics Data System (ADS)
Lapert, M.; Tehini, R.; Turinici, G.; Sugny, D.
2008-08-01
We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a nonstandard choice of the cost, which is not quadratic in the field. These algorithms can be constructed for pure- and mixed-state quantum systems. The efficiency of the method is shown numerically for molecular orientation with a nonlinearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.
NASA Technical Reports Server (NTRS)
Byrnes, C. I.
1980-01-01
It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Management of redundancy in flight control systems using optimal decision theory
NASA Technical Reports Server (NTRS)
1981-01-01
The problem of using redundancy that exists between dissimilar systems in aircraft flight control is addressed. That is, using the redundancy that exists between a rate gyro and an accelerometer--devices that have dissimilar outputs which are related only through the dynamics of the aircraft motion. Management of this type of redundancy requires advanced logic so that the system can monitor failure status and can reconfigure itself in the event of one or more failures. An optimal decision theory was tutorially developed for the management of sensor redundancy and the theory is applied to two aircraft examples. The first example is the space shuttle and the second is a highly maneuvering high performance aircraft--the F8-C. The examples illustrate the redundancy management design process and the performance of the algorithms presented in failure detection and control law reconfiguration.
Application of optimal control theory to the design of the NASA/JPL 70-meter antenna servos
NASA Technical Reports Server (NTRS)
Alvarez, L. S.; Nickerson, J.
1989-01-01
The application of Linear Quadratic Gaussian (LQG) techniques to the design of the 70-m axis servos is described. Linear quadratic optimal control and Kalman filter theory are reviewed, and model development and verification are discussed. Families of optimal controller and Kalman filter gain vectors were generated by varying weight parameters. Performance specifications were used to select final gain vectors.
NASA Astrophysics Data System (ADS)
Lapert, M.; Tehini, R.; Turinici, G.; Sugny, D.
2009-06-01
We propose a monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration, the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using bandpass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse-shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.
Sustainable ecosystem management using optimal control theory: part 1 (deterministic systems).
Shastri, Y; Diwekar, U
2006-08-01
The concept of sustainability, an abstract one by its nature, has been given a mathematical representation through the use of Fisher information as a measure. It is used to propose the sustainability hypotheses for dynamical systems, which has paved the way to achieve sustainable development through externally enforced control schemes. For natural systems, this refers to the task of ecosystem management, which is complicated due the lack of clear objectives. This work attempts to incorporate the idea of sustainability in ecosystem management. The natural regulation of ecosystems suggests two possible control options, top-down control and bottom-up control. A comparison of these two control philosophies is made on generic food chain models using the objectives derived from the sustainability hypotheses. Optimal control theory is used to derive the control profiles to handle the complex nature of the models and the objectives. The results indicate a strong relationship between the hypotheses and the dynamic behavior of the models, supporting the use of Fisher information as a measure. As regards to ecosystem management, it has been observed that top-down control is more aggressive but can result in instability, while bottom-up control is guaranteed to give a stable and improved dynamic response. The results also indicate that bottom-up control is a better option to affect shifts in the dynamic regimes of a system, which may be required to recover the system from a natural disaster like the hurricane Katrina.
Optimal control theory investigation of proprotor/wing response to vertical gust
NASA Technical Reports Server (NTRS)
Frick, J. K. D.; Johnson, W.
1974-01-01
Optimal control theory is used to design linear state variable feedback to improve the dynamic characteristics of a rotor and cantilever wing representing the tilting proprotor aircraft in cruise flight. The response to a vertical gust and system damping are used as criteria for the open and closed loop performance. The improvement in the dynamic characteristics achievable is examined for a gimballed rotor and for a hingeless rotor design. Several features of the design process are examined, including: (1) using only the wing or only the rotor dynamics in the control system design; (2) the use of a wing flap as well as the rotor controls for inputs; (3) and the performance of the system designed for one velocity at other forward speeds.
Optimal control theory (OWEM) applied to a helicopter in the hover and approach phase
NASA Technical Reports Server (NTRS)
Born, G. J.; Kai, T.
1975-01-01
A major difficulty in the practical application of linear-quadratic regulator theory is how to choose the weighting matrices in quadratic cost functions. The control system design with optimal weighting matrices was applied to a helicopter in the hover and approach phase. The weighting matrices were calculated to extremize the closed loop total system damping subject to constraints on the determinants. The extremization is really a minimization of the effects of disturbances, and interpreted as a compromise between the generalized system accuracy and the generalized system response speed. The trade-off between the accuracy and the response speed is adjusted by a single parameter, the ratio of determinants. By this approach an objective measure can be obtained for the design of a control system. The measure is to be determined by the system requirements.
Sustainable ecosystem management using optimal control theory: part 2 (stochastic systems).
Shastri, Y; Diwekar, U
2006-08-01
Sustainable development of ecosystems through external ecosystem management is assuming importance for the environmentalists. To that effect, previous work by the authors looked at the option of manipulating population dynamics of the species in an ecosystem to achieve sustainability. Fisher information is used as the quantifying measure of sustainability and optimal control theory is used to derive the control profiles. However, that work considered only deterministic systems. Uncertainty being prevalent in all systems, particularly in natural systems, this paper extends that work to analyse uncertain systems. Predator-prey models are used to model the species populations and different control philosophies are compared. Ito mean reverting process is used to model the stochastic process, and stochastic maximum principle is used to derive the control profiles. The results for the objective of FI variance minimization qualitatively agree with those for the deterministic system, while the results for the FI maximization objective differ. It is observed that the instability associated with the FI maximization objective for deterministic systems is absorbed by the noise introduced by the uncertainty. Quantitatively, it is observed that the degree of uncertainty, along with its presence, is also important to identify the most appropriate management strategy.
ERIC Educational Resources Information Center
Toso, Robert B.
2000-01-01
Inspired by William Glasser's Reality Therapy ideas, Control Theory (CT) is a disciplinary approach that stresses people's ability to control only their own behavior, based on internal motivations to satisfy five basic needs. At one North Dakota high school, CT-trained teachers are the program's best recruiters. (MLH)
Theory of Optimal Human Motion
NASA Astrophysics Data System (ADS)
Chan, Albert Loongtak
1990-01-01
This thesis presents optimal theories for punching and running. The first is a theory of the optimal karate punch in terms of the duration and the speed of the punch. This theory is solved and compared with experimental data. The theory incorporates the force vs velocity equation (Hill's eq.) and Wilkie's equation for elbow flexation in determining the optimal punch. The time T and the final speed of the punch are dependent on a few physiological parameters for arm muscles. The theoretical punch agrees fairly well with our experiments and other independent experiments. Second, a theory of optimal running is presented, solved and compared with world track records. The theory is similar to Keller's theory for running (1973) except that the power consumed by a runner is assumed to be proportional to the runner's speed v, P = Hv, whereas Keller took P = constant. There are differential equations for velocity and energy, two initial conditions and two constraint inequalities, involving a total of four free parameters. Optimal control techniques are used to solve this problem and minimize the running time T given the race distance D. The resultant predicted times T agree well with the records and the parameter values are consistent with independent physiological measurements.
NASA Astrophysics Data System (ADS)
Dutton, Kevin E.
1994-07-01
The personnel launch system (PLS) being studied by NASA is a system to complement the space shuttle and provide alternative access to space. The PLS consists of a manned spacecraft launched by an expendable launch vehicle (ELV). A candidate for the manned spacecraft is the HL-20 lifting body. In the event of an ELV malfunction during the initial portion of the ascent trajectory, the HL-20 will separate from the rocket and perform an unpowered return to launch site (RTLS) abort. This work details an investigation, using optimal control theory, of the RTLS abort scenario. The objective of the optimization was to maximize final altitude. With final altitude as the cost function, the feasibility of an RTLS abort at different times during the ascent was determined. The method of differential inclusions was used to determine the optimal state trajectories, and the optimal controls were then calculated from the optimal states and state rates.
NASA Technical Reports Server (NTRS)
Dutton, Kevin E.
1994-01-01
The personnel launch system (PLS) being studied by NASA is a system to complement the space shuttle and provide alternative access to space. The PLS consists of a manned spacecraft launched by an expendable launch vehicle (ELV). A candidate for the manned spacecraft is the HL-20 lifting body. In the event of an ELV malfunction during the initial portion of the ascent trajectory, the HL-20 will separate from the rocket and perform an unpowered return to launch site (RTLS) abort. This work details an investigation, using optimal control theory, of the RTLS abort scenario. The objective of the optimization was to maximize final altitude. With final altitude as the cost function, the feasibility of an RTLS abort at different times during the ascent was determined. The method of differential inclusions was used to determine the optimal state trajectories, and the optimal controls were then calculated from the optimal states and state rates.
ERIC Educational Resources Information Center
Heppler, Brad
2008-01-01
This is a book about quality and how to control quality through deliberate actions on the part of the professionals developing and implementing the instances of instruction available at an organization. Quality control theory favors no particular learning philosophy and is only directed towards aspects of how, what, where and when measurements are…
An optimal controller for an electric ventricular-assist device: theory, implementation, and testing
NASA Technical Reports Server (NTRS)
Klute, G. K.; Tasch, U.; Geselowitz, D. B.
1992-01-01
This paper addresses the development and testing of an optimal position feedback controller for the Penn State electric ventricular-assist device (EVAD). The control law is designed to minimize the expected value of the EVAD's power consumption for a targeted patient population. The closed-loop control law is implemented on an Intel 8096 microprocessor and in vitro test runs show that this controller improves the EVAD's efficiency by 15-21%, when compared with the performance of the currently used feedforward control scheme.
UAV path planning using artificial potential field method updated by optimal control theory
NASA Astrophysics Data System (ADS)
Chen, Yong-bo; Luo, Guan-chen; Mei, Yue-song; Yu, Jian-qiao; Su, Xiao-long
2016-04-01
The unmanned aerial vehicle (UAV) path planning problem is an important assignment in the UAV mission planning. Based on the artificial potential field (APF) UAV path planning method, it is reconstructed into the constrained optimisation problem by introducing an additional control force. The constrained optimisation problem is translated into the unconstrained optimisation problem with the help of slack variables in this paper. The functional optimisation method is applied to reform this problem into an optimal control problem. The whole transformation process is deduced in detail, based on a discrete UAV dynamic model. Then, the path planning problem is solved with the help of the optimal control method. The path following process based on the six degrees of freedom simulation model of the quadrotor helicopters is introduced to verify the practicability of this method. Finally, the simulation results show that the improved method is more effective in planning path. In the planning space, the length of the calculated path is shorter and smoother than that using traditional APF method. In addition, the improved method can solve the dead point problem effectively.
Orlando, Paul A; Gatenby, Robert A; Brown, Joel S
2012-12-01
Chemotherapy for metastatic cancer commonly fails due to evolution of drug resistance in tumor cells. Here, we view cancer treatment as a game in which the oncologists choose a therapy and tumors 'choose' an adaptive strategy. We propose the oncologist can gain an upper hand in the game by choosing treatment strategies that anticipate the adaptations of the tumor. In particular, we examine the potential benefit of exploiting evolutionary tradeoffs in tumor adaptations to therapy. We analyze a math model where cancer cells face tradeoffs in allocation of resistance to two drugs. The tumor 'chooses' its strategy by natural selection and the oncologist chooses her strategy by solving a control problem. We find that when tumor cells perform best by investing resources to maximize response to one drug the optimal therapy is a time-invariant delivery of both drugs simultaneously. However, if cancer cells perform better using a generalist strategy allowing resistance to both drugs simultaneously, then the optimal protocol is a time varying solution in which the two drug concentrations negatively covary. However, drug interactions can significantly alter these results. We conclude that knowledge of both evolutionary tradeoffs and drug interactions is crucial in planning optimal chemotherapy schedules for individual patients.
Application of Optimal Production Control theory for Home Energy Management in a Micro Grid
Malikopoulos, Andreas; Djouadi, Seddik M; Kuruganti, Teja
2016-01-01
We consider the optimal stochastic control problem for home energy systems with solar and energy storage devices when the demand is realized from the grid. The demand is subject to Brownian motions with both drift and variance parameters modulated by a continuous-time Markov chain that represents the regime of electricity price. We model the systems as pure stochastic differential equation models, and then we follow the completing square technique to solve the stochastic home energy management problem. The effectiveness of the efficiency of the proposed approach is validated through a simulation example. For practical situations with constraints consistent to those studied here, our results imply the proposed framework could reduce the electricity cost from short-term purchase in peak hour market.
Neighboring optimal guidance theory and computer program
NASA Technical Reports Server (NTRS)
Powers, W. F.
1974-01-01
Developments of the linear quadratic optimal control problem are discussed. The theory is applicable to the development of neighboring optimal feedback guidance gains, and is useful as a tool for synthesizing feedback control laws. A computer program which requires only the pertinent matrices of the linear quadratic problem is described.
NASA Astrophysics Data System (ADS)
Kim, Keon-Gee
The Balian-Veneroni time-dependent variational method (R. Balian and M. Veneroni, Phys. Rev. Lett. 47, 1353 and 1765(E) (1981)) is applied to calculate the radial oscillations of an atomic electron after the beta decay of a tritium atom using an L^2-Sturmian function basis. Various Sturmian function matrix elements are evaluated in a compact form. The results from the variational calculations employing 4-, 6-, and 8-basis states are compared with one another and also compared with the result of a conventional expansion calculation using 70 hydrogenic bound eigenstates with the nuclear charge Z = 2 after the beta decay. Numerical instabilities associated with the calculational scheme for the "tracking" control theory proposed by Rabitz and co-workers (P. Gross, H. Singh, H. Rabitz, K. Mease, and G. M. Huang, Phys. Rev. A 47, 4593 (1993)) are illustrated through a simple example of a driven two-state system. Also demonstrated are possible situations both where no finite control field exists and where multiple control fields can exist. After constructing a generalized Bloch vector for a driven N-state system, an effective calculational scheme utilizing the observable dynamics is presented, which is expected to be applicable to any finite-dimensional problem. Finally, an integral equation approach to optimal control theory, which is nonperturbative and hence applicable to strong-field cases, is suggested. It combines the Balian-Veneroni variational equations for the density and target operators, possibly including other operators depending on the Hamiltonian under consideration. By deriving a closed, symmetric expression for the exact kernel of the Fredholm nonlinear integral equation of the second kind, it is guaranteed that a globally optimal control field is obtained at each stage of the iteration in this calculational scheme.
NASA Technical Reports Server (NTRS)
Leyland, Jane Anne
2001-01-01
Given the predicted growth in air transportation, the potential exists for significant market niches for rotary wing subsonic vehicles. Technological advances which optimise rotorcraft aeromechanical behaviour can contribute significantly to both their commercial and military development, acceptance, and sales. Examples of the optimisation of rotorcraft aeromechanical behaviour which are of interest include the minimisation of vibration and/or loads. The reduction of rotorcraft vibration and loads is an important means to extend the useful life of the vehicle and to improve its ride quality. Although vibration reduction can be accomplished by using passive dampers and/or tuned masses, active closed-loop control has the potential to reduce vibration and loads throughout a.wider flight regime whilst requiring less additional weight to the aircraft man that obtained by using passive methads. It is ernphasised that the analysis described herein is applicable to all those rotorcraft aeromechanical behaviour optimisation problems for which the relationship between the harmonic control vector and the measurement vector can be adequately described by a neural-network model.
NASA Technical Reports Server (NTRS)
Chukwu, Ethelbert Nwakuche
1992-01-01
The author derives an equation determining the dynamics of the deterministic model of a flying vehicle. He next examines a simplified mechanical problem whose optimal feedback control strategy is investigated. From there robotics are incorporated into the mathematical model to develop an equation describing optimal control of the dynamics.
Economic policy optimization based on both one stochastic model and the parametric control theory
NASA Astrophysics Data System (ADS)
Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit
2016-06-01
A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)
Optimality principles in sensorimotor control.
Todorov, Emanuel
2004-09-01
The sensorimotor system is a product of evolution, development, learning and adaptation-which work on different time scales to improve behavioral performance. Consequently, many theories of motor function are based on 'optimal performance': they quantify task goals as cost functions, and apply the sophisticated tools of optimal control theory to obtain detailed behavioral predictions. The resulting models, although not without limitations, have explained more empirical phenomena than any other class. Traditional emphasis has been on optimizing desired movement trajectories while ignoring sensory feedback. Recent work has redefined optimality in terms of feedback control laws, and focused on the mechanisms that generate behavior online. This approach has allowed researchers to fit previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor function. At the heart of the framework is the relationship between high-level goals, and the real-time sensorimotor control strategies most suitable for accomplishing those goals.
Control and optimization system
Xinsheng, Lou
2013-02-12
A system for optimizing a power plant includes a chemical loop having an input for receiving an input parameter (270) and an output for outputting an output parameter (280), a control system operably connected to the chemical loop and having a multiple controller part (230) comprising a model-free controller. The control system receives the output parameter (280), optimizes the input parameter (270) based on the received output parameter (280), and outputs an optimized input parameter (270) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
Optimality theory in phonological acquisition.
Barlow, J A; Gierut, J A
1999-12-01
This tutorial presents an introduction to the contemporary linguistic framework known as optimality theory (OT). The basic assumptions of this constraint-based theory as a general model of grammar are first outlined, with formal notation being defined and illustrated. Concepts unique to the theory, including "emergence of the unmarked," are also described. OT is then examined more specifically within the context of phonological acquisition. The theory is applied in descriptions of children's common error patterns, observed inter- and intrachild variation, and productive change over time. The particular error patterns of fronting, stopping, final-consonant deletion, and cluster simplification are considered from an OT perspective. The discussion concludes with potential clinical applications and extensions of the theory to the diagnosis and treatment of children with functional phonological disorders.
Semiclassical guided optimal control of molecular dynamics
Kondorskiy, A.; Mil'nikov, G.; Nakamura, H.
2005-10-15
An efficient semiclassical optimal control theory applicable to multidimensional systems is formulated for controlling wave packet dynamics on a single adiabatic potential energy surface. The approach combines advantages of different formulations of optimal control theory: quantum and classical on one hand and global and local on the other. Numerical applications to the control of HCN-CNH isomerization demonstrate that this theory can provide an efficient tool to manipulate molecular dynamics of many degrees of freedom by laser pulses.
Optimal control computer programs
NASA Technical Reports Server (NTRS)
Kuo, F.
1992-01-01
The solution of the optimal control problem, even with low order dynamical systems, can usually strain the analytical ability of most engineers. The understanding of this subject matter, therefore, would be greatly enhanced if a software package existed that could simulate simple generic problems. Surprisingly, despite a great abundance of commercially available control software, few, if any, address the part of optimal control in its most generic form. The purpose of this paper is, therefore, to present a simple computer program that will perform simulations of optimal control problems that arise from the first necessary condition and the Pontryagin's maximum principle.
Integrated controls design optimization
Lou, Xinsheng; Neuschaefer, Carl H.
2015-09-01
A control system (207) for optimizing a chemical looping process of a power plant includes an optimizer (420), an income algorithm (230) and a cost algorithm (225) and a chemical looping process models. The process models are used to predict the process outputs from process input variables. Some of the process in puts and output variables are related to the income of the plant; and some others are related to the cost of the plant operations. The income algorithm (230) provides an income input to the optimizer (420) based on a plurality of input parameters (215) of the power plant. The cost algorithm (225) provides a cost input to the optimizer (420) based on a plurality of output parameters (220) of the power plant. The optimizer (420) determines an optimized operating parameter solution based on at least one of the income input and the cost input, and supplies the optimized operating parameter solution to the power plant.
Fuzzy logic controller optimization
Sepe, Jr., Raymond B; Miller, John Michael
2004-03-23
A method is provided for optimizing a rotating induction machine system fuzzy logic controller. The fuzzy logic controller has at least one input and at least one output. Each input accepts a machine system operating parameter. Each output produces at least one machine system control parameter. The fuzzy logic controller generates each output based on at least one input and on fuzzy logic decision parameters. Optimization begins by obtaining a set of data relating each control parameter to at least one operating parameter for each machine operating region. A model is constructed for each machine operating region based on the machine operating region data obtained. The fuzzy logic controller is simulated with at least one created model in a feedback loop from a fuzzy logic output to a fuzzy logic input. Fuzzy logic decision parameters are optimized based on the simulation.
NASA Technical Reports Server (NTRS)
Zhang, Zhimin; Tomlinson, John; Martin, Clyde
1994-01-01
In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.
Johnson, E.A.; Leung, C.; Schira, J.J.
1983-03-01
A closed loop timing optimization control for an internal combustion engine closed about the instantaneous rotational velocity of the engine's crankshaft is disclosed herein. The optimization control computes from the instantaneous rotational velocity of the engine's crankshaft, a signal indicative of the angle at which the crankshaft has a maximum rotational velocity for the torque impulses imparted to the engine's crankshaft by the burning of an air/fuel mixture in each of the engine's combustion chambers and generates a timing correction signal for each of the engine's combustion chambers. The timing correction signals, applied to the engine timing control, modifies the time at which the ignition signal, injection signals or both are generated such that the rotational velocity of the engine's crankshaft has a maximum value at a predetermined angle for each torque impulse generated optimizing the conversion of the combustion energy to rotational torque.
Optimal control of native predators
Martin, Julien; O'Connell, Allan F.; Kendall, William L.; Runge, Michael C.; Simons, Theodore R.; Waldstein, Arielle H.; Schulte, Shiloh A.; Converse, Sarah J.; Smith, Graham W.; Pinion, Timothy; Rikard, Michael; Zipkin, Elise F.
2010-01-01
We apply decision theory in a structured decision-making framework to evaluate how control of raccoons (Procyon lotor), a native predator, can promote the conservation of a declining population of American Oystercatchers (Haematopus palliatus) on the Outer Banks of North Carolina. Our management objective was to maintain Oystercatcher productivity above a level deemed necessary for population recovery while minimizing raccoon removal. We evaluated several scenarios including no raccoon removal, and applied an adaptive optimization algorithm to account for parameter uncertainty. We show how adaptive optimization can be used to account for uncertainties about how raccoon control may affect Oystercatcher productivity. Adaptive management can reduce this type of uncertainty and is particularly well suited for addressing controversial management issues such as native predator control. The case study also offers several insights that may be relevant to the optimal control of other native predators. First, we found that stage-specific removal policies (e.g., yearling versus adult raccoon removals) were most efficient if the reproductive values among stage classes were very different. Second, we found that the optimal control of raccoons would result in higher Oystercatcher productivity than the minimum levels recommended for this species. Third, we found that removing more raccoons initially minimized the total number of removals necessary to meet long term management objectives. Finally, if for logistical reasons managers cannot sustain a removal program by removing a minimum number of raccoons annually, managers may run the risk of creating an ecological trap for Oystercatchers.
Optimal Control of Evolution Mixed Variational Inclusions
Alduncin, Gonzalo
2013-12-15
Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.
Adaptive hybrid optimal quantum control for imprecisely characterized systems.
Egger, D J; Wilhelm, F K
2014-06-20
Optimal quantum control theory carries a huge promise for quantum technology. Its experimental application, however, is often hindered by imprecise knowledge of the input variables, the quantum system's parameters. We show how to overcome this by adaptive hybrid optimal control, using a protocol named Ad-HOC. This protocol combines open- and closed-loop optimal control by first performing a gradient search towards a near-optimal control pulse and then an experimental fidelity estimation with a gradient-free method. For typical settings in solid-state quantum information processing, adaptive hybrid optimal control enhances gate fidelities by an order of magnitude, making optimal control theory applicable and useful. PMID:24996074
Lie algebroids and optimal control: abnormality
NASA Astrophysics Data System (ADS)
Barbero-Liñán, M.; de Diego, D. Martín; Muñoz-Lecanda, M. C.
2009-05-01
Candidates to be solutions to optimal control problems, called extremals, are found using Pontryagin's Maximum Principle [9]. This Principle gives necessary conditions for optimality and, under suitable assumptions, starts a presymplectic constraint algorithm in the sense given in [3]. This procedure, first considered in optimal control theory in [6], can be adapted to characterize the different kinds of extremals [1]. In this paper, we describe the constraints given by the algorithm for the so-called abnormal extremals for optimal control problems defined on Lie algebroids [4, 7, 8]. The peculiarity of the abnormal extremals is their independence on the cost function to characterize them. In particular, we are interested in how useful the geometry provided by the Lie algebroid is to study the constraints obtained in the optimal control problems for affine connection control systems. These systems model the motion of different types of mechanical systems such as rigid bodies, nonholonomic systems and robotic arms [2].
NASA Technical Reports Server (NTRS)
Tumin, Anatoli; Ashpis, David E.
2003-01-01
An analysis of the non-modal growth of perturbations in a boundary layer in the presence of a streamwise pressure gradient is presented. The analysis is based on PSE equations for an incompressible fluid. Examples with Falkner-Skan profiles indicate that a favorable pressure gradient decreases the non-modal growth while an unfavorable pressure gradient leads to an increase of the amplification. It is suggested that the transient growth mechanism be utilized to choose optimal parameters of tripping elements on a low-pressure turbine (LPT) airfoil. As an example, a boundary layer flow with a streamwise pressure gradient corresponding to the pressure distribution over a LPT airfoil is considered. It is shown that there is an optimal spacing of the tripping elements and that the transient growth effect depends on the starting point. At very low Reynolds numbers, there is a possibility to enhance the transient energy growth by means of wall cooling.
Optimal control of HIV/AIDS dynamic: Education and treatment
NASA Astrophysics Data System (ADS)
Sule, Amiru; Abdullah, Farah Aini
2014-07-01
A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.
Di Giacomo, S.M.
1999-10-01
Demand control ventilation (DCV) utilizing continuous outdoor and indoor (differential) carbon dioxide (CO{sub 2}) measurements is an elegant closed loop feedback control methodology for determining damper position in a continuously changing HVAC system environment and subsequently maintaining a constant steady-state ventilation air (CFM) per person level. This article deals directly with the numerous misconceptions surrounding this technology as well as its applications as an energy conservation measure and commissioning tool. Summarized below are some of the benefits of adopting the DCV technology utilizing differential CO{sub 2} measurements. DCV, when used as an HVAC VAV or CV mix air return system energy savings retrofit tool, can save energy when it functions in conjunction with existing (base case) energy savings control methodologies. This means that DCV control algorithms must be suspended, through computer programming, whenever normal free cooling opportunities exist--otherwise, energy consumption will increase. For example: If free cooling economizer controls exist in the base case, then the engineer must ensure that they continue to exist in the retrofit case.
Automated beam steering using optimal control
Allen, C. K.
2004-01-01
We present a steering algorithm which, with the aid of a model, allows the user to specify beam behavior throughout a beamline, rather than just at specified beam position monitor (BPM) locations. The model is used primarily to compute the values of the beam phase vectors from BPM measurements, and to define cost functions that describe the steering objectives. The steering problem is formulated as constrained optimization problem; however, by applying optimal control theory we can reduce it to an unconstrained optimization whose dimension is the number of control signals.
On Restructurable Control System Theory
NASA Technical Reports Server (NTRS)
Athans, M.
1983-01-01
The state of stochastic system and control theory as it impacts restructurable control issues is addressed. The multivariable characteristics of the control problem are addressed. The failure detection/identification problem is discussed as a multi-hypothesis testing problem. Control strategy reconfiguration, static multivariable controls, static failure hypothesis testing, dynamic multivariable controls, fault-tolerant control theory, dynamic hypothesis testing, generalized likelihood ratio (GLR) methods, and adaptive control are discussed.
Metacognitive Control and Optimal Learning
ERIC Educational Resources Information Center
Son, Lisa K.; Sethi, Rajiv
2006-01-01
The notion of optimality is often invoked informally in the literature on metacognitive control. We provide a precise formulation of the optimization problem and show that optimal time allocation strategies depend critically on certain characteristics of the learning environment, such as the extent of time pressure, and the nature of the uptake…
Supercomputer optimizations for stochastic optimal control applications
NASA Technical Reports Server (NTRS)
Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang
1991-01-01
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
Optimal search behavior and classic foraging theory
NASA Astrophysics Data System (ADS)
Bartumeus, F.; Catalan, J.
2009-10-01
Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statistical patterns of movement suggests that, beyond movement quantification, statistical physics may prove to be an adequate framework to understand animal behavior across scales from an ecological and evolutionary perspective. Recently developed random search theory has served to critically re-evaluate classic ecological questions on animal foraging. For instance, during the last few years, there has been a growing debate on whether search behavior can include traits that improve success by optimizing random (stochastic) searches. Here, we stress the need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching. By sketching the assumptions of optimal foraging theory (OFT) and by summarizing recent results on random search strategies, we pinpoint ways to extend classic OFT, and integrate the study of search strategies and its main results into the more general theory of optimal foraging.
Optimal management strategies in variable environments: Stochastic optimal control methods
Williams, B.K.
1985-01-01
Dynamic optimization was used to investigate the optimal defoliation of salt desert shrubs in north-western Utah. Management was formulated in the context of optimal stochastic control theory, with objective functions composed of discounted or time-averaged biomass yields. Climatic variability and community patterns of salt desert shrublands make the application of stochastic optimal control both feasible and necessary. A primary production model was used to simulate shrub responses and harvest yields under a variety of climatic regimes and defoliation patterns. The simulation results then were used in an optimization model to determine optimal defoliation strategies. The latter model encodes an algorithm for finite state, finite action, infinite discrete time horizon Markov decision processes. Three questions were addressed: (i) What effect do changes in weather patterns have on optimal management strategies? (ii) What effect does the discounting of future returns have? (iii) How do the optimal strategies perform relative to certain fixed defoliation strategies? An analysis was performed for the three shrub species, winterfat (Ceratoides lanata), shadscale (Atriplex confertifolia) and big sagebrush (Artemisia tridentata). In general, the results indicate substantial differences among species in optimal control strategies, which are associated with differences in physiological and morphological characteristics. Optimal policies for big sagebrush varied less with variation in climate, reserve levels and discount rates than did either shadscale or winterfat. This was attributed primarily to the overwintering of photosynthetically active tissue and to metabolic activity early in the growing season. Optimal defoliation of shadscale and winterfat generally was more responsive to differences in plant vigor and climate, reflecting the sensitivity of these species to utilization and replenishment of carbohydrate reserves. Similarities could be seen in the influence of both
Fuel consumption in optimal control
NASA Technical Reports Server (NTRS)
Redmond, Jim; Silverberg, Larry
1992-01-01
A method has been developed for comparing three optimal control strategies based on fuel consumption. A general cost function minimization procedure was developed by applying two theorems associated with convex sets. Three cost functions associated with control saturation, pseudofuel, and absolute fuel are introduced and minimized. The first two cost functions led to the bang-bang and continuous control strategies, and the minimization of absolute fuel led to an impulsive strategy. The three control strategies were implemented on two elementary systems and a comparison of fuel consumption was made. The impulse control strategy consumes significantly less fuel than the continuous and bang-bang control strategies. This comparison suggests a potential for fuel savings in higher-order systems using impulsive control strategies. However, since exact solutions to fuel-optimal control for large-order systems are difficult if not impossible to achieve, the alternative is to develop near-optimal control strategies.
Investigating Optimal Foraging Theory in the Laboratory
ERIC Educational Resources Information Center
Harden, Siegfried; Grilliot, Matthew E.
2014-01-01
Optimal foraging theory is a principle that is often presented in the community ecology section of biology textbooks, but also can be demonstrated in the laboratory. We introduce a lab activity that uses an interactive strategy to teach high school and/or college students about this ecological concept. The activity is ideal because it engages…
Intelligent control: integrating AI and control theory
De Jong, K.
1983-01-01
The increasing complexity of the requirements placed upon computer-controlled systems is forcing a departure from rigid, predetermined control sequences toward more flexible, intelligent control regimes. The basic premise of this research is that such systems can be developed by exploiting the strengths of both standard control theory and recent developments in artificial intelligence. A framework is described for integrating artificial intelligence (AI) techniques with more traditional control theory approaches both at the design stages as well as online control. Its potential is then discussed in the context of several complex navy control problems including automatic tracking systems, autonomous vehicles, and large-scale, flexible space structures. 8 references.
Optimal control of a quantum measurement
NASA Astrophysics Data System (ADS)
Egger, D. J.; Wilhelm, F. K.
2014-11-01
Pulses to steer the time evolution of quantum systems can be designed with optimal control theory. In most cases it is the coherent processes that can be controlled and one optimizes the time evolution toward a target unitary process, sometimes also in the presence of noncontrollable incoherent processes. Here we show how to extend the gradient ascent pulse engineering (GRAPE) algorithm in the case where the incoherent processes are controllable and the target time evolution is a nonunitary quantum channel. We perform a gradient search on a fidelity measure based on Choi matrices. We illustrate our algorithm by optimizing a phase qubit measurement pulse. We show how this technique can lead to a large measurement contrast close to 99 % . We also show, within the validity of our model, that this algorithm can produce short 1.4 -ns pulses with 98.2 % contrast.
Cancer Behavior: An Optimal Control Approach
Gutiérrez, Pedro J.; Russo, Irma H.; Russo, J.
2009-01-01
With special attention to cancer, this essay explains how Optimal Control Theory, mainly used in Economics, can be applied to the analysis of biological behaviors, and illustrates the ability of this mathematical branch to describe biological phenomena and biological interrelationships. Two examples are provided to show the capability and versatility of this powerful mathematical approach in the study of biological questions. The first describes a process of organogenesis, and the second the development of tumors. PMID:22247736
Optimality principles in sensorimotor control (review)
Todorov, Emanuel
2006-01-01
The sensorimotor system is a product of evolution, development, learning, adaptation – processes that work on different time scales to improve behavioral performance. Consequenly, many theories of motor function are based on the notion of optimal performance: they quantify the task goals, and apply the sophisticated tools of optimal control theory to obtain detailed behavioral predictions. The resulting models, although not without limitations, has explained a wider range of empirical phenomena than any other class of models. Traditional emphasis has been on optimizing average trajectories while ignoring sensory feedback. Recent work has redefined optimality on the level of feedback control laws, and focused on the mechanisms that generate behavior online. This has made it possible to fit a number of previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor function. At the heart of the framework is the relationship between high-level goals, and the realtime sensorimotor control strategies most suitable for accomplishing those goals. PMID:15332089
Optimal control of motorsport differentials
NASA Astrophysics Data System (ADS)
Tremlett, A. J.; Massaro, M.; Purdy, D. J.; Velenis, E.; Assadian, F.; Moore, A. P.; Halley, M.
2015-12-01
Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.
Optimal and robust control of transition
NASA Technical Reports Server (NTRS)
Bewley, T. R.; Agarwal, R.
1996-01-01
Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.
Optimal Feedback Control of Thermal Networks
NASA Technical Reports Server (NTRS)
Papalexandris, Miltiadis
2003-01-01
An improved approach to the mathematical modeling of feedback control of thermal networks has been devised. Heretofore software for feedback control of thermal networks has been developed by time-consuming trial-and-error methods that depend on engineers expertise. In contrast, the present approach is a systematic means of developing algorithms for feedback control that is optimal in the sense that it combines performance with low cost of implementation. An additional advantage of the present approach is that a thermal engineer need not be expert in control theory. Thermal networks are lumped-parameter approximations used to represent complex thermal systems. Thermal networks are closely related to electrical networks commonly represented by lumped-parameter circuit diagrams. Like such electrical circuits, thermal networks are mathematically modeled by systems of differential-algebraic equations (DAEs) that is, ordinary differential equations subject to a set of algebraic constraints. In the present approach, emphasis is placed on applications in which thermal networks are subject to constant disturbances and, therefore, integral control action is necessary to obtain steady-state responses. The mathematical development of the present approach begins with the derivation of optimal integral-control laws via minimization of an appropriate cost functional that involves augmented state vectors. Subsequently, classical variational arguments provide optimality conditions in the form of the Hamiltonian equations for the standard linear-quadratic-regulator (LQR) problem. These equations are reduced to an algebraic Riccati equation (ARE) with respect to the augmented state vector. The solution of the ARE leads to the direct computation of the optimal proportional- and integral-feedback control gains. In cases of very complex networks, large numbers of state variables make it difficult to implement optimal controllers in the manner described in the preceding paragraph.
Optimization of constrained density functional theory
NASA Astrophysics Data System (ADS)
O'Regan, David D.; Teobaldi, Gilberto
2016-07-01
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.
Optimal control of hydroelectric facilities
NASA Astrophysics Data System (ADS)
Zhao, Guangzhi
This thesis considers a simple yet realistic model of pump-assisted hydroelectric facilities operating in a market with time-varying but deterministic power prices. Both deterministic and stochastic water inflows are considered. The fluid mechanical and engineering details of the facility are described by a model containing several parameters. We present a dynamic programming algorithm for optimizing either the total energy produced or the total cash generated by these plants. The algorithm allows us to give the optimal control strategy as a function of time and to see how this strategy, and the associated plant value, varies with water inflow and electricity price. We investigate various cases. For a single pumped storage facility experiencing deterministic power prices and water inflows, we investigate the varying behaviour for an oversimplified constant turbine- and pump-efficiency model with simple reservoir geometries. We then generalize this simple model to include more realistic turbine efficiencies, situations with more complicated reservoir geometry, and the introduction of dissipative switching costs between various control states. We find many results which reinforce our physical intuition about this complicated system as well as results which initially challenge, though later deepen, this intuition. One major lesson of this work is that the optimal control strategy does not differ much between two differing objectives of maximizing energy production and maximizing its cash value. We then turn our attention to the case of stochastic water inflows. We present a stochastic dynamic programming algorithm which can find an on-average optimal control in the face of this randomness. As the operator of a facility must be more cautious when inflows are random, the randomness destroys facility value. Following this insight we quantify exactly how much a perfect hydrological inflow forecast would be worth to a dam operator. In our final chapter we discuss the
Mean-field sparse optimal control
Fornasier, Massimo; Piccoli, Benedetto; Rossi, Francesco
2014-01-01
We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ-limit of the finite dimensional sparse optimal control problems. PMID:25288818
Distributed optimization and flight control using collectives
NASA Astrophysics Data System (ADS)
Bieniawski, Stefan Richard
The increasing complexity of aerospace systems demands new approaches for their design and control. Approaches are required to address the trend towards aerospace systems comprised of a large number of inherently distributed and highly nonlinear components with complex and sometimes competing interactions. This work introduces collectives to address these challenges. Although collectives have been used for distributed optimization problems in computer science, recent developments based upon Probability Collectives (PC) theory enhance their applicability to discrete, continuous, mixed, and constrained optimization problems. Further, they are naturally applied to distributed systems and those involving uncertainty, such as control in the presence of noise and disturbances. This work describes collectives theory and its implementation, including its connections to multi-agent systems, machine learning, statistics, and gradient-based optimization. To demonstrate the approach, two experiments were developed. These experiments built upon recent advances in actuator technology that resulted in small, simple flow control devices. Miniature-Trailing Edge Effectors (MiTE), consisting of a small, 1-5% chord, moveable surface mounted at the wing trailing edge, are used for the experiments. The high bandwidth, distributed placement, and good control authority make these ideal candidates for rigid and flexible mode control of flight vehicles. This is demonstrated in two experiments: flutter suppression of a flexible wing, and flight control of a remotely piloted aircraft. The first experiment successfully increased the flutter speed by over 25%. The second experiment included a novel distributed flight control system based upon the MiTEs that includes distributed sensing, logic, and actuation. Flight tests validated the control capability of the MiTEs and the associated flight control architecture. The collectives approach was used to design controllers for the distributed
Helvik, Anne-Sofie; Iversen, Valentina Cabral; Steiring, Randi; Hallberg, Lillemor R-M
2011-01-01
Aim This study aims at exploring the main concern for elderly individuals with somatic health problems and what they do to manage this. Method In total, 14 individuals (mean=74.2 years; range=68–86 years) of both gender including hospitalized and outpatient persons participated in the study. Open interviews were conducted and analyzed according to grounded theory, an inductive theory-generating method. Results The main concern for the elderly individuals with somatic health problems was identified as their striving to maintain control and balance in life. The analysis ended up in a substantive theory explaining how elderly individuals with somatic disease were calibrating and adjusting their expectations in life in order to adapt to their reduced energy level, health problems, and aging. By adjusting the expectations to their actual abilities, the elderly can maintain a sense of that they still have the control over their lives and create stability. The ongoing adjustment process is facilitated by different strategies and result despite lower expectations in subjective well-being. The facilitating strategies are utilizing the network of important others, enjoying cultural heritage, being occupied with interests, having a mission to fulfill, improving the situation by limiting boundaries and, finally, creating meaning in everyday life. Conclusion The main concern of the elderly with somatic health problems was to maintain control and balance in life. The emerging theory explains how elderly people with somatic health problems calibrate their expectations of life in order to adjust to reduced energy, health problems, and aging. This process is facilitated by different strategies and result despite lower expectation in subjective well-being. PMID:21468299
Reentry trajectory optimization and control
NASA Astrophysics Data System (ADS)
Strohmaier, P.; Kiefer, A.; Burkhardt, D.; Horn, K.
1990-06-01
There are several possible methods to increase the cross range capability of a winged reentry vehicle, for instance, skip trajectories, a powered cruise phase, or high lift/drag ratio flight. However, most of these alternative descent strategies have not yet been investigated sufficiently with respect to aero-thermodynamic effects and the design of the thermal protection system. This problem is treated by two different means. First, a nominal reentry trajectory is generated based on a phase concept, and then the same problem is again solved using a numerical optimization code to determine the control functions. The nominal reentry trajectory design presented first subdivides the total reentry trajectory into several segments with partially constant control/state parameters such as maximum heat flux and deceleration. The optimal conditions for a given segment can then be selected. In contrast, the parameterized optimization code selects the control functions freely. Both approaches consider a mass point simulation which uses realistic model assumptions for atmosphere, earth and gravity. Likewise, both approaches satisfy all flight regime limitations and boundary conditions such as thermal constraints throughout the flight path and specified speed and altitude at the final time. For the optimization of high cross reentry trajectories the cross range per total absorbed heat represents an appropriate cost function. The optimization code delivers quite a different flight strategy than that usually generated by the nominal reentry design program, first flying longer along the temperature boundary at highest possible angle of attack (AOAs) (utilizing higher average turn rates), and afterwards performing flare-dive segments to reduce heat flux and to increase range. Finally, the aspect of guiding the nominal or optimized reentry trajectory during a cross range flight is considered. The vertical guidance is performed with both angles of attack and roll angle control. The
Combined control-structure optimization
NASA Technical Reports Server (NTRS)
Salama, M.; Milman, M.; Bruno, R.; Scheid, R.; Gibson, S.
1989-01-01
An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.
Practical synchronization on complex dynamical networks via optimal pinning control.
Li, Kezan; Sun, Weigang; Small, Michael; Fu, Xinchu
2015-07-01
We consider practical synchronization on complex dynamical networks under linear feedback control designed by optimal control theory. The control goal is to minimize global synchronization error and control strength over a given finite time interval, and synchronization error at terminal time. By utilizing the Pontryagin's minimum principle, and based on a general complex dynamical network, we obtain an optimal system to achieve the control goal. The result is verified by performing some numerical simulations on Star networks, Watts-Strogatz networks, and Barabási-Albert networks. Moreover, by combining optimal control and traditional pinning control, we propose an optimal pinning control strategy which depends on the network's topological structure. Obtained results show that optimal pinning control is very effective for synchronization control in real applications. PMID:26274112
Intertemporal optimization, the Hotelling theory, and nonrenewable resource markets
Toman, M.A.
1983-01-01
Essay 1, Optimal Control With a Variable Horizon, generalizes the theory of optimal control by showing existence of a solution for problems in which the terminal date is a choice variable and may be finite or infinite, and for problems with an infinite horizon. Results are direct extensions of previous theorems, provided net benefit flows are uniformly bounded above by an integrable function and the value of any terminal stocks in a finite-horizon program becomes negligible as the terminal date becomes large. Essay 2, The Theory of Nonrenewable Resource Exploitation: Existence of an Optimal Plan, applies these results to the decision problem of an individual mining firm facing rising costs as the resource base is depleted. Essay 3, Perfect Foresight Market Equilibrium With a Nonrenewable Resource, develops sufficient conditions for existence and uniqueness of socially optimal and competitive equilibrium programs of production and consumption with a nonrenewable resource and a backstop substitute when agents have perfect foresight of future prices and costs.
NASA Technical Reports Server (NTRS)
Broussard, J. R.; Halyo, N.
1984-01-01
This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.
Aerodynamic design via control theory
NASA Technical Reports Server (NTRS)
Jameson, Antony
1988-01-01
The question of how to modify aerodynamic design in order to improve performance is addressed. Representative examples are given to demonstrate the computational feasibility of using control theory for such a purpose. An introduction and historical survey of the subject is included.
Quasivelocities and Optimal Control for underactuated Mechanical Systems
NASA Astrophysics Data System (ADS)
Colombo, L.; de Diego, D. Martín
2010-07-01
This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system subjected to constraints. The equations of motion are geometrically derived using an adaptation of the classical Skinner and Rusk formalism.
Optimal coordination and control of posture and movements.
Johansson, Rolf; Fransson, Per-Anders; Magnusson, Måns
2009-01-01
This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided. PMID:19671443
Optimal control of complex atomic quantum systems
NASA Astrophysics Data System (ADS)
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-10-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.
Optimal control of complex atomic quantum systems
van Frank, S.; Bonneau, M.; Schmiedmayer, J.; Hild, S.; Gross, C.; Cheneau, M.; Bloch, I.; Pichler, T.; Negretti, A.; Calarco, T.; Montangero, S.
2016-01-01
Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations. PMID:27725688
HCCI Engine Optimization and Control
Rolf D. Reitz
2005-09-30
The goal of this project was to develop methods to optimize and control Homogeneous-Charge Compression Ignition (HCCI) engines, with emphasis on diesel-fueled engines. HCCI offers the potential of nearly eliminating IC engine NOx and particulate emissions at reduced cost over Compression Ignition Direct Injection engines (CIDI) by controlling pollutant emissions in-cylinder. The project was initiated in January, 2002, and the present report is the final report for work conducted on the project through December 31, 2004. Periodic progress has also been reported at bi-annual working group meetings held at USCAR, Detroit, MI, and at the Sandia National Laboratories. Copies of these presentation materials are available on CD-ROM, as distributed by the Sandia National Labs. In addition, progress has been documented in DOE Advanced Combustion Engine R&D Annual Progress Reports for FY 2002, 2003 and 2004. These reports are included as the Appendices in this Final report.
An Affect Control Theory of Technology
ERIC Educational Resources Information Center
Shank, Daniel B.
2010-01-01
Affect control theory is a theory of interaction that takes into account cultural meanings. Affect control research has previously considered interaction with technology, but there remains a lack of theorizing about inclusion of technology within the theory. This paper lays a foundation for an affect control theory of technology by addressing key…
Adaptive, predictive controller for optimal process control
Brown, S.K.; Baum, C.C.; Bowling, P.S.; Buescher, K.L.; Hanagandi, V.M.; Hinde, R.F. Jr.; Jones, R.D.; Parkinson, W.J.
1995-12-01
One can derive a model for use in a Model Predictive Controller (MPC) from first principles or from experimental data. Until recently, both methods failed for all but the simplest processes. First principles are almost always incomplete and fitting to experimental data fails for dimensions greater than one as well as for non-linear cases. Several authors have suggested the use of a neural network to fit the experimental data to a multi-dimensional and/or non-linear model. Most networks, however, use simple sigmoid functions and backpropagation for fitting. Training of these networks generally requires large amounts of data and, consequently, very long training times. In 1993 we reported on the tuning and optimization of a negative ion source using a special neural network[2]. One of the properties of this network (CNLSnet), a modified radial basis function network, is that it is able to fit data with few basis functions. Another is that its training is linear resulting in guaranteed convergence and rapid training. We found the training to be rapid enough to support real-time control. This work has been extended to incorporate this network into an MPC using the model built by the network for predictive control. This controller has shown some remarkable capabilities in such non-linear applications as continuous stirred exothermic tank reactors and high-purity fractional distillation columns[3]. The controller is able not only to build an appropriate model from operating data but also to thin the network continuously so that the model adapts to changing plant conditions. The controller is discussed as well as its possible use in various of the difficult control problems that face this community.
Aerospace plane guidance using geometric control theory
NASA Technical Reports Server (NTRS)
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Dynamics systems vs. optimal control--a unifying view.
Schaal, Stefan; Mohajerian, Peyman; Ijspeert, Auke
2007-01-01
In the past, computational motor control has been approached from at least two major frameworks: the dynamic systems approach and the viewpoint of optimal control. The dynamic system approach emphasizes motor control as a process of self-organization between an animal and its environment. Nonlinear differential equations that can model entrainment and synchronization behavior are among the most favorable tools of dynamic systems modelers. In contrast, optimal control approaches view motor control as the evolutionary or development result of a nervous system that tries to optimize rather general organizational principles, e.g., energy consumption or accurate task achievement. Optimal control theory is usually employed to develop appropriate theories. Interestingly, there is rather little interaction between dynamic systems and optimal control modelers as the two approaches follow rather different philosophies and are often viewed as diametrically opposing. In this paper, we develop a computational approach to motor control that offers a unifying modeling framework for both dynamic systems and optimal control approaches. In discussions of several behavioral experiments and some theoretical and robotics studies, we demonstrate how our computational ideas allow both the representation of self-organizing processes and the optimization of movement based on reward criteria. Our modeling framework is rather simple and general, and opens opportunities to revisit many previous modeling results from this novel unifying view.
Testing Optimal Foraging Theory Using Bird Predation on Goldenrod Galls
ERIC Educational Resources Information Center
Yahnke, Christopher J.
2006-01-01
All animals must make choices regarding what foods to eat, where to eat, and how much time to spend feeding. Optimal foraging theory explains these behaviors in terms of costs and benefits. This laboratory exercise focuses on optimal foraging theory by investigating the winter feeding behavior of birds on the goldenrod gall fly by comparing…
Neighboring extremal optimal control design including model mismatch errors
Kim, T.J.; Hull, D.G.
1994-11-01
The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.
New Applications of Variational Analysis to Optimization and Control
NASA Astrophysics Data System (ADS)
Mordukhovich, Boris S.
We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculus rules for generalized differentiation of nonsmooth and set-valued mappings; necessary and sufficient conditions for new notions of linear subextremality and suboptimality in constrained problems; optimality conditions for mathematical problems with equilibrium constraints; necessary optimality conditions for optimistic bilevel programming with smooth and nonsmooth data; existence theorems and optimality conditions for various notions of Pareto-type optimality in problems of multiobjective optimization with vector-valued and set-valued cost mappings; Lipschitzian stability and metric regularity aspects for constrained and variational systems.
Fuzzy logic control and optimization system
Lou, Xinsheng
2012-04-17
A control system (300) for optimizing a power plant includes a chemical loop having an input for receiving an input signal (369) and an output for outputting an output signal (367), and a hierarchical fuzzy control system (400) operably connected to the chemical loop. The hierarchical fuzzy control system (400) includes a plurality of fuzzy controllers (330). The hierarchical fuzzy control system (400) receives the output signal (367), optimizes the input signal (369) based on the received output signal (367), and outputs an optimized input signal (369) to the input of the chemical loop to control a process of the chemical loop in an optimized manner.
The neural optimal control hierarchy for motor control
NASA Astrophysics Data System (ADS)
DeWolf, T.; Eliasmith, C.
2011-10-01
Our empirical, neuroscientific understanding of biological motor systems has been rapidly growing in recent years. However, this understanding has not been systematically mapped to a quantitative characterization of motor control based in control theory. Here, we attempt to bridge this gap by describing the neural optimal control hierarchy (NOCH), which can serve as a foundation for biologically plausible models of neural motor control. The NOCH has been constructed by taking recent control theoretic models of motor control, analyzing the required processes, generating neurally plausible equivalent calculations and mapping them on to the neural structures that have been empirically identified to form the anatomical basis of motor control. We demonstrate the utility of the NOCH by constructing a simple model based on the identified principles and testing it in two ways. First, we perturb specific anatomical elements of the model and compare the resulting motor behavior with clinical data in which the corresponding area of the brain has been damaged. We show that damaging the assigned functions of the basal ganglia and cerebellum can cause the movement deficiencies seen in patients with Huntington's disease and cerebellar lesions. Second, we demonstrate that single spiking neuron data from our model's motor cortical areas explain major features of single-cell responses recorded from the same primate areas. We suggest that together these results show how NOCH-based models can be used to unify a broad range of data relevant to biological motor control in a quantitative, control theoretic framework.
Control optimization of the cryoplant warm compressor station for EAST
Zhuang, M.; Hu, L. B.; Zhou, Z. W.; Xia, G. H.
2014-01-29
The cryogenic control system for EAST (Experimental Advanced Superconducting Tokamak) was designed based on DeltaV DCS of Emerson Corporation. The automatic control of the cryoplant warm compressors has been implemented. However, with ever-degrading performance of critical equipment, the cryoplant operation in the partial design conditions makes the control system fluctuate and unstable. In this paper, the warm compressor control system was optimized to eliminate the pressure oscillation based on the expert PID theory.
Optimal and robust control of robot manipulators
NASA Astrophysics Data System (ADS)
Grabbe, Michael Thomas
1992-01-01
The problem of controlling a robot manipulator typically requires determining the actuating torques at each joint, in the form of a feedback control law, which force the manipulator joint angles to follow a prescribed trajectory. This problem is often referred to as the trajectory tracking problem, and is difficult to solve due to the highly nonlinear dynamics associated with the robot manipulator and the time variance of the system induced by the prescribed trajectory. The complexity of the problem is compounded in cases where the manipulator end effector is constrained by contact with a surface, there are modeling or parametric uncertainties in the manipulator dynamics, or there are disturbances to the system. The trajectory tracking problem is addressed in two distinct cases. The first case involves the ideal situation in which the manipulator is unconstrained in its motion and there are no uncertainties or disturbances in the system. Optimal control theory is used to develop a class of feedback control laws which produce a globally uniformly asymptotically stable (GUAS) system. The second case involves both constrained motion and the possibilities of uncertainties and disturbances in the system. Two feedback control laws are developed which are robust with respect to uncertainties and disturbances, provide globally exponentially stable (GES) position tracking error, and provide a means of regulating the force applied.
Optimal singular control with applications to trajectory optimization
NASA Technical Reports Server (NTRS)
Vinh, N. X.
1979-01-01
The switching conditions are expressed explicitly in terms of the derivatives of the Hamiltonians at the two ends of the switching. A new expression of the Kelley-Contensou necessary condition for the optimality of a singular arc is given. Some examples illustrating the application of the theory are presented.
Optimal control, geometry, and quantum computing
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Dowling, Mark R.; Gu, Mile; Doherty, Andrew C.
2006-06-01
We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U , to the optimal control cost associated to the synthesis of U . These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.
Fundamental Solutions and Optimal Control of Neutral Systems
NASA Astrophysics Data System (ADS)
Liu, Kai
In this work, we shall consider standard optimal control problems for a class of neutral functional differential equations in Banach spaces. As the basis of a systematic theory of neutral models, the fundamental solution is constructed and a variation of constants formula of mild solutions is established. Necessary conditions in terms of the solutions of neutral adjoint systems are established to deal with the fixed time integral convex cost problem of optimality. Based on optimality conditions, the maximum principle for time varying control domain is presented.
Backward bifurcation and optimal control of Plasmodium Knowlesi malaria
NASA Astrophysics Data System (ADS)
Abdullahi, Mohammed Baba; Hasan, Yahya Abu; Abdullah, Farah Aini
2014-07-01
A deterministic model for the transmission dynamics of Plasmodium Knowlesi malaria with direct transmission is developed. The model is analyzed using dynamical system techniques and it shows that the backward bifurcation occurs for some range of parameters. The model is extended to assess the impact of time dependent preventive (biological and chemical control) against the mosquitoes and vaccination for susceptible humans, while treatment for infected humans. The existence of optimal control is established analytically by the use of optimal control theory. Numerical simulations of the problem, suggest that applying the four control measure can effectively reduce if not eliminate the spread of Plasmodium Knowlesi in a community.
Adaptive optimization and control using neural networks
Mead, W.C.; Brown, S.K.; Jones, R.D.; Bowling, P.S.; Barnes, C.W.
1993-10-22
Recent work has demonstrated the ability of neural-network-based controllers to optimize and control machines with complex, non-linear, relatively unknown control spaces. We present a brief overview of neural networks via a taxonomy illustrating some capabilities of different kinds of neural networks. We present some successful control examples, particularly the optimization and control of a small-angle negative ion source.
Optimal singular control with applications to trajectory optimization
NASA Technical Reports Server (NTRS)
Vinh, N. X.
1977-01-01
A comprehensive discussion of the problem of singular control is presented. Singular control enters an optimal trajectory when the so called switching function vanishes identically over a finite time interval. Using the concept of domain of maneuverability, the problem of optical switching is analyzed. Criteria for the optimal direction of switching are presented. The switching, or junction, between nonsingular and singular subarcs is examined in detail. Several theorems concerning the necessary, and also sufficient conditions for smooth junction are presented. The concepts of quasi-linear control and linearized control are introduced. They are designed for the purpose of obtaining approximate solution for the difficult Euler-Lagrange type of optimal control in the case where the control is nonlinear.
Optimized coordinates for anharmonic vibrational structure theories.
Yagi, Kiyoshi; Keçeli, Murat; Hirata, So
2012-11-28
A procedure to determine optimal vibrational coordinates is developed on the basis of an earlier idea of Thompson and Truhlar [J. Chem. Phys. 77, 3031 (1982)]. For a given molecule, these coordinates are defined as the unitary transform of the normal coordinates that minimizes the energy of the vibrational self-consistent-field (VSCF) method for the ground state. They are justified by the fact that VSCF in these coordinates becomes exact in two limiting cases: harmonic oscillators, where the optimized coordinates are normal, and noninteracting anharmonic oscillators, in which the optimized coordinates are localized on individual oscillators. A robust and general optimization algorithm is developed, which decomposes the transformation matrix into a product of Jacobi matrices, determines the rotation angle of each Jacobi matrix that minimizes the energy, and iterates the process until a minimum in the whole high dimension is reached. It is shown that the optimized coordinates are neither entirely localized nor entirely delocalized (or normal) in any of the molecules (the water, water dimer, and ethylene molecules) examined (apart from the aforementioned limiting cases). Rather, high-frequency stretching modes tend to be localized, whereas low-frequency skeletal vibrations remain normal. On the basis of these coordinates, we introduce two new vibrational structure methods: optimized-coordinate VSCF (oc-VSCF) and optimized-coordinate vibrational configuration interaction (oc-VCI). For the modes that become localized, oc-VSCF is found to outperform VSCF, whereas, for both classes of modes, oc-VCI exhibits much more rapid convergence than VCI with respect to the rank of excitations. We propose a rational configuration selection for oc-VCI when the optimized coordinates are localized. The use of the optimized coordinates in VCI with this configuration selection scheme reduces the mean absolute errors in the frequencies of the fundamentals and the first overtones
Optimizing Dynamical Network Structure for Pinning Control.
Orouskhani, Yasin; Jalili, Mahdi; Yu, Xinghuo
2016-04-12
Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.
Optimizing Dynamical Network Structure for Pinning Control
NASA Astrophysics Data System (ADS)
Orouskhani, Yasin; Jalili, Mahdi; Yu, Xinghuo
2016-04-01
Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.
Mixed-Strategy Chance Constrained Optimal Control
NASA Technical Reports Server (NTRS)
Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J.
2013-01-01
This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.
Integrated control/structure optimization by multilevel decomposition
NASA Technical Reports Server (NTRS)
Zeiler, Thomas A.; Gilbert, Michael G.
1990-01-01
A method for integrated control/structure optimization by multilevel decomposition is presented. It is shown that several previously reported methods were actually partial decompositions wherein only the control was decomposed into a subsystem design. One of these partially decomposed problems was selected as a benchmark example for comparison. The present paper fully decomposes the system into structural and control subsystem designs and produces an improved design. Theory, implementation, and results for the method are presented and compared with the benchmark example.
Optimal Discrete Event Supervisory Control of Aircraft Gas Turbine Engines
NASA Technical Reports Server (NTRS)
Litt, Jonathan (Technical Monitor); Ray, Asok
2004-01-01
This report presents an application of the recently developed theory of optimal Discrete Event Supervisory (DES) control that is based on a signed real measure of regular languages. The DES control techniques are validated on an aircraft gas turbine engine simulation test bed. The test bed is implemented on a networked computer system in which two computers operate in the client-server mode. Several DES controllers have been tested for engine performance and reliability.
Integrated control/structure optimization by multilevel decomposition
NASA Technical Reports Server (NTRS)
Zeiler, Thomas A.; Gilbert, Michael G.
1990-01-01
A method for integrated control/structure optimization by multilevel decomposition is presented. It is shown that several previously reported methods were actually partial decompositions wherein only the control was decomposed into a subsystem design. One of these partially decomposed problems was selected as a benchmark example for comparison. The system is fully decomposed into structural and control subsystem designs and an improved design is produced. Theory, implementation, and results for the method are presented and compared with the benchmark example.
The Optimization of Decision Studies in Generalizability Theory.
ERIC Educational Resources Information Center
Sanders, Petrus Franciscus
The application of mathematical programming techniques is extended to the construction of measurement instruments in generalizability theory. Key concepts in generalizability theory are explained and a description is given of: (1) the one-facet crossed design; (2) the two-facet crossed design; and (3) a two-facet nested design. The optimization of…
The Clinical Significance of Optimality Theory for Phonological Disorders
ERIC Educational Resources Information Center
Gierut, Judith A.; Morrisette, Michele L.
2005-01-01
Linguistic theory has made important contributions to the clinical assessment and treatment of children with functional phonological disorders. In this article, Optimality Theory (OT) is introduced as a new linguistic model of grammar. Basic assumptions of the model are described and extended to clinical assessment and treatment. The aim is (1) to…
Discover for Yourself: An Optimal Control Model in Insect Colonies
ERIC Educational Resources Information Center
Winkel, Brian
2013-01-01
We describe the enlightening path of self-discovery afforded to the teacher of undergraduate mathematics. This is demonstrated as we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at…
Optimal digestion theory does not predict the effect of pathogens on intestinal plasticity
Venesky, Matthew D.; Hanlon, Shane M.; Lynch, Kyle; Parris, Matthew J.; Rohr, Jason R.
2013-01-01
One prediction of optimal digestion theory is that organisms will increase the relative length of their digestive tracts when food resources become limited. We used theory of optimal digestion to test whether tadpoles can adjust the relative length of their intestines when challenged with the fungal pathogen Batrachochytrium dendrobatidis (Bd). The degree of tadpole mouthpart damage, a symptom of Bd infections that reduces food consumption, was associated positively with the length of tadpole intestines relative to their body size, consistent with optimal digestion theory. After controlling for mouthpart damage, tadpoles exposed to Bd had shorter intestines relative to their body size, opposite to the predictions of optimal digestion theory. One explanation of why tadpoles with higher Bd loads have shorter relative intestinal lengths is that they divert energy from maintaining intestinal and overall growth towards anti-parasite defences. PMID:23445950
Approximation in control of flexible structures, theory and application
NASA Technical Reports Server (NTRS)
Gibson, J. S.
1983-01-01
The sense in which the feedback control law based on an approximate finite dimensional model of a continuous structure approximates a control law which is optimal for the distributed, or infinite dimensional, model of the structure is studied. From the analysis of the various control and stability issues associated with this basis question, useful information for designing finite dimensional compensators which produce near-optimal performance in infinite dimensional systems is gained. Some of the important predictions that can be made about large-order finite dimensional control laws, using the theory of infinite dimensional Riccati equations are indicated.
Lie theory and control systems defined on spheres
NASA Technical Reports Server (NTRS)
Brockett, R. W.
1972-01-01
It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case.
Dynamics and linear quadratic optimal control of flexible multibody systems
NASA Astrophysics Data System (ADS)
Tung, Chin-Wei
1994-12-01
An efficient algorithm for the modeling, dynamic analysis, and optimal control of flexible multibody systems (FMBS) is presented. The cantilevered Bernoulli-Euler beam model and the assumed mode method are used to represent flexibility of elastic bodies in 3D vibration problems. Centrifugal stiffening effects are introduced to correctly represent the dynamic response. The governing equations of motion are based on Kane's equations, adopting a recursive formulation and strategic positioning of the generalized coordinates. The linear quadratic optimization scheme is employed to formulate the vibration control problem. The solutions to the Riccati equation and the use of Kalman gain as optimal control feedbacks to the control of flexibility are also introduced. Based on the optimal control theory and the property of the built-in redundancy for flexible multibody systems, the performance index measure in the optimization control of such systems can be classified into two manifolds: (1) using the extra degrees of freedom resulting from redundancy as control inputs and choosing an integral-type performance index which results in a global optimization scheme and (2) using the joint forces and torques as control inputs and allowing the system output state to keep close track to a reference state while the performance index is kept minimum. Several numerical examples are presented to demonstrate the effectiveness of the methodologies developed.
Control optimization, stabilization and computer algorithms for aircraft applications
NASA Technical Reports Server (NTRS)
Athans, M. (Editor); Willsky, A. S. (Editor)
1982-01-01
The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory.
Optimal birth control of population dynamics.
Chan, W L; Guo, B Z
1989-11-01
The authors studied optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition and fixed final horizon are developed, and the time optimal control problems, the problem with target sets, and infinite planning horizon case are investigated.
Dynamic optimization and adaptive controller design
NASA Astrophysics Data System (ADS)
Inamdar, S. R.
2010-10-01
In this work I present a new type of controller which is an adaptive tracking controller which employs dynamic optimization for optimizing current value of controller action for the temperature control of nonisothermal continuously stirred tank reactor (CSTR). We begin with a two-state model of nonisothermal CSTR which are mass and heat balance equations and then add cooling system dynamics to eliminate input multiplicity. The initial design value is obtained using local stability of steady states where approach temperature for cooling action is specified as a steady state and a design specification. Later we make a correction in the dynamics where material balance is manipulated to use feed concentration as a system parameter as an adaptive control measure in order to avoid actuator saturation for the main control loop. The analysis leading to design of dynamic optimization based parameter adaptive controller is presented. The important component of this mathematical framework is reference trajectory generation to form an adaptive control measure.
NASA Astrophysics Data System (ADS)
Hocker, David Lance
The control of quantum systems occurs across a broad range of length and energy scales in modern science, and efforts have demonstrated that locating suitable controls to perform a range of objectives has been widely successful. The justification for this success arises from a favorable topology of a quantum control landscape, defined as a mapping of the controls to a cost function measuring the success of the operation. This is summarized in the landscape principle that no suboptimal extrema exist on the landscape for well-suited control problems, explaining a trend of successful optimizations in both theory and experiment. This dissertation explores what additional lessons may be gleaned from the quantum control landscape through numerical and theoretical studies. The first topic examines the experimentally relevant problem of assessing and reducing disturbances due to noise. The local curvature of the landscape is found to play an important role on noise effects in the control of targeted quantum unitary operations, and provides a conceptual framework for assessing robustness to noise. Software for assessing noise effects in quantum computing architectures was also developed and applied to survey the performance of current quantum control techniques for quantum computing. A lack of competition between robustness and perfect unitary control operation was discovered to fundamentally limit noise effects, and highlights a renewed focus upon system engineering for reducing noise. This convergent behavior generally arises for any secondary objective in the situation of high primary objective fidelity. The other dissertation topic examines the utility of quantum control for a class of nonlinear Hamiltonians not previously considered under the landscape principle. Nonlinear Schrodinger equations are commonly used to model the dynamics of Bose-Einstein condensates (BECs), one of the largest known quantum objects. Optimizations of BEC dynamics were performed in which the
Control theory based airfoil design using the Euler equations
NASA Technical Reports Server (NTRS)
Jameson, Antony; Reuther, James
1994-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.
Role of controllability in optimizing quantum dynamics
Wu Rebing; Hsieh, Michael A.; Rabitz, Herschel
2011-06-15
This paper reveals an important role that controllability plays in the complexity of optimizing quantum control dynamics. We show that the loss of controllability generally leads to multiple locally suboptimal controls when gate fidelity in a quantum control system is maximized, which does not happen if the system is controllable. Such local suboptimal controls may attract an optimization algorithm into a local trap when a global optimal solution is sought, even if the target gate can be perfectly realized. This conclusion results from an analysis of the critical topology of the corresponding quantum control landscape, which refers to the gate fidelity objective as a functional of the control fields. For uncontrollable systems, due to SU(2) and SU(3) dynamical symmetries, the control landscape corresponding to an implementable target gate is proven to possess multiple locally optimal critical points, and its ruggedness can be further increased if the target gate is not realizable. These results imply that the optimization of quantum dynamics can be seriously impeded when operating with local search algorithms under these conditions, and thus full controllability is demanded.
Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.
Neuhauser, Daniel; Rabani, Eran; Cytter, Yael; Baer, Roi
2016-05-19
We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe-Salpeter approach. PMID:26651840
Direct Optimal Control of Duffing Dynamics
NASA Technical Reports Server (NTRS)
Oz, Hayrani; Ramsey, John K.
2002-01-01
The "direct control method" is a novel concept that is an attractive alternative and competitor to the differential-equation-based methods. The direct method is equally well applicable to nonlinear, linear, time-varying, and time-invariant systems. For all such systems, the method yields explicit closed-form control laws based on minimization of a quadratic control performance measure. We present an application of the direct method to the dynamics and optimal control of the Duffing system where the control performance measure is not restricted to a quadratic form and hence may include a quartic energy term. The results we present in this report also constitute further generalizations of our earlier work in "direct optimal control methodology." The approach is demonstrated for the optimal control of the Duffing equation with a softening nonlinear stiffness.
Network Anomaly Detection System with Optimized DS Evidence Theory
Liu, Yuan; Wang, Xiaofeng; Liu, Kaiyu
2014-01-01
Network anomaly detection has been focused on by more people with the fast development of computer network. Some researchers utilized fusion method and DS evidence theory to do network anomaly detection but with low performance, and they did not consider features of network—complicated and varied. To achieve high detection rate, we present a novel network anomaly detection system with optimized Dempster-Shafer evidence theory (ODS) and regression basic probability assignment (RBPA) function. In this model, we add weights for each senor to optimize DS evidence theory according to its previous predict accuracy. And RBPA employs sensor's regression ability to address complex network. By four kinds of experiments, we find that our novel network anomaly detection model has a better detection rate, and RBPA as well as ODS optimization methods can improve system performance significantly. PMID:25254258
Theory and practice of parallel direct optimization.
Janies, Daniel A; Wheeler, Ward C
2002-01-01
Our ability to collect and distribute genomic and other biological data is growing at a staggering rate (Pagel, 1999). However, the synthesis of these data into knowledge of evolution is incomplete. Phylogenetic systematics provides a unifying intellectual approach to understanding evolution but presents formidable computational challenges. A fundamental goal of systematics, the generation of evolutionary trees, is typically approached as two distinct NP-complete problems: multiple sequence alignment and phylogenetic tree search. The number of cells in a multiple alignment matrix are exponentially related to sequence length. In addition, the number of evolutionary trees expands combinatorially with respect to the number of organisms or sequences to be examined. Biologically interesting datasets are currently comprised of hundreds of taxa and thousands of nucleotides and morphological characters. This standard will continue to grow with the advent of highly automated sequencing and development of character databases. Three areas of innovation are changing how evolutionary computation can be addressed: (1) novel concepts for determination of sequence homology, (2) heuristics and shortcuts in tree-search algorithms, and (3) parallel computing. In this paper and the online software documentation we describe the basic usage of parallel direct optimization as implemented in the software POY (ftp://ftp.amnh.org/pub/molecular/poy).
Neuro-optimal control of helicopter UAVs
NASA Astrophysics Data System (ADS)
Nodland, David; Ghosh, Arpita; Zargarzadeh, H.; Jagannathan, S.
2011-05-01
Helicopter UAVs can be extensively used for military missions as well as in civil operations, ranging from multirole combat support and search and rescue, to border surveillance and forest fire monitoring. Helicopter UAVs are underactuated nonlinear mechanical systems with correspondingly challenging controller designs. This paper presents an optimal controller design for the regulation and vertical tracking of an underactuated helicopter using an adaptive critic neural network framework. The online approximator-based controller learns the infinite-horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation and then calculates the corresponding optimal control input that minimizes the HJB equation forward-in-time. In the proposed technique, optimal regulation and vertical tracking is accomplished by a single neural network (NN) with a second NN necessary for the virtual controller. Both of the NNs are tuned online using novel weight update laws. Simulation results are included to demonstrate the effectiveness of the proposed control design in hovering applications.
Modal insensitivity with optimality. [in feedback control
NASA Technical Reports Server (NTRS)
Calise, A. J.; Raman, K. V.
1984-01-01
This paper deals with the design of a constant gain, feedback controller which results in selected modal insensitivity, and at the same time optimizes a quadratic performance index representative of desired system performance for nominal plant parameter values. Both full state and output feedback control are considered. A constraint is established for the feedback gain matrix that results in modal insensitivity, and necessary conditions for optimality subject to this constraint are given. This forms the basis for a numerical algorithm to compute the optimal feedback gain. To illustrate the procedure, a design is carried out using the lateral dynamics of an L-1011 aircraft.
Optimal control of systems with capacity: Related noises
NASA Technical Reports Server (NTRS)
Ruan, Milfang; Choudhury, Ajit K.
1991-01-01
In the ordinary theory of optimal control (LQR and Kalman filter), the variances of the actuators and the sensors are assumed to be known (not related to the capacities of the devices). This assumption is not true in practice. Generally, a device with greater capacity to exert actuating forces and a sensor capable of sensing greater sensing range will generate noise of greater power spectral density. When the ordinary theory of optimal control is used to estimate the errors of the outputs in such cases it will lead to faulty results, because the capacities of such devices are unknown before the system is designed. The performance of the system designed by the ordinary theory will not be optimal as the variances of the sensors and the actuators are neither known nor constant. The interaction between the control system and structure could be serious because the ordinary method will lead to greater feedback (Kalman gain) matrices. Methods which can optimize the performance of systems when noises of the actuators and the sensors are related to their capacities are developed. These methods will result in smaller feedback (Kalman gain) matrix.
Applications of robust control theory - Educational implications
NASA Technical Reports Server (NTRS)
Dorato, P.; Yedavalli, R. K.
1992-01-01
A survey is made of applications of robust control theory to problems of flight control, control of flexible space structures, and engine control which have appeared in recent conferences and journals. An analysis is made of which theoretical techniques are most commonly used and what implications this has for graduate and undergraduate education in aerospace engineering.
Optimal cooperative control synthesis of active displays
NASA Technical Reports Server (NTRS)
Garg, S.; Schmidt, D. K.
1986-01-01
The utility of augmenting displays to aid the human operator in controlling high order complex systems is well known. Analytical evaluation of various display designs for a simple k/s sup 2 plant in a compensatory tracking task using an optimal Control Model (OCM) of human behavior is carried out. This analysis reveals that significant improvement in performance should be obtained by skillful integration of key information into the display dynamics. The cooperative control synthesis technique previously developed to design pilot-optimal control augmentation is extended to incorporate the simultaneous design of performance enhancing augmented displays. The application of the cooperative control synthesis technique to the design of augmented displays is discussed for the simple k/s sup 2 plant. This technique is intended to provide a systematic approach to design optimally augmented displays tailored for specific tasks.
Optimal cooperative control synthesis of active displays
NASA Technical Reports Server (NTRS)
Gary, Sanjay; Schmidt, David K.
1987-01-01
A technique is developed that is intended to provide a systematic approach to synthesizing display augmentation for optimal manual control in complex, closed-loop tasks. A cooperative control synthesis technique, previously developed to design pilot-optimal control augmentation for the plant, is extended to incorporate the simultaneous design of performance enhancing displays. The technique utilizes an optimal control model of the man in the loop. It is applied to the design of a quickening control law for a display and a simple K/(s squared) plant, and then to an F-15 type aircraft in a multichannel task. Utilizing the closed-loop modeling and analysis procedures, the results from the display design algorithm are evaluated and an analytical validation is performed. Experimental validation is recommended for future efforts.
Optimal cooperative control synthesis of active displays
NASA Technical Reports Server (NTRS)
Garg, S.; Schmidt, D. K.
1985-01-01
The utility of augmenting displays to aid the human operator in controlling high order complex systems is well known. Analytical evaluations of various display designs for a simple k/s-squared plant in a compensatory tracking task using an Optimal Control Model (OCM) of human behavior is carried out. This analysis reveals that significant improvement in performance should be obtained by skillful integration of key information into the display dynamics. The cooperative control synthesis technique previously developed to design pilot-optimal control augmentation is extended to incorporate the simultaneous design of performance enhancing augmented displays. The application of the cooperative control synthesis technique to the design of augmented displays is discussed for the simple k/s-squared plant. This technique is intended to provide a systematic approach to design optimally augmented displays tailored for specific tasks.
Optimal cooperative control synthesis of active displays
NASA Technical Reports Server (NTRS)
Garg, S.; Schmidt, D. K.
1985-01-01
A technique is developed that is intended to provide a systematic approach to synthesizing display augmentation for optimal manual control in complex, closed-loop tasks. A cooperative control synthesis technique, previously developed to design pilot-optimal control augmentation for the plant, is extended to incorporate the simultaneous design of performance enhancing displays. The technique utilizes an optimal control model of the man in the loop. It is applied to the design of a quickening control law for a display and a simple K/s(2) plant, and then to an F-15 type aircraft in a multi-channel task. Utilizing the closed loop modeling and analysis procedures, the results from the display design algorithm are evaluated and an analytical validation is performed. Experimental validation is recommended for future efforts.
Stochastic Optimal Control via Bellman's Principle
NASA Technical Reports Server (NTRS)
Crespo, Luis G.; Sun, Jian Q.
2003-01-01
This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.
Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity
Oizumi, Ryo
2014-01-01
Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258
An optimal control approach to probabilistic Boolean networks
NASA Astrophysics Data System (ADS)
Liu, Qiuli
2012-12-01
External control of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases. For this purpose, a number of stochastic optimal control approaches have been proposed. Probabilistic Boolean networks (PBNs) as powerful tools for modeling gene regulatory systems have attracted considerable attention in systems biology. In this paper, we deal with a problem of optimal intervention in a PBN with the help of the theory of discrete time Markov decision process. Specifically, we first formulate a control model for a PBN as a first passage model for discrete time Markov decision processes and then find, using a value iteration algorithm, optimal effective treatments with the minimal expected first passage time over the space of all possible treatments. In order to demonstrate the feasibility of our approach, an example is also displayed.
A reliable algorithm for optimal control synthesis
NASA Technical Reports Server (NTRS)
Vansteenwyk, Brett; Ly, Uy-Loi
1992-01-01
In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.
Lagrange duality theory for convex control problems
NASA Technical Reports Server (NTRS)
Hager, W. W.; Mitter, S. K.
1976-01-01
The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.
Evaluating Student Assessments: The Use of Optimal Foraging Theory
ERIC Educational Resources Information Center
Whalley, W. Brian
2016-01-01
The concepts of optimal foraging theory and the marginal value theorem are used to investigate possible student behaviour in accruing marks in various forms of assessment. The ideas of predator energy consumption, handling and search times can be evaluated in terms of student behaviour and gaining marks or "attainment". These ideas can…
"Cruel Optimism" and Contemporary Australian Critical Theory in Educational Research
ERIC Educational Resources Information Center
Rasmussen, Mary Lou
2015-01-01
"Cruel optimism" is a term coined by Lauren Berlant. In conceptualizing this term, Berlant draws on the resources of critical theory to interrogate people's desires for things they think may improve their lot, but actually act as obstacles to flourishing. This notion may be useful for analysing the current state of education in…
Optimal control alleviation of tilting proprotor gust response
NASA Technical Reports Server (NTRS)
Johnson, W.
1975-01-01
Optimal control theory is applied to the design of a control system for alleviation of the gust response of tilting proprotor aircraft. Using a proprotor and cantilever wing analytical model, the uncontrolled and controlled gust response is examined over the entire operating range of the aircraft except for hover: helicopter mode, conversion, and airplane mode flight. Substantial improvements in the loads, ride quality, and aeroelastic stability are possible with a properly designed controller. A single controller, nominally optimal only at the design point speed (160 knots here), operated efficiently over the entire speed range, with the possible exception of very low speed in helicopter mode. Kalman-Bucy filters were used as compensation networks to provide state estimates from various measurements in the wing motion, rotor speed perturbation, and tip-path-plane tilt.
OPTIMIZATION OF COMBINED SEWER OVERFLOW CONTROL SYSTEMS
The highly variable and intermittent pollutant concentrations and flowrates associated with wet-weather events in combined sewersheds necessitates the use of storage-treatment systems to control pollution.An optimized combined-sewer-overflow (CSO) control system requires a manage...
OPTIMAL CONTROL THEORY FOR SUSTAINABLE ENVIRONMENTAL MANAGEMENT
With growing world population, diminishing resources, and realization of the harmful effects of various pollutants, research focus in environmental management has shifted towards sustainability. The goal of a sustainable management strategy is to promote the structure and operati...
Algorithm For Optimal Control Of Large Structures
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Garba, John A..; Utku, Senol
1989-01-01
Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.
Centralized Stochastic Optimal Control of Complex Systems
Malikopoulos, Andreas
2015-01-01
In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.
A danger-theory-based immune network optimization algorithm.
Zhang, Ruirui; Li, Tao; Xiao, Xin; Shi, Yuanquan
2013-01-01
Existing artificial immune optimization algorithms reflect a number of shortcomings, such as premature convergence and poor local search ability. This paper proposes a danger-theory-based immune network optimization algorithm, named dt-aiNet. The danger theory emphasizes that danger signals generated from changes of environments will guide different levels of immune responses, and the areas around danger signals are called danger zones. By defining the danger zone to calculate danger signals for each antibody, the algorithm adjusts antibodies' concentrations through its own danger signals and then triggers immune responses of self-regulation. So the population diversity can be maintained. Experimental results show that the algorithm has more advantages in the solution quality and diversity of the population. Compared with influential optimization algorithms, CLONALG, opt-aiNet, and dopt-aiNet, the algorithm has smaller error values and higher success rates and can find solutions to meet the accuracies within the specified function evaluation times.
Control theory for random systems
NASA Technical Reports Server (NTRS)
Bryson, A. E., Jr.
1972-01-01
A survey is presented of the current knowledge available for designing and predicting the effectiveness of controllers for dynamic systems which can be modeled by ordinary differential equations. A short discussion of feedback control is followed by a description of deterministic controller design and the concept of system state. The need for more realistic disturbance models led to the use of stochastic process concepts, in particular the Gauss-Markov process. A compensator controlled system, with random forcing functions, random errors in the measurements, and random initial conditions, is treated as constituting a Gauss-Markov random process; hence the mean-square behavior of the controlled system is readily predicted. As an example, a compensator is designed for a helicopter to maintain it in hover in a gusty wind over a point on the ground.
Product Distribution Theory for Control of Multi-Agent Systems
NASA Technical Reports Server (NTRS)
Lee, Chia Fan; Wolpert, David H.
2004-01-01
Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.
Control theory meets synthetic biology.
Del Vecchio, Domitilla; Dy, Aaron J; Qian, Yili
2016-07-01
The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology. PMID:27440256
Control theory meets synthetic biology.
Del Vecchio, Domitilla; Dy, Aaron J; Qian, Yili
2016-07-01
The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology.
Control theory meets synthetic biology
2016-01-01
The past several years have witnessed an increased presence of control theoretic concepts in synthetic biology. This review presents an organized summary of how these control design concepts have been applied to tackle a variety of problems faced when building synthetic biomolecular circuits in living cells. In particular, we describe success stories that demonstrate how simple or more elaborate control design methods can be used to make the behaviour of synthetic genetic circuits within a single cell or across a cell population more reliable, predictable and robust to perturbations. The description especially highlights technical challenges that uniquely arise from the need to implement control designs within a new hardware setting, along with implemented or proposed solutions. Some engineering solutions employing complex feedback control schemes are also described, which, however, still require a deeper theoretical analysis of stability, performance and robustness properties. Overall, this paper should help synthetic biologists become familiar with feedback control concepts as they can be used in their application area. At the same time, it should provide some domain knowledge to control theorists who wish to enter the rising and exciting field of synthetic biology. PMID:27440256
Optimal performance of constrained control systems
NASA Astrophysics Data System (ADS)
Harvey, P. Scott, Jr.; Gavin, Henri P.; Scruggs, Jeffrey T.
2012-08-01
This paper presents a method to compute optimal open-loop trajectories for systems subject to state and control inequality constraints in which the cost function is quadratic and the state dynamics are linear. For the case in which inequality constraints are decentralized with respect to the controls, optimal Lagrange multipliers enforcing the inequality constraints may be found at any time through Pontryagin’s minimum principle. In so doing, the set of differential algebraic Euler-Lagrange equations is transformed into a nonlinear two-point boundary-value problem for states and costates whose solution meets the necessary conditions for optimality. The optimal performance of inequality constrained control systems is calculable, allowing for comparison to previous, sub-optimal solutions. The method is applied to the control of damping forces in a vibration isolation system subjected to constraints imposed by the physical implementation of a particular controllable damper. An outcome of this study is the best performance achievable given a particular objective, isolation system, and semi-active damper constraints.
Geometrically constrained observability. [control theory
NASA Technical Reports Server (NTRS)
Brammer, R. F.
1974-01-01
This paper deals with observed processes in situations in which observations are available only when the state vector lies in certain regions. For linear autonomous observed processes, necessary and sufficient conditions are obtained for half-space observation regions. These results are shown to contain a theorem dual to a controllability result proved by the author for a linear autonomous control system whose control restraint set does not contain the origin as an interior point. Observability results relating to continuous observation systems and sampled data systems are presented, and an example of observing the state of an electrical network is given.
Conjunctive Multibasin Management: An Optimal Control Approach
NASA Astrophysics Data System (ADS)
Noel, Jay E.; Howitt, Richard E.
1982-08-01
The economic effects of conjunctive management of ground and surface water supplies for irrigation are formulated as an optimal control model. An empirical hydroeconomic model is estimated for the Yolo County district in California. Two alternative solution methodologies (analytic Riccatti and mathematical programing) are applied and compared. Results show the economic potential for interbasin transfers and the impact of increased electricity prices on optimal groundwater management.
Advanced rotorcraft control using parameter optimization
NASA Technical Reports Server (NTRS)
Vansteenwyk, Brett; Ly, Uy-Loi
1991-01-01
A reliable algorithm for the evaluation of a quadratic performance index and its gradients with respect to the controller design parameters is presented. The algorithm is part of a design algorithm for an optimal linear dynamic output feedback controller that minimizes a finite time quadratic performance index. The numerical scheme is particularly robust when it is applied to the control law synthesis for systems with densely packed modes and where there is a high likelihood of encountering degeneracies in the closed loop eigensystem. This approach through the use of a accurate Pade series approximation does not require the closed loop system matrix to be diagonalizable. The algorithm has been included in a control design package for optimal robust low order controllers. Usefulness of the proposed numerical algorithm has been demonstrated using numerous practical design cases where degeneracies occur frequently in the closed loop system under an arbitrary controller design initialization and during the numerical search.
Stochastic time-optimal control problems
NASA Technical Reports Server (NTRS)
Zhang, W.; Elliot, D.
1988-01-01
Two types of stochastic time-optimal controls in a one-dimensional setting are considered. Multidimensional problems, in the case of complete state information available and the system modeled by stochastic differential equations, are studied under the formulation of minimizing the expected transient-response time. The necessary condition of optimality is the satisfaction for the value function of a parabolic partial differential equation with boundary conditions. The sufficient condition of optimality is also provided, based on Dynkin's formula. Finally, three examples are given.
A general weight matrix formulation using optimal control
NASA Technical Reports Server (NTRS)
Farotimi, Oluseyi; Dembo, Amir; Kailath, Thomas
1991-01-01
Classical methods from optimal control theory are used in deriving general forms for neural network weights. The network learning or application task is encoded in a performance index of a general structure. Consequently, different instances of this performance index lead to special cases of weight rules, including some well-known forms. Comparisons are made with the outer product rule, spectral methods, and recurrent back-propagation. Simulation results and comparisons are presented.
Road map to adaptive optimal control. [jet engine control
NASA Technical Reports Server (NTRS)
Boyer, R.
1980-01-01
A building block control structure leading toward adaptive, optimal control for jet engines is developed. This approach simplifies the addition of new features and allows for easier checkout of the control by providing a baseline system for comparison. Also, it is possible to eliminate certain features that do not have payoff by being selective in the addition of new building blocks to be added to the baseline system. The minimum risk approach specifically addresses the need for active identification of the plant to be controlled in real time and real time optimization of the control for the identified plant.
Solving inverse problems of identification type by optimal control methods
Lenhart, S.; Protopopescu, V.; Jiongmin Yong
1997-06-01
Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations.
Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels
NASA Technical Reports Server (NTRS)
Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.
2011-01-01
We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.
Multimodel methods for optimal control of aeroacoustics.
Chen, Guoquan; Collis, Samuel Scott
2005-01-01
A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully applied to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.
Development of a digital adaptive optimal linear regulator flight controller
NASA Technical Reports Server (NTRS)
Berry, P.; Kaufman, H.
1975-01-01
Digital adaptive controllers have been proposed as a means for retaining uniform handling qualities over the flight envelope of a high-performance aircraft. Towards such an implementation, an explicit adaptive controller, which makes direct use of online parameter identification, has been developed and applied to the linearized lateral equations of motion for a typical fighter aircraft. The system is composed of an online weighted least-squares parameter identifier, a Kalman state filter, and a model following control law designed using optimal linear regulator theory. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for onboard implementation.
Applications of fuzzy theories to multi-objective system optimization
NASA Technical Reports Server (NTRS)
Rao, S. S.; Dhingra, A. K.
1991-01-01
Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.
Quantum optimal control of photoelectron spectra and angular distributions
NASA Astrophysics Data System (ADS)
Goetz, R. Esteban; Karamatskou, Antonia; Santra, Robin; Koch, Christiane P.
2016-01-01
Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on, e.g., charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can account for specific desired properties in the photoelectron angular distribution alone, in the photoelectron spectrum, or in both. We demonstrate the method for hydrogen and then apply it to argon under strong XUV radiation, maximizing the difference of emission into the upper and lower hemispheres, in order to realize directed electron emission in the XUV regime.
Optimal control of systems with intermediate phase constraints
Kirichenko, S.B.
1995-03-01
In this paper, we derive necessary conditions of minimum for the general optimal control problem with the following characteristics: the trajectory is corrected at intermediate time instants using matching relationships; the system dynamics may vary in each time interval; the optimand functional and the functional constraints depend on the intermediate time instants, the momenta, and the phase coordinates of the trajectories. The result is derived by the methods of modern optimization theory and nonsmooth analysis. It is presented in the form of a maximum principle. The specific solution scheme for this problem has been developed in greater detail elsewhere for systems of the form x{sub i}={line_integral}{sub i}(t, x{sub i}). Much of the previous manipulations and results on the structure of the conjugate cone and the form of the directional derivatives are used also in this paper. This is legitimate because the optimized parameters and controls are independent.
Optimal control of the Starfire Beam Director
NASA Astrophysics Data System (ADS)
Lanier, Troy V.
1992-12-01
The Starfire Beam Director (SBD) is located at the Starfire Optical Range at Kirtland Air Force Base in Albuquerque, New Mexico. The SBD capabilities include tracking celestial objects and active or passive tracking of artificial satellites to support the Phillips Laboratory Ground Based Laser Acquisition, Tracking, and Pointing (GBL ATP) program. The pointing and tracking accuracy needed to support such experiments is micron rad to sub-grad level. To accomplish this goal requires precise pointing of the massive 6 ton 1-meter clear aperture coelostat. Optimal control design techniques are used to develop a controller to meet the stringent pointing requirements. A nominal linear state-space model was built which included gimbal dynamics, plant disturbances, and sensor noise. Then optimal control design techniques were used to develop unity feedback and two degree of freedom controllers. The various controllers were simulated with the coelostat truth model, which incorporated the higher frequency control loop and motor dynamics, nonlinearities, plant disturbances, sensor noise, and discrete control effects. The best of the designs, the H2 unity feedback controller, was compared and contrasted with the performance of the controller currently being used, which was obtained by classical control design. The H2 controller exceeded tracking requirements and in most areas performed better than the current controller.
Optimal control strategy for abnormal innate immune response.
Tan, Jinying; Zou, Xiufen
2015-01-01
Innate immune response plays an important role in control and clearance of pathogens following viral infection. However, in the majority of virus-infected individuals, the response is insufficient because viruses are known to use different evasion strategies to escape immune response. In this study, we use optimal control theory to investigate how to control the innate immune response. We present an optimal control model based on an ordinary-differential-equation system from a previous study, which investigated the dynamics and regulation of virus-triggered innate immune signaling pathways, and we prove the existence of a solution to the optimal control problem involving antiviral treatment or/and interferon therapy. We conduct numerical experiments to investigate the treatment effects of different control strategies through varying the cost function and control efficiency. The results show that a separate treatment, that is, only inhibiting viral replication (u1(t)) or enhancing interferon activity (u2(t)), has more advantages for controlling viral infection than a mixed treatment, that is, controlling both (u1(t)) and (u2(t)) simultaneously, including the smallest cost and operability. These findings would provide new insight for developing effective strategies for treatment of viral infectious diseases.
Theory of diffusion controlled growth
NASA Astrophysics Data System (ADS)
Ball, R. C.; Somfai, E.
2003-03-01
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models (DBM) in two dimensions [R. C. Ball and E. Somfai; PRL 89, 135503 (2002); and cond-mat/0210598]. The first key step is to understand how these models interrelate when the ultra-violet cut-off strategy is changed, leading us to propose a new set of equivalence relations between generalisations of the original DBM. This enables us to approach these models through the dynamics of conformal maps with a fixed charge cut-off. Using logarithmic field variables then leads to coupled moment equations which appear to be renormalisable. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is discussed. We find angular resonances relatable to the cone angle theory, and we are led to predict a new Screening Transition in the DBM at large η.
An information theory account of cognitive control
Fan, Jin
2014-01-01
Our ability to efficiently process information and generate appropriate responses depends on the processes collectively called cognitive control. Despite a considerable focus in the literature on the cognitive control of information processing, neural mechanisms underlying control are still unclear, and have not been characterized by considering the quantity of information to be processed. A novel and comprehensive account of cognitive control is proposed using concepts from information theory, which is concerned with communication system analysis and the quantification of information. This account treats the brain as an information-processing entity where cognitive control and its underlying brain networks play a pivotal role in dealing with conditions of uncertainty. This hypothesis and theory article justifies the validity and properties of such an account and relates experimental findings to the frontoparietal network under the framework of information theory. PMID:25228875
An information theory account of cognitive control.
Fan, Jin
2014-01-01
Our ability to efficiently process information and generate appropriate responses depends on the processes collectively called cognitive control. Despite a considerable focus in the literature on the cognitive control of information processing, neural mechanisms underlying control are still unclear, and have not been characterized by considering the quantity of information to be processed. A novel and comprehensive account of cognitive control is proposed using concepts from information theory, which is concerned with communication system analysis and the quantification of information. This account treats the brain as an information-processing entity where cognitive control and its underlying brain networks play a pivotal role in dealing with conditions of uncertainty. This hypothesis and theory article justifies the validity and properties of such an account and relates experimental findings to the frontoparietal network under the framework of information theory.
Digital robust control law synthesis using constrained optimization
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivekananda
1989-01-01
Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.
Finite set control transcription for optimal control applications
NASA Astrophysics Data System (ADS)
Stanton, Stuart Andrew
An enhanced method in optimization rooted in direct collocation is formulated to treat the finite set optimal control problem. This is motivated by applications in which a hybrid dynamical system is subject to ordinary differential continuity constraints, but control variables are contained within finite spaces. Resulting solutions display control discontinuities as variables switch between one feasible value to another. Solutions derived are characterized as optimal switching schedules between feasible control values. The methodology allows control switches to be determined over a continuous spectrum, overcoming many of the limitations associated with discretized solutions. Implementation details are presented and several applications demonstrate the method's utility and capability. Simple applications highlight the effectiveness of the methodology, while complicated dynamic systems showcase its relevance. A key example considers the challenges associated with libration point formations. Extensions are proposed for broader classes of hybrid systems.
Integrated control-system design via generalized LQG (GLQG) theory
NASA Technical Reports Server (NTRS)
Bernstein, Dennis S.; Hyland, David C.; Richter, Stephen; Haddad, Wassim M.
1989-01-01
Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.
Optimal control of gypsy moth populations.
Whittle, Andrew; Lenhart, Suzanne; White, K A J
2008-02-01
This study investigates an optimal strategy for the cost effective control of gypsy moth populations. Gypsy moth populations cycle between low sparse numbers to high outbreak levels and it is during the outbreak levels that the moths cause extensive damage to plant foliage which can lead to deforestation. Deforestation can result in significant economic damage to infested areas, and consequently, there have been many efforts to control moth populations. One effective method of control is the use of the biocontrol agent, Gypchek, but its production is costly. We develop a mathematical model which combines population dynamics and optimal control of the moth population to explore strategies by which the total cost of the gypsy moth problem (economic damage and cost of Gypchek) can be minimized.
Integration of Large-Scale Optimization and Game Theory for Sustainable Water Quality Management
NASA Astrophysics Data System (ADS)
Tsao, J.; Li, J.; Chou, C.; Tung, C.
2009-12-01
Sustainable water quality management requires total mass control in pollutant discharge based on both the principles of not exceeding assimilative capacity in a river and equity among generations. The stream assimilative capacity is the carrying capacity of a river for the maximum waste load without violating the water quality standard and the spirit of total mass control is to optimize the waste load allocation in subregions. For the goal of sustainable watershed development, this study will use large-scale optimization theory to optimize the profit, and find the marginal values of loadings as reference of the fair price and then the best way to get the equilibrium by water quality trading for the whole of watershed will be found. On the other hand, game theory plays an important role to maximize both individual and entire profits. This study proves the water quality trading market is available in some situation, and also makes the whole participants get a better outcome.
Mathematical theory of a relaxed design problem in structural optimization
NASA Technical Reports Server (NTRS)
Kikuchi, Noboru; Suzuki, Katsuyuki
1990-01-01
Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.
Linear stochastic optimal control and estimation problem
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, F. K. B.
1980-01-01
Problem involves design of controls for linear time-invariant system disturbed by white noise. Solution is Kalman filter coupled through set of optimal regulator gains to produce desired control signal. Key to solution is solving matrix Riccati differential equation. LSOCE effectively solves problem for wide range of practical applications. Program is written in FORTRAN IV for batch execution and has been implemented on IBM 360.
Optimal control solutions to sodic soil reclamation
NASA Astrophysics Data System (ADS)
Mau, Yair; Porporato, Amilcare
2016-05-01
We study the reclamation process of a sodic soil by irrigation with water amended with calcium cations. In order to explore the entire range of time-dependent strategies, this task is framed as an optimal control problem, where the amendment rate is the control and the total rehabilitation time is the quantity to be minimized. We use a minimalist model of vertically averaged soil salinity and sodicity, in which the main feedback controlling the dynamics is the nonlinear coupling of soil water and exchange complex, given by the Gapon equation. We show that the optimal solution is a bang-bang control strategy, where the amendment rate is discontinuously switched along the process from a maximum value to zero. The solution enables a reduction in remediation time of about 50%, compared with the continuous use of good-quality irrigation water. Because of its general structure, the bang-bang solution is also shown to work for the reclamation of other soil conditions, such as saline-sodic soils. The novelty in our modeling approach is the capability of searching the entire "strategy space" for optimal time-dependent protocols. The optimal solutions found for the minimalist model can be then fine-tuned by experiments and numerical simulations, applicable to realistic conditions that include spatial variability and heterogeneities.
Optimally Controlled Flexible Fuel Powertrain System
Hakan Yilmaz; Mark Christie; Anna Stefanopoulou
2010-12-31
The primary objective of this project was to develop a true Flex Fuel Vehicle capable of running on any blend of ethanol from 0 to 85% with reduced penalty in usable vehicle range. A research and development program, targeting 10% improvement in fuel economy using a direct injection (DI) turbocharged spark ignition engine was conducted. In this project a gasoline-optimized high-technology engine was considered and the hardware and configuration modifications were defined for the engine, fueling system, and air path. Combined with a novel engine control strategy, control software, and calibration this resulted in a highly efficient and clean FFV concept. It was also intended to develop robust detection schemes of the ethanol content in the fuel integrated with adaptive control algorithms for optimized turbocharged direct injection engine combustion. The approach relies heavily on software-based adaptation and optimization striving for minimal modifications to the gasoline-optimized engine hardware system. Our ultimate objective was to develop a compact control methodology that takes advantage of any ethanol-based fuel mixture and not compromise the engine performance under gasoline operation.
Determination of optimal gains for constrained controllers
Kwan, C.M.; Mestha, L.K.
1993-08-01
In this report, we consider the determination of optimal gains, with respect to a certain performance index, for state feedback controllers where some elements in the gain matrix are constrained to be zero. Two iterative schemes for systematically finding the constrained gain matrix are presented. An example is included to demonstrate the procedures.
Optimal singular control for nonlinear semistabilisation
NASA Astrophysics Data System (ADS)
L'Afflitto, Andrea; Haddad, Wassim M.
2016-06-01
The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton-Jacobi-Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.
Research on optimal control, stabilization and computational algorithms for aerospace applications
NASA Technical Reports Server (NTRS)
Athans, M.
1985-01-01
The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented.
Research on optimal control, stabilization and computational algorithms for aerospace applications
NASA Technical Reports Server (NTRS)
Athans, M.
1984-01-01
The research carried out in the areas of optimal control and estimation theory and its applications under this grant is reviewed. A listing of the 257 publications that document the research results is presented.
Renormalization group optimized perturbation theory at finite temperatures
NASA Astrophysics Data System (ADS)
Kneur, Jean-Loïc; Pinto, Marcus B.
2015-12-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar λ ϕ4 field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-N results of the O (N ) model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard thermal loop perturbation theory. The latter approaches exhibit a sensibly degrading scale dependence at higher orders, which we identify as a consequence of missing RG invariance. In contrast RGOPT gives a considerably reduced scale dependence at two-loop level, even for relatively large coupling values √{λ /24 }˜O (1 ), making results much more stable as compared with standard perturbation theory, with expected similar properties for thermal QCD.
Optimization for efficient structure-control systems
NASA Technical Reports Server (NTRS)
Oz, Hayrani; Khot, Narendra S.
1993-01-01
The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure.
Age-structured optimal control in population economics.
Feichtinger, Gustav; Prskawetz, Alexia; Veliov, Vladimir M
2004-06-01
This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.
Algorithms for optimizing CT fluence control
NASA Astrophysics Data System (ADS)
Hsieh, Scott S.; Pelc, Norbert J.
2014-03-01
The ability to customize the incident x-ray fluence in CT via beam-shaping filters or mA modulation is known to improve image quality and/or reduce radiation dose. Previous work has shown that complete control of x-ray fluence (ray-by-ray fluence modulation) would further improve dose efficiency. While complete control of fluence is not currently possible, emerging concepts such as dynamic attenuators and inverse-geometry CT allow nearly complete control to be realized. Optimally using ray-by-ray fluence modulation requires solving a very high-dimensional optimization problem. Most optimization techniques fail or only provide approximate solutions. We present efficient algorithms for minimizing mean or peak variance given a fixed dose limit. The reductions in variance can easily be translated to reduction in dose, if the original variance met image quality requirements. For mean variance, a closed form solution is derived. The peak variance problem is recast as iterated, weighted mean variance minimization, and at each iteration it is possible to bound the distance to the optimal solution. We apply our algorithms in simulations of scans of the thorax and abdomen. Peak variance reductions of 45% and 65% are demonstrated in the abdomen and thorax, respectively, compared to a bowtie filter alone. Mean variance shows smaller gains (about 15%).
Simultaneous structure and control optimization of tensegrities
NASA Astrophysics Data System (ADS)
Masic, Milenko; Skelton, Robert E.
2005-05-01
This paper concerns optimization of prestress of a tensegrity structure to achieve the optimal mixed dynamic and control performance. A linearized dynamic model of the structure is derived. The force density variables that parameterize prestress of the structure appear linearly in the model. The feasible region of these parameters is defined in terms of the extreme directions of the prestress cone. Several properties of the problem are established inside the feasible region of the parameters. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.
PDEMOD: Software for control/structures optimization
NASA Technical Reports Server (NTRS)
Taylor, Lawrence W., Jr.; Zimmerman, David
1991-01-01
Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.
Research on two different mathematical theories on control
NASA Astrophysics Data System (ADS)
Wu, Qing-E.; Wang, Tuo; Pang, Xue-Min; Huang, Yong-Xuan; Li, Ji-Sheng
2008-12-01
With a brand-new theory, this paper not only provides the differences of attributes in concept, formula expression and function type between fuzzy rough sets and probability statistics, but also introduces their differences in algorithms on target control for better solving the control problem. Some new definitions and theorems concerning fuzzy rough sets and probability statistics are given, but this paper mainly makes a comparison of two control algorithms for the target tracking. The simulation results show that the comprehensive performance of the fuzzy rough sets algorithm is better than that of the probability statistics algorithm, but its control effect is not as good as that of the latter on multisensor target control. Finally, some problems concerning the combination of fuzzy rough sets and the probability statistics phenomenon to be solved and development trends are discussed. By these investigations, we can choose the optimal control algorithms for accomplishing better target control.
On The Theory Of Intelligent Controls
NASA Astrophysics Data System (ADS)
Saridis, George N.; Valavanis, Kimon P.
1988-02-01
The recent need of generating machines with enough intelligence to perform autonomously in uncertain environments has imposed new demands on the design of control systems. The new discipline draws its ideas not only from Control Systems Theory but from Artificial Intelligence and Operations Research, as well, in order to meet the needs of intelligent operation with similarities to human behavior. Even though several approaches have been proposed, this paper will deal with the evolution of control theory that leads into the definition of Hierarchically Intelligent Control and the Principle of Decreasing Precision with Increasing Intelligence. A three-level structure representing Organization, Coordination and Execution will be developed as a probabilistic model of such a system and the approaches necessary to implement each one of them will be discussed. Finally, Entropy will be proposed as a common measure of all three levels and the problem of Intelligent Control will be cast as the mathematical programming solution that minimizes the total entropy.
Theory of cellwise optimization for solar central receiver system
NASA Astrophysics Data System (ADS)
Lipps, F. W.
1985-05-01
Cost effective optimization of the solar central receiver system is primarily concerned with the distribution of heliostats in the collector field, including the boundaries of the field. The cellwise optimization procedure determines the optimum cell usage and heliostat spacing parameters for each cell in the collector field. Spacing parameters determine the heliostat density and neighborhood structure uniformly in each cell. Consequently, the cellwise approach ignores heliostat mismatch at cell boundaries. Ignoring the cell boundary problem permits an easy solution for the optimum in terms of appropriately defined annual average data. Insolation, receiver interception, shading and blocking, cosine effects, and the cost parameters combine to control the optimum. Many trade offs are represented. Outputs include the receiver flux density distribution for design time, coefficients for an actual layout, the optimum boundary and various performance and cost estimates for the optimum field. It is also possible to optimize receiver size and tower height by a repeated application of the field optimization procedure.
Optimal control of multiplicative control systems arising from cancer therapy
NASA Technical Reports Server (NTRS)
Bahrami, K.; Kim, M.
1975-01-01
This study deals with ways of curtailing the rapid growth of cancer cell populations. The performance functional that measures the size of the population at the terminal time as well as the control effort is devised. With use of the discrete maximum principle, the Hamiltonian for this problem is determined and the condition for optimal solutions are developed. The optimal strategy is shown to be a bang-bang control. It is shown that the optimal control for this problem must be on the vertices of an N-dimensional cube contained in the N-dimensional Euclidean space. An algorithm for obtaining a local minimum of the performance function in an orderly fashion is developed. Application of the algorithm to the design of antitumor drug and X-irradiation schedule is discussed.
The productive structure and thermoeconomic theories of system optimization
Torres, C.; Serra, L.; Valero, A.; Lozano, M.A.
1996-12-31
The aim of this paper is to achieve a better understanding of the Thermoeconomic Theory of System Optimization and the Structural Theory of Cost (Valero et al., 1992, 1993), in order to unify and to take advantage of both theories. As the Thermoeconomic Functional Analysis (Frangopoulos, 1987, von Spakovsky, 1986), the methodology introduced in this paper, established that, each unit of the system has a purpose, i.e., a product to obtain, a function. For example, the function of a gas turbine is the work obtained when expanding the gases. This methodology is a general development of the Fuel-Product representation (Torres, 1991), based on the Structural Theory of Thermoeconomics. It gives a systematic and easy way to get a functional diagram from the physical scheme. This diagram represents the units, and the relations among themselves and the environment. Each unit uses a set of functions, or resources, from the environment or other units to obtain its function or product. Using as a starting point the functional diagram, it is shown that the Structural Theory and the Thermoeconomic Functional Analysis are equivalent methods and get the same costs result values. Finally, the productive structure (causal diagram) is presented as the key structure to understand the formation of each product and then, to interrelate the whole structure. So, it could be used as a criterion to system disagregation, to obtain more accurate costs.
Optimal Control via Self-Generated Stochasticity
NASA Technical Reports Server (NTRS)
Zak, Michail
2011-01-01
The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.
Optimal motor control may mask sensory dynamics
Kiemel, Tim; Cowan, Noah J.; Jeka, John J.
2009-01-01
Properties of neural controllers for closed-loop sensorimotor behavior can be inferred with system identification. Under the standard paradigm, the closed-loop system is perturbed (input), measurements are taken (output), and the relationship between input and output reveals features of the system under study. Here we show that under common assumptions made about such systems (e.g. the system implements optimal control with a penalty on mechanical, but not sensory, states) important aspects of the neural controller (its zeros mask the modes of the sensors) remain hidden from standard system identification techniques. Only by perturbing or measuring the closed-loop system “between” the sensor and the control can these features be exposed with closed-loop system identification methods; while uncommon, there exist noninvasive techniques such as galvanic vestibular stimulation that perturb between sensor and controller in this way. PMID:19408009
Optimization approaches to nonlinear model predictive control
Biegler, L.T. . Dept. of Chemical Engineering); Rawlings, J.B. . Dept. of Chemical Engineering)
1991-01-01
With the development of sophisticated methods for nonlinear programming and powerful computer hardware, it now becomes useful and efficient to formulate and solve nonlinear process control problems through on-line optimization methods. This paper explores and reviews control techniques based on repeated solution of nonlinear programming (NLP) problems. Here several advantages present themselves. These include minimization of readily quantifiable objectives, coordinated and accurate handling of process nonlinearities and interactions, and systematic ways of dealing with process constraints. We motivate this NLP-based approach with small nonlinear examples and present a basic algorithm for optimization-based process control. As can be seen this approach is a straightforward extension of popular model-predictive controllers (MPCs) that are used for linear systems. The statement of the basic algorithm raises a number of questions regarding stability and robustness of the method, efficiency of the control calculations, incorporation of feedback into the controller and reliable ways of handling process constraints. Each of these will be treated through analysis and/or modification of the basic algorithm. To highlight and support this discussion, several examples are presented and key results are examined and further developed. 74 refs., 11 figs.
Intermittent locomotion as an optimal control strategy
Paoletti, P.; Mahadevan, L.
2014-01-01
Birds, fish and other animals routinely use unsteady effects to save energy by alternating between phases of active propulsion and passive coasting. Here, we construct a minimal model for such behaviour that can be couched as an optimal control problem via an analogy to travelling with a rechargeable battery. An analytical solution of the optimal control problem proves that intermittent locomotion has lower energy requirements relative to steady-state strategies. Additional realistic hypotheses, such as the assumption that metabolic cost at a given power should be minimal (the fixed gear hypothesis), a nonlinear dependence of the energy storage rate on propulsion and/or a preferred average speed, allow us to generalize the model and demonstrate the flexibility of intermittent locomotion with implications for biological and artificial systems. PMID:24711718
Optimization of EB plant by constraint control
Hummel, H.K.; de Wit, G.B.C.; Maarleveld, A. )
1991-03-01
Optimum plant operation can often be achieved by means of constraint control instead of model- based on-line optimization. This is because optimum operation is seldom at the top of the hill but usually at the intersection of constraints. This article describes the development of a constraint control system for a plant producing ethylbenzene (EB) by the Mobil/Badger Ethylbenzene Process. Plant optimization can be defined as the maximization of a profit function describing the economics of the plant. This function contains terms with product values, feedstock prices and operational costs. Maximization of the profit function can be obtained by varying relevant degrees of freedom in the plant, such as a column operating pressure or a reactor temperature. These degrees of freedom can be varied within the available operating margins of the plant.
Discrete-time neural inverse optimal control for nonlinear systems via passivation.
Ornelas-Tellez, Fernando; Sanchez, Edgar N; Loukianov, Alexander G
2012-08-01
This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot. PMID:24807528
Control theory and multiple placebo effects.
Jensen, M P; Karoly, P
The importance of the placebo in medicine is well documented, yet our understanding of placebo effects remains limited. One obstacle to a greater understanding is the fact that the phrase "placebo effect" has been used to refer to a number of qualitatively distinct behavioral events. Thus, different theories have been promulgated, each one tending to explain a selective portion of the placebo phenomenon. To help clarify matters, three kinds of placebo effects are described, and theories that have been used to explain them are reviewed. Limitations of these theories are then discussed, and a general model of placebo effects, based on a control theory perspective, is presented. Some implications and limitations of this model are outlined.
A model for HIV/AIDS pandemic with optimal control
NASA Astrophysics Data System (ADS)
Sule, Amiru; Abdullah, Farah Aini
2015-05-01
Human immunodeficiency virus and acquired immune deficiency syndrome (HIV/AIDS) is pandemic. It has affected nearly 60 million people since the detection of the disease in 1981 to date. In this paper basic deterministic HIV/AIDS model with mass action incidence function are developed. Stability analysis is carried out. And the disease free equilibrium of the basic model was found to be locally asymptotically stable whenever the threshold parameter (RO) value is less than one, and unstable otherwise. The model is extended by introducing two optimal control strategies namely, CD4 counts and treatment for the infective using optimal control theory. Numerical simulation was carried out in order to illustrate the analytic results.
The Research on Optimization of Edge Drop Control for Cold Tandem Rolling Mill
NASA Astrophysics Data System (ADS)
Zhou, Xiao-Min; Yue, Xiao-Xue
2016-05-01
The cold tandem rolling of metal strip presents a significant control challenge because of nonlinearities and process complexities. And reducing edge drop of cold rolling strips and meeting uniform thickness will be a new tough shape theories and technologies. In this paper, the existing edge drop control are analyzed and optimized. The simulation results and practical data show that the optimized control system can effectively control the edge drop.
Optimal strategy for controlling the spread of Plasmodium Knowlesi malaria: Treatment and culling
NASA Astrophysics Data System (ADS)
Abdullahi, Mohammed Baba; Hasan, Yahya Abu; Abdullah, Farah Aini
2015-05-01
Plasmodium Knowlesi malaria is a parasitic mosquito-borne disease caused by a eukaryotic protist of genus Plasmodium Knowlesi transmitted by mosquito, Anopheles leucosphyrus to human and macaques. We developed and analyzed a deterministic Mathematical model for the transmission of Plasmodium Knowlesi malaria in human and macaques. The optimal control theory is applied to investigate optimal strategies for controlling the spread of Plasmodium Knowlesi malaria using treatment and culling as control strategies. The conditions for optimal control of the Plasmodium Knowlesi malaria are derived using Pontryagin's Maximum Principle. Finally, numerical simulations suggested that the combination of the control strategies is the best way to control the disease in any community.
On necessary optimality conditions in discrete control systems
NASA Astrophysics Data System (ADS)
Mardanov, M. J.; Melikov, T. K.; Mahmudov, N. I.
2015-10-01
The paper deals with a nonlinear discrete-time optimal control problem with a cost functional of terminal type. Using a new variation of the control and new properties of optimal controls, we prove the linearised optimality conditions extending such classical optimality conditions. Along with this, various optimality conditions of quasi-singular controls are obtained. Finally, the examples illustrating the rich content of the obtained results are illustrated.
Model Identification for Optimal Diesel Emissions Control
Stevens, Andrew J.; Sun, Yannan; Song, Xiaobo; Parker, Gordon
2013-06-20
In this paper we develop a model based con- troller for diesel emission reduction using system identification methods. Specifically, our method minimizes the downstream readings from a production NOx sensor while injecting a minimal amount of urea upstream. Based on the linear quadratic estimator we derive the closed form solution to a cost function that accounts for the case some of the system inputs are not controllable. Our cost function can also be tuned to trade-off between input usage and output optimization. Our approach performs better than a production controller in simulation. Our NOx conversion efficiency was 92.7% while the production controller achieved 92.4%. For NH3 conversion, our efficiency was 98.7% compared to 88.5% for the production controller.
Design, optimization, and control of tensegrity structures
NASA Astrophysics Data System (ADS)
Masic, Milenko
The contributions of this dissertation may be divided into four categories. The first category involves developing a systematic form-finding method for general and symmetric tensegrity structures. As an extension of the available results, different shape constraints are incorporated in the problem. Methods for treatment of these constraints are considered and proposed. A systematic formulation of the form-finding problem for symmetric tensegrity structures is introduced, and it uses the symmetry to reduce both the number of equations and the number of variables in the problem. The equilibrium analysis of modular tensegrities exploits their peculiar symmetry. The tensegrity similarity transformation completes the contributions in the area of enabling tools for tensegrity form-finding. The second group of contributions develops the methods for optimal mass-to-stiffness-ratio design of tensegrity structures. This technique represents the state-of-the-art for the static design of tensegrity structures. It is an extension of the results available for the topology optimization of truss structures. Besides guaranteeing that the final design satisfies the tensegrity paradigm, the problem constrains the structure from different modes of failure, which makes it very general. The open-loop control of the shape of modular tensegrities is the third contribution of the dissertation. This analytical result offers a closed form solution for the control of the reconfiguration of modular structures. Applications range from the deployment and stowing of large-scale space structures to the locomotion-inducing control for biologically inspired structures. The control algorithm is applicable regardless of the size of the structures, and it represents a very general result for a large class of tensegrities. Controlled deployments of large-scale tensegrity plates and tensegrity towers are shown as examples that demonstrate the full potential of this reconfiguration strategy. The last
Vibrational computing: simulation of a full adder by optimal control.
Bomble, L; Lauvergnat, D; Remacle, F; Desouter-Lecomte, M
2008-02-14
Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale. PMID:18282031
Adaptive dynamic programming as a theory of sensorimotor control.
Jiang, Yu; Jiang, Zhong-Ping
2014-08-01
Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment.
Adaptive dynamic programming as a theory of sensorimotor control.
Jiang, Yu; Jiang, Zhong-Ping
2014-08-01
Many characteristics of sensorimotor control can be explained by models based on optimization and optimal control theories. However, most of the previous models assume that the central nervous system has access to the precise knowledge of the sensorimotor system and its interacting environment. This viewpoint is difficult to be justified theoretically and has not been convincingly validated by experiments. To address this problem, this paper presents a new computational mechanism for sensorimotor control from a perspective of adaptive dynamic programming (ADP), which shares some features of reinforcement learning. The ADP-based model for sensorimotor control suggests that a command signal for the human movement is derived directly from the real-time sensory data, without the need to identify the system dynamics. An iterative learning scheme based on the proposed ADP theory is developed, along with rigorous convergence analysis. Interestingly, the computational model as advocated here is able to reproduce the motor learning behavior observed in experiments where a divergent force field or velocity-dependent force field was present. In addition, this modeling strategy provides a clear way to perform stability analysis of the overall system. Hence, we conjecture that human sensorimotor systems use an ADP-type mechanism to control movements and to achieve successful adaptation to uncertainties present in the environment. PMID:24962078
Control theory for scanning probe microscopy revisited.
Stirling, Julian
2014-01-01
We derive a theoretical model for studying SPM feedback in the context of control theory. Previous models presented in the literature that apply standard models for proportional-integral-derivative controllers predict a highly unstable feedback environment. This model uses features specific to the SPM implementation of the proportional-integral controller to give realistic feedback behaviour. As such the stability of SPM feedback for a wide range of feedback gains can be understood. Further consideration of mechanical responses of the SPM system gives insight into the causes of exciting mechanical resonances of the scanner during feedback operation.
Control theory for scanning probe microscopy revisited.
Stirling, Julian
2014-01-01
We derive a theoretical model for studying SPM feedback in the context of control theory. Previous models presented in the literature that apply standard models for proportional-integral-derivative controllers predict a highly unstable feedback environment. This model uses features specific to the SPM implementation of the proportional-integral controller to give realistic feedback behaviour. As such the stability of SPM feedback for a wide range of feedback gains can be understood. Further consideration of mechanical responses of the SPM system gives insight into the causes of exciting mechanical resonances of the scanner during feedback operation. PMID:24778957
Control theory for scanning probe microscopy revisited
2014-01-01
Summary We derive a theoretical model for studying SPM feedback in the context of control theory. Previous models presented in the literature that apply standard models for proportional-integral-derivative controllers predict a highly unstable feedback environment. This model uses features specific to the SPM implementation of the proportional-integral controller to give realistic feedback behaviour. As such the stability of SPM feedback for a wide range of feedback gains can be understood. Further consideration of mechanical responses of the SPM system gives insight into the causes of exciting mechanical resonances of the scanner during feedback operation. PMID:24778957
Passive Motion Paradigm: An Alternative to Optimal Control
Mohan, Vishwanathan; Morasso, Pietro
2011-01-01
In the last years, optimal control theory (OCT) has emerged as the leading approach for investigating neural control of movement and motor cognition for two complementary research lines: behavioral neuroscience and humanoid robotics. In both cases, there are general problems that need to be addressed, such as the “degrees of freedom (DoFs) problem,” the common core of production, observation, reasoning, and learning of “actions.” OCT, directly derived from engineering design techniques of control systems quantifies task goals as “cost functions” and uses the sophisticated formal tools of optimal control to obtain desired behavior (and predictions). We propose an alternative “softer” approach passive motion paradigm (PMP) that we believe is closer to the biomechanics and cybernetics of action. The basic idea is that actions (overt as well as covert) are the consequences of an internal simulation process that “animates” the body schema with the attractor dynamics of force fields induced by the goal and task-specific constraints. This internal simulation offers the brain a way to dynamically link motor redundancy with task-oriented constraints “at runtime,” hence solving the “DoFs problem” without explicit kinematic inversion and cost function computation. We argue that the function of such computational machinery is not only restricted to shaping motor output during action execution but also to provide the self with information on the feasibility, consequence, understanding and meaning of “potential actions.” In this sense, taking into account recent developments in neuroscience (motor imagery, simulation theory of covert actions, mirror neuron system) and in embodied robotics, PMP offers a novel framework for understanding motor cognition that goes beyond the engineering control paradigm provided by OCT. Therefore, the paper is at the same time a review of the PMP rationale, as a computational theory, and a perspective presentation of
Approximation of the optimal-time problem for controlled differential inclusions
Otakulov, S.
1995-01-01
One of the common methods for numerical solution of optimal control problems constructs an approximating sequence of discrete control problems. The approximation method is also attractive because it can be used as an effective tool for analyzing optimality conditions and other topics in optimization theory. In this paper, we consider the approximation of optimal-time problems for controlled differential inclusions. The sequence of approximating problems is constructed using a finite-difference scheme, i.e., the differential inclusions are replaced with difference inclusions.
Analytical and experimental performance of optimal controller designs for a supersonic inlet
NASA Technical Reports Server (NTRS)
Zeller, J. R.; Lehtinen, B.; Geyser, L. C.; Batterton, P. G.
1973-01-01
The techniques of modern optimal control theory were applied to the design of a control system for a supersonic inlet. The inlet control problem was approached as a linear stochastic optimal control problem using as the performance index the expected frequency of unstarts. The details of the formulation of the stochastic inlet control problem are presented. The computational procedures required to obtain optimal controller designs are discussed, and the analytically predicted performance of controllers designed for several different inlet conditions is tabulated. The experimental implementation of the optimal control laws is described, and the experimental results obtained in a supersonic wind tunnel are presented. The control laws were implemented with analog and digital computers. Comparisons are made between the experimental and analytically predicted performance results. Comparisons are also made between the results obtained with continuous analog computer controllers and discrete digital computer versions.
Optimal tuning of a control system for a second-order plant with time delay
NASA Astrophysics Data System (ADS)
Golinko, I. M.
2014-07-01
An engineering method for optimizing the parameters of PI and PID controllers for a second-order controlled plant with time delay is considered. An integral quality criterion involving minimization of the control output is proposed for optimizing the control system, which differs from the existing ones in that the effect the control output has on the technological process is taken into account in a correct way. The use of such control makes it possible to minimize the expenditure of material and/or energy resources, to limit the wear, and to increase the service life of the control devices. The unimodal nature of the proposed quality criterion for solving optimal controller tuning problems is numerically confirmed using the optimization theory. A functional correlation between the optimal controller parameters and dynamic properties of a controlled plant is determined for a single-loop control system with the use of calculation methods. The results from simulating the transients in the control system using the proposed and existing functional dependences are compared. The proposed calculation formulas differ from the existing ones by having simple structure, high accuracy of searching for the optimal controller parameters; they allow efficient control to be obtained and can be used for tuning automatic control systems in a wide range of controlled plant dynamic properties. The obtained calculation formulas are recommended for being used by engineers specializing in automation for designing new and optimizing the existing control systems.
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
Hybrid intelligent control concepts for optimal data fusion
NASA Astrophysics Data System (ADS)
Llinas, James
1994-02-01
In the post-Cold War era, Naval surface ship operations will be largely conducted in littoral waters to support regional military missions of all types, including humanitarian and evacuation activities, and amphibious mission execution. Under these conditions, surface ships will be much more isolated and vulnerable to a variety of threats, including maneuvering antiship missiles. To deal with these threats, the optimal employment of multiple shipborne sensors for maximum vigilance is paramount. This paper characterizes the sensor management problem as one of intelligent control, identifies some of the key issues in controller design, and presents one approach to controller design which is soon to be implemented and evaluated. It is argued that the complexity and hierarchical nature of problem formulation demands a hybrid combination of knowledge-based methods and scheduling techniques from 'hard' real-time systems theory for its solution.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
Optimal haptic feedback control of artificial muscles
NASA Astrophysics Data System (ADS)
Chen, Daniel; Besier, Thor; Anderson, Iain; McKay, Thomas
2014-03-01
As our population ages, and trends in obesity continue to grow, joint degenerative diseases like osteoarthritis (OA) are becoming increasingly prevalent. With no cure currently in sight, the only effective treatments for OA are orthopaedic surgery and prolonged rehabilitation, neither of which is guaranteed to succeed. Gait retraining has tremendous potential to alter the contact forces in the joints due to walking, reducing the risk of one developing hip and knee OA. Dielectric Elastomer Actuators (DEAs) are being explored as a potential way of applying intuitive haptic feedback to alter a patient's walking gait. The main challenge with the use of DEAs in this application is producing large enough forces and strains to induce sensation when coupled to a patient's skin. A novel controller has been proposed to solve this issue. The controller uses simultaneous capacitive self-sensing and actuation which will optimally apply a haptic sensation to the patient's skin independent of variability in DEAs and patient geometries.
Hypersonic Vehicle Trajectory Optimization and Control
NASA Technical Reports Server (NTRS)
Balakrishnan, S. N.; Shen, J.; Grohs, J. R.
1997-01-01
Two classes of neural networks have been developed for the study of hypersonic vehicle trajectory optimization and control. The first one is called an 'adaptive critic'. The uniqueness and main features of this approach are that: (1) they need no external training; (2) they allow variability of initial conditions; and (3) they can serve as feedback control. This is used to solve a 'free final time' two-point boundary value problem that maximizes the mass at the rocket burn-out while satisfying the pre-specified burn-out conditions in velocity, flightpath angle, and altitude. The second neural network is a recurrent network. An interesting feature of this network formulation is that when its inputs are the coefficients of the dynamics and control matrices, the network outputs are the Kalman sequences (with a quadratic cost function); the same network is also used for identifying the coefficients of the dynamics and control matrices. Consequently, we can use it to control a system whose parameters are uncertain. Numerical results are presented which illustrate the potential of these methods.
Feedback Implementation of Zermelo's Optimal Control by Sugeno Approximation
NASA Technical Reports Server (NTRS)
Clifton, C.; Homaifax, A.; Bikdash, M.
1997-01-01
This paper proposes an approach to implement optimal control laws of nonlinear systems in real time. Our methodology does not require solving two-point boundary value problems online and may not require it off-line either. The optimal control law is learned using the original Sugeno controller (OSC) from a family of optimal trajectories. We compare the trajectories generated by the OSC and the trajectories yielded by the optimal feedback control law when applied to Zermelo's ship steering problem.
Xu, Hao; Jagannathan, Sarangapani
2015-03-01
The stochastic optimal control of nonlinear networked control systems (NNCSs) using neuro-dynamic programming (NDP) over a finite time horizon is a challenging problem due to terminal constraints, system uncertainties, and unknown network imperfections, such as network-induced delays and packet losses. Since the traditional iteration or time-based infinite horizon NDP schemes are unsuitable for NNCS with terminal constraints, a novel time-based NDP scheme is developed to solve finite horizon optimal control of NNCS by mitigating the above-mentioned challenges. First, an online neural network (NN) identifier is introduced to approximate the control coefficient matrix that is subsequently utilized in conjunction with the critic and actor NNs to determine a time-based stochastic optimal control input over finite horizon in a forward-in-time and online manner. Eventually, Lyapunov theory is used to show that all closed-loop signals and NN weights are uniformly ultimately bounded with ultimate bounds being a function of initial conditions and final time. Moreover, the approximated control input converges close to optimal value within finite time. The simulation results are included to show the effectiveness of the proposed scheme. PMID:25720004
Induction factor optimization through variable lift control
NASA Astrophysics Data System (ADS)
Cooney, John; Corke, Thomas; Nelson, Robert; Williams, Theodore
2011-11-01
Due to practical design limitations coupled with the detrimental effects posed by complex wind regimes, modern wind turbines struggle to maintain or even reach ideal operational states. With additional gains through traditional approaches becoming more difficult and costly, active lift control represents a more attractive option for future designs. Here, plasma actuators have been explored experimentally in trailing edge applications for use in attached flow regimes. This authority would be used to drive the axial induction factor toward the ideal given by the Betz limit through distributed lift control thereby enhancing energy capture. Predictions of power improvement achievable by this methodology are made with blade - element momentum theory but will eventually be demonstrated in the field at the Laboratory for Enhanced Wind Energy Design, currently under construction at the University of Notre Dame.
The predictive power of optimality theory for phonological treatment*
Dinnsen, Daniel A.; Gierut, Judith A.
2009-01-01
The phonology and clinically induced learning patterns of a female child with a phonological delay (age 4;11) were examined from the analytical perspective of Optimality Theory. The analysis revealed that a Consonant Harmony error pattern affected alveolar stops from two different sources—from underlying lexical representations and from representations derived by an interacting error pattern of Deaffrication. The implications of that analysis for the selection of treatment targets were explored in a treatment study. It was found that treatment aimed at the derived source of Consonant Harmony resulted in the suppression of both Consonant Harmony and Deaffrication. The explanation for these results was attributed to a fixed ranking among certain constraints. PMID:20098628
Optimal Control of Distributed Energy Resources using Model Predictive Control
Mayhorn, Ebony T.; Kalsi, Karanjit; Elizondo, Marcelo A.; Zhang, Wei; Lu, Shuai; Samaan, Nader A.; Butler-Purry, Karen
2012-07-22
In an isolated power system (rural microgrid), Distributed Energy Resources (DERs) such as renewable energy resources (wind, solar), energy storage and demand response can be used to complement fossil fueled generators. The uncertainty and variability due to high penetration of wind makes reliable system operations and controls challenging. In this paper, an optimal control strategy is proposed to coordinate energy storage and diesel generators to maximize wind penetration while maintaining system economics and normal operation. The problem is formulated as a multi-objective optimization problem with the goals of minimizing fuel costs and changes in power output of diesel generators, minimizing costs associated with low battery life of energy storage and maintaining system frequency at the nominal operating value. Two control modes are considered for controlling the energy storage to compensate either net load variability or wind variability. Model predictive control (MPC) is used to solve the aforementioned problem and the performance is compared to an open-loop look-ahead dispatch problem. Simulation studies using high and low wind profiles, as well as, different MPC prediction horizons demonstrate the efficacy of the closed-loop MPC in compensating for uncertainties in wind and demand.
Optimal Feedback Controlled Assembly of Perfect Crystals.
Tang, Xun; Rupp, Bradley; Yang, Yuguang; Edwards, Tara D; Grover, Martha A; Bevan, Michael A
2016-07-26
Perfectly ordered states are targets in diverse molecular to microscale systems involving, for example, atomic clusters, protein folding, protein crystallization, nanoparticle superlattices, and colloidal crystals. However, there is no obvious approach to control the assembly of perfectly ordered global free energy minimum structures; near-equilibrium assembly is impractically slow, and faster out-of-equilibrium processes generally terminate in defective states. Here, we demonstrate the rapid and robust assembly of perfect crystals by navigating kinetic bottlenecks using closed-loop control of electric field mediated crystallization of colloidal particles. An optimal policy is computed with dynamic programming using a reaction coordinate based dynamic model. By tracking real-time stochastic particle configurations and adjusting applied fields via feedback, the evolution of unassembled particles is guided through polycrystalline states into single domain crystals. This approach to controlling the assembly of a target structure is based on general principles that make it applicable to a broad range of processes from nano- to microscales (where tuning a global thermodynamic variable yields temporal control over thermal sampling of different states via their relative free energies).
ERIC Educational Resources Information Center
Penningroth, Suzanna L.; Scott, Walter D.
2012-01-01
Two prominent theories of lifespan development, socioemotional selectivity theory and selection, optimization, and compensation theory, make similar predictions for differences in the goal representations of younger and older adults. Our purpose was to test whether the goals of younger and older adults differed in ways predicted by these two…
Optimal control and cold war dynamics between plant and herbivore.
Low, Candace; Ellner, Stephen P; Holden, Matthew H
2013-08-01
Herbivores eat the leaves that a plant needs for photosynthesis. However, the degree of antagonism between plant and herbivore may depend critically on the timing of their interactions and the intrinsic value of a leaf. We present a model that investigates whether and when the timing of plant defense and herbivore feeding activity can be optimized by evolution so that their interactions can move from antagonistic to neutral. We assume that temporal changes in environmental conditions will affect intrinsic leaf value, measured as potential carbon gain. Using optimal-control theory, we model herbivore evolution, first in response to fixed plant strategies and then under coevolutionary dynamics in which the plant also evolves in response to the herbivore. In the latter case, we solve for the evolutionarily stable strategies of plant defense induction and herbivore hatching rate under different ecological conditions. Our results suggest that the optimal strategies for both plant and herbivore are to avoid direct conflict. As long as the plant has the capability for moderately lethal defense, the herbivore will modify its hatching rate to avoid plant defenses, and the plant will never have to use them. Insights from this model offer a possible solution to the paradox of sublethal defenses and provide a mechanism for stable plant-herbivore interactions without the need for natural enemy control.
Optimal control and cold war dynamics between plant and herbivore.
Low, Candace; Ellner, Stephen P; Holden, Matthew H
2013-08-01
Herbivores eat the leaves that a plant needs for photosynthesis. However, the degree of antagonism between plant and herbivore may depend critically on the timing of their interactions and the intrinsic value of a leaf. We present a model that investigates whether and when the timing of plant defense and herbivore feeding activity can be optimized by evolution so that their interactions can move from antagonistic to neutral. We assume that temporal changes in environmental conditions will affect intrinsic leaf value, measured as potential carbon gain. Using optimal-control theory, we model herbivore evolution, first in response to fixed plant strategies and then under coevolutionary dynamics in which the plant also evolves in response to the herbivore. In the latter case, we solve for the evolutionarily stable strategies of plant defense induction and herbivore hatching rate under different ecological conditions. Our results suggest that the optimal strategies for both plant and herbivore are to avoid direct conflict. As long as the plant has the capability for moderately lethal defense, the herbivore will modify its hatching rate to avoid plant defenses, and the plant will never have to use them. Insights from this model offer a possible solution to the paradox of sublethal defenses and provide a mechanism for stable plant-herbivore interactions without the need for natural enemy control. PMID:23852361
Computational methods to obtain time optimal jet engine control
NASA Technical Reports Server (NTRS)
Basso, R. J.; Leake, R. J.
1976-01-01
Dynamic Programming and the Fletcher-Reeves Conjugate Gradient Method are two existing methods which can be applied to solve a general class of unconstrained fixed time, free right end optimal control problems. New techniques are developed to adapt these methods to solve a time optimal control problem with state variable and control constraints. Specifically, they are applied to compute a time optimal control for a jet engine control problem.
Quantum demolition filtering and optimal control of unstable systems.
Belavkin, V P
2012-11-28
A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one. PMID:23091216
Towards Quantum Cybernetics:. Optimal Feedback Control in Quantum Bio Informatics
NASA Astrophysics Data System (ADS)
Belavkin, V. P.
2009-02-01
A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.
Modelling Optimal Control of Cholera in Communities Linked by Migration.
Njagarah, J B H; Nyabadza, F
2015-01-01
A mathematical model for the dynamics of cholera transmission with permissible controls between two connected communities is developed and analysed. The dynamics of the disease in the adjacent communities are assumed to be similar, with the main differences only reflected in the transmission and disease related parameters. This assumption is based on the fact that adjacent communities often have different living conditions and movement is inclined toward the community with better living conditions. Community specific reproduction numbers are given assuming movement of those susceptible, infected, and recovered, between communities. We carry out sensitivity analysis of the model parameters using the Latin Hypercube Sampling scheme to ascertain the degree of effect the parameters and controls have on progression of the infection. Using principles from optimal control theory, a temporal relationship between the distribution of controls and severity of the infection is ascertained. Our results indicate that implementation of controls such as proper hygiene, sanitation, and vaccination across both affected communities is likely to annihilate the infection within half the time it would take through self-limitation. In addition, although an infection may still break out in the presence of controls, it may be up to 8 times less devastating when compared with the case when no controls are in place. PMID:26246850
Application of queuing theory in production-inventory optimization
NASA Astrophysics Data System (ADS)
Rashid, Reza; Hoseini, Seyed Farzad; Gholamian, M. R.; Feizabadi, Mohammad
2015-07-01
This paper presents a mathematical model for an inventory control system in which customers' demands and suppliers' service time are considered as stochastic parameters. The proposed problem is solved through queuing theory for a single item. In this case, transitional probabilities are calculated in steady state. Afterward, the model is extended to the case of multi-item inventory systems. Then, to deal with the complexity of this problem, a new heuristic algorithm is developed. Finally, the presented bi-level inventory-queuing model is implemented as a case study in Electroestil Company.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
Kmet', Tibor; Kmet'ova, Maria
2009-09-09
A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Di Donato, Daniela; Mugnai, Dimitri
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
A new linear quadratic optimal controller for the 34-meter high efficiency antenna position loop
NASA Technical Reports Server (NTRS)
Nickerson, J. A.
1987-01-01
The design of a new position loop controller for the 34-meter High Efficiency Deep Space antennas using linear quadratic (LQ) optimal control techniques is discussed. The LQ optimal control theory is reviewed, and model development and verification are discussed. Families of optimal gain vectors are generated by varying weight parameters. Performance specifications were used to select a final gain vector. Estimator dynamics were selected and the corresponding gain vectors were computed. Final estimator selection was based on position, commanded rate, and estimator error responses.
Skinner Rusk unified formalism for optimal control systems and applications
NASA Astrophysics Data System (ADS)
Barbero-Liñán, María; Echeverría-Enríquez, Arturo; Martín de Diego, David; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
2007-10-01
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal control systems allows us to formulate geometrically the necessary conditions given by a weak form of Pontryagin's maximum principle, provided that the differentiability with respect to controls is assumed and the space of controls is open. Furthermore, our method is also valid for implicit optimal control systems and, in particular, for the so-called descriptor systems (optimal control problems including both differential and algebraic equations).
Heterogeneous Nuclear Reactor Models for Optimal Xenon Control.
NASA Astrophysics Data System (ADS)
Gondal, Ishtiaq Ahmad
Nuclear reactors are generally modeled as homogeneous mixtures of fuel, control, and other materials while in reality they are heterogeneous-homogeneous configurations comprised of fuel and control rods along with other materials. Similarly, for space-time studies of a nuclear reactor, homogeneous, usually one-group diffusion theory, models are used, and the system equations are solved by either nodal or modal expansion approximations. Study of xenon-induced problems has also been carried out using similar models and with the help of dynamic programming or classical calculus of variations or the minimum principle. In this study a thermal nuclear reactor is modeled as a two-dimensional lattice of fuel and control rods placed in an infinite-moderator in plane geometry. The two-group diffusion theory approximation is used for neutron transport. Space -time neutron balance equations are written for two groups and reduced to one space-time algebraic equation by using the two-dimensional Fourier transform. This equation is written at all fuel and control rod locations. Iodine -xenon and promethium-samarium dynamic equations are also written at fuel rod locations only. These equations are then linearized about an equilibrium point which is determined from the steady-state form of the original nonlinear system equations. After studying poisonless criticality, with and without control, and the stability of the open-loop system and after checking its controllability, a performance criterion is defined for the xenon-induced spatial flux oscillation problem in the form of a functional to be minimized. Linear -quadratic optimal control theory is then applied to solve the problem. To perform a variety of different additional useful studies, this formulation has potential for various extensions and variations; for example, different geometry of the problem, with possible extension to three dimensions, heterogeneous -homogeneous formulation to include, for example, homogeneously
NASA Astrophysics Data System (ADS)
Yushkevich, A. A.; Chitashvili, R. Ya
1982-12-01
CONTENTSIntroduction Chapter I. Foundations of the general theory of controlled random sequences and Markov chains with the expected reward criterion § 1. Controlled random sequences, Markov chains, and models § 2. Necessary and sufficient conditions for optimality § 3. The Bellman equation for the value function and the existence of (ε-) optimal strategies Chapter II. Some problems in the theory of controlled homogeneous Markov chains § 4. Description of the solutions of the Bellman equation, a characterization of the value function, and the Bellman operator § 5. Sufficiency of stationary strategies in homogeneous Markov models § 6. The lexicographic Bellman equation References
Optimal control of a supersonic inlet to minimize frequency of inlet unstart
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Zeller, J. R.; Geyser, L. C.
1978-01-01
A preliminary investigation into the use of modern control theory for the design of controls for a supersonic inlet is described. In particular, the task of controlling a mixed-compression supersonic inlet is formulated as a linear optimal stochastic control and estimation problem. An inlet can exhibit an undesirable instability due to excessive inlet normal shock motion. For the optimal control formulation of the inlet problem, a non quadratic performance index, which is equal to the expected frequency of inlet unstarts, is used. This physically meaningful performance index is minimized for a range of inlet disturbance and measurement noise covariances.
Optimally controlling the human connectome: the role of network topology
Betzel, Richard F.; Gu, Shi; Medaglia, John D.; Pasqualetti, Fabio; Bassett, Danielle S.
2016-01-01
To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain’s network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions’ weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input to another region is suppressed. Finally, we identify optimal states in which the brain should start (and finish) in order to minimize transition energy. We show that the optimal target states display high activity in hub regions, implicating the brain’s rich club. Furthermore, when rich club organization is destroyed, the energy cost associated with state transitions increases significantly, demonstrating that it is the richness of brain regions that makes them ideal targets. PMID:27468904
Optimally controlling the human connectome: the role of network topology.
Betzel, Richard F; Gu, Shi; Medaglia, John D; Pasqualetti, Fabio; Bassett, Danielle S
2016-01-01
To meet ongoing cognitive demands, the human brain must seamlessly transition from one brain state to another, in the process drawing on different cognitive systems. How does the brain's network of anatomical connections help facilitate such transitions? Which features of this network contribute to making one transition easy and another transition difficult? Here, we address these questions using network control theory. We calculate the optimal input signals to drive the brain to and from states dominated by different cognitive systems. The input signals allow us to assess the contributions made by different brain regions. We show that such contributions, which we measure as energy, are correlated with regions' weighted degrees. We also show that the network communicability, a measure of direct and indirect connectedness between brain regions, predicts the extent to which brain regions compensate when input to another region is suppressed. Finally, we identify optimal states in which the brain should start (and finish) in order to minimize transition energy. We show that the optimal target states display high activity in hub regions, implicating the brain's rich club. Furthermore, when rich club organization is destroyed, the energy cost associated with state transitions increases significantly, demonstrating that it is the richness of brain regions that makes them ideal targets. PMID:27468904
Gradient Optimization for Analytic conTrols - GOAT
NASA Astrophysics Data System (ADS)
Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank
Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.
The role of modern control theory in the design of controls for aircraft turbine engines
NASA Technical Reports Server (NTRS)
Zeller, J.; Lehtinen, B.; Merrill, W.
1982-01-01
The development, applications, and current research in modern control theory (MCT) are reviewed, noting the importance for fuel-efficient operation of turbines with variable inlet guide vanes, compressor stators, and exhaust nozzle area. The evolution of multivariable propulsion control design is examined, noting a basis in a matrix formulation of the differential equations defining the process, leading to state space formulations. Reports and papers which appeared from 1970-1982 which dealt with problems in MCT applications to turbine engine control design are outlined, including works on linear quadratic regulator methods, frequency domain methods, identification, estimation, and model reduction, detection, isolation, and accommodation, and state space control, adaptive control, and optimization approaches. Finally, NASA programs in frequency domain design, sensor failure detection, computer-aided control design, and plant modeling are explored
Decentralized optimal control of dynamical systems under uncertainty
NASA Astrophysics Data System (ADS)
Gabasov, R.; Dmitruk, N. M.; Kirillova, F. M.
2011-07-01
The problem of optimal control of a group of interconnected dynamical objects under uncertainty is considered. The cases are examined in which the centralized control of the group of objects is impossible due to delay in the channel for information exchange between the group members. Optimal self-control algorithms in real time for each dynamical object are proposed. Various types of a priori and current information about the behavior of the group members and about uncertainties in the system are examined. The proposed methods supplement the earlier developed optimal control methods for an individual dynamical system and the methods of decentralized optimal control of deterministic objects. The results are illustrated with examples.
A Multiobjective Optimization Framework for Stochastic Control of Complex Systems
Malikopoulos, Andreas; Maroulas, Vasileios; Xiong, Professor Jie
2015-01-01
This paper addresses the problem of minimizing the long-run expected average cost of a complex system consisting of subsystems that interact with each other and the environment. We treat the stochastic control problem as a multiobjective optimization problem of the one-stage expected costs of the subsystems, and we show that the control policy yielding the Pareto optimal solution is an optimal control policy that minimizes the average cost criterion for the entire system. For practical situations with constraints consistent to those we study here, our results imply that the Pareto control policy may be of value in deriving online an optimal control policy in complex systems.
A Transformation Approach to Optimal Control Problems with Bounded State Variables
NASA Technical Reports Server (NTRS)
Hanafy, Lawrence Hanafy
1971-01-01
A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.
NASA Astrophysics Data System (ADS)
Kim, Yoonsoo
This dissertation focuses on cooperative control between multiple agents (e.g., spacecraft, UAVs). In particular, motivated by future NASA's multiple spacecraft missions, we have been guided to consider fundamental aspects of spacecraft formation flying, including collision avoidance issues; constraints on the relative position and attitude. In this venue, we have realized that one of the main challenges is dealing with nonconvex state constraints. In this dissertation, we will address such complications using classical control theory, heuristic techniques, and more recent semidefinite programming-based approaches. We then proceed to consider communication and interspacecraft sensing issues in multiple agent dynamic system setting. In this direction, we will study (1) how conventional control techniques should be augmented to meet our design objectives when the information flow between multiple agents is taken into account; (2) which information structures (e.g., information graphs) yield best performance guarantees in terms of stability, robustness, or fast agreement. In this work, we provide theoretical answers to these problems. Moreover, as many design problems involving information networks and graphs lead to combinatorial problems, which can be formulated as rank optimization problems over matrices, we consider these class of problems in this dissertation. Rank optimization problems also arise in system theory and are considered to be of paramount importance in modern control synthesis problems.
ERIC Educational Resources Information Center
Thrasher, James F.; Campbell, Marci Kramish; Oates, Veronica
2004-01-01
This study used data from 850 African Americans to test optimal matching theory (OMT). OMT predicts that (1) the most important dimensions of social support depend on the controllability of the behavior and (2) different network members often provide support across health behaviors. Data were gathered on social support source for physical…
Optimality Conditions for Semilinear Hyperbolic Equations with Controls in Coefficients
Li Bo; Lou Hongwei
2012-06-15
An optimal control problem for semilinear hyperbolic partial differential equations is considered. The control variable appears in coefficients. Necessary conditions for optimal controls are established by method of two-scale convergence and homogenized spike variation. Results for problems with state constraints are also stated.
Optimal stochastic control in natural resource management: Framework and examples
Williams, B.K.
1982-01-01
A framework is presented for the application of optimal control methods to natural resource problems. An expression of the optimal control problem appropriate for renewable natural resources is given and its application to Markovian systems is presented in some detail. Three general approaches are outlined for determining optimal control of infinite time horizon systems and three examples from the natural resource literature are used for illustration.
Optimality of incompletely measurable active and passive attitude control systems. [for satellites
NASA Technical Reports Server (NTRS)
Schiehlen, W.; Popp, K.
1973-01-01
Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.
Optimal control of nonlinear continuous-time systems in strict-feedback form.
Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani
2015-10-01
This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results. PMID:26111400
Optimal and robust control of invasive alien species spreading in homogeneous landscapes
Carrasco, L. R.; Baker, R.; MacLeod, A.; Knight, J. D.; Mumford, J. D.
2010-01-01
Government agencies lack robust modelling tools to manage the spread of invasive alien species (IAS). In this paper, we combine optimal control and simulation methods with biological invasion spread theory to estimate the type of optimal policy and switching point of control efforts against a spreading IAS. We employ information-gap (info-gap) theory to assess how the optimal solutions differ from a policy that is most robustly immune to unacceptable outcomes. The model is applied to the potential invasion of the Colorado potato beetle in the UK. Under no uncertainty, we demonstrate that for many of the parameter combinations the optimal control policy corresponds to slowing down the invasion. The info-gap analysis shows that eradication policies identified as optimal under no uncertainty are robustly the best policies even under severe uncertainty, i.e. even if they are likely to turn into slowing down policies. We also show that the control of satellite colonies, if identified as optimal under no uncertainty, will also be a robust slowing down policy for IAS that can spread by long distance dispersal even for relatively ineffective control measures. The results suggest that agencies adopt management strategies that are robustly optimal, despite the severe uncertainties they face. PMID:19740923
NASA Astrophysics Data System (ADS)
Briceño-Arias, Luis M.; Hoang, Nguyen Dinh; Peypouquet, Juan
2016-01-01
We study optimal control problems governed by maximal monotone differential inclusions with mixed control-state constraints in infinite dimensional spaces. We obtain some existence results for this kind of dynamics and construct the discrete approximations that allows us to strongly approximate optimal solutions of the continuous-type optimal control problems by their discrete counterparts. Our approach allows us to apply our results for a wide class of mappings that are applicable in mechanics and material sciences.
Optimal Control for a Parallel Hybrid Hydraulic Excavator Using Particle Swarm Optimization
Wang, Dong-yun; Guan, Chen
2013-01-01
Optimal control using particle swarm optimization (PSO) is put forward in a parallel hybrid hydraulic excavator (PHHE). A power-train mathematical model of PHHE is illustrated along with the analysis of components' parameters. Then, the optimal control problem is addressed, and PSO algorithm is introduced to deal with this nonlinear optimal problem which contains lots of inequality/equality constraints. Then, the comparisons between the optimal control and rule-based one are made, and the results show that hybrids with the optimal control would increase fuel economy. Although PSO algorithm is off-line optimization, still it would bring performance benchmark for PHHE and also help have a deep insight into hybrid excavators. PMID:23818832
Optimizing the controllability of arbitrary networks with genetic algorithm
NASA Astrophysics Data System (ADS)
Li, Xin-Feng; Lu, Zhe-Ming
2016-04-01
Recently, as the controllability of complex networks attracts much attention, how to optimize networks' controllability has become a common and urgent problem. In this paper, we develop an efficient genetic algorithm oriented optimization tool to optimize the controllability of arbitrary networks consisting of both state nodes and control nodes under Popov-Belevitch-Hautus rank condition. The experimental results on a number of benchmark networks show the effectiveness of this method and the evolution of network topology is captured. Furthermore, we explore how network structure affects its controllability and find that the sparser a network is, the more control nodes are needed to control it and the larger the differences between node degrees, the more control nodes are needed to achieve the full control. Our framework provides an alternative to controllability optimization and can be applied to arbitrary networks without any limitations.
Testing optimal foraging theory in a penguin–krill system
Watanabe, Yuuki Y.; Ito, Motohiro; Takahashi, Akinori
2014-01-01
Food is heterogeneously distributed in nature, and understanding how animals search for and exploit food patches is a fundamental challenge in ecology. The classic marginal value theorem (MVT) formulates optimal patch residence time in response to patch quality. The MVT was generally proved in controlled animal experiments; however, owing to the technical difficulties in recording foraging behaviour in the wild, it has been inadequately examined in natural predator–prey systems, especially those in the three-dimensional marine environment. Using animal-borne accelerometers and video cameras, we collected a rare dataset in which the behaviour of a marine predator (penguin) was recorded simultaneously with the capture timings of mobile, patchily distributed prey (krill). We provide qualitative support for the MVT by showing that (i) krill capture rate diminished with time in each dive, as assumed in the MVT, and (ii) dive duration (or patch residence time, controlled for dive depth) increased with short-term, dive-scale krill capture rate, but decreased with long-term, bout-scale krill capture rate, as predicted from the MVT. Our results demonstrate that a single environmental factor (i.e. patch quality) can have opposite effects on animal behaviour depending on the time scale, emphasizing the importance of multi-scale approaches in understanding complex foraging strategies. PMID:24478293
Testing optimal foraging theory in a penguin-krill system.
Watanabe, Yuuki Y; Ito, Motohiro; Takahashi, Akinori
2014-03-22
Food is heterogeneously distributed in nature, and understanding how animals search for and exploit food patches is a fundamental challenge in ecology. The classic marginal value theorem (MVT) formulates optimal patch residence time in response to patch quality. The MVT was generally proved in controlled animal experiments; however, owing to the technical difficulties in recording foraging behaviour in the wild, it has been inadequately examined in natural predator-prey systems, especially those in the three-dimensional marine environment. Using animal-borne accelerometers and video cameras, we collected a rare dataset in which the behaviour of a marine predator (penguin) was recorded simultaneously with the capture timings of mobile, patchily distributed prey (krill). We provide qualitative support for the MVT by showing that (i) krill capture rate diminished with time in each dive, as assumed in the MVT, and (ii) dive duration (or patch residence time, controlled for dive depth) increased with short-term, dive-scale krill capture rate, but decreased with long-term, bout-scale krill capture rate, as predicted from the MVT. Our results demonstrate that a single environmental factor (i.e. patch quality) can have opposite effects on animal behaviour depending on the time scale, emphasizing the importance of multi-scale approaches in understanding complex foraging strategies.
Application of control theory to dynamic systems simulation
NASA Technical Reports Server (NTRS)
Auslander, D. M.; Spear, R. C.; Young, G. E.
1982-01-01
The application of control theory is applied to dynamic systems simulation. Theory and methodology applicable to controlled ecological life support systems are considered. Spatial effects on system stability, design of control systems with uncertain parameters, and an interactive computing language (PARASOL-II) designed for dynamic system simulation, report quality graphics, data acquisition, and simple real time control are discussed.
Factorization and reduction methods for optimal control of distributed parameter systems
NASA Technical Reports Server (NTRS)
Burns, J. A.; Powers, R. K.
1985-01-01
A Chandrasekhar-type factorization method is applied to the linear-quadratic optimal control problem for distributed parameter systems. An aeroelastic control problem is used as a model example to demonstrate that if computationally efficient algorithms, such as those of Chandrasekhar-type, are combined with the special structure often available to a particular problem, then an abstract approximation theory developed for distributed parameter control theory becomes a viable method of solution. A numerical scheme based on averaging approximations is applied to hereditary control problems. Numerical examples are given.
NASA Astrophysics Data System (ADS)
Viola, Lorenza; Tannor, David
2011-08-01
, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment, with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory-experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open
A multiple objective optimization approach to aircraft control systems design
NASA Technical Reports Server (NTRS)
Tabak, D.; Schy, A. A.; Johnson, K. G.; Giesy, D. P.
1979-01-01
The design of an aircraft lateral control system, subject to several performance criteria and constraints, is considered. While in the previous studies of the same model a single criterion optimization, with other performance requirements expressed as constraints, has been pursued, the current approach involves a multiple criteria optimization. In particular, a Pareto optimal solution is sought.
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
NASA Technical Reports Server (NTRS)
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
Searching for quantum optimal controls under severe constraints
NASA Astrophysics Data System (ADS)
Riviello, Gregory; Tibbetts, Katharine Moore; Brif, Constantin; Long, Ruixing; Wu, Re-Bing; Ho, Tak-San; Rabitz, Herschel
2015-04-01
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitates successful optimization.
Optimizing Computer Assisted Instruction By Applying Principles of Learning Theory.
ERIC Educational Resources Information Center
Edwards, Thomas O.
The development of learning theory and its application to computer-assisted instruction (CAI) are described. Among the early theoretical constructs thought to be important are E. L. Thorndike's concept of learning connectisms, Neal Miller's theory of motivation, and B. F. Skinner's theory of operant conditioning. Early devices incorporating those…
Optimizing Sensor and Actuator Arrays for ASAC Noise Control
NASA Technical Reports Server (NTRS)
Palumbo, Dan; Cabell, Ran
2000-01-01
This paper summarizes the development of an approach to optimizing the locations for arrays of sensors and actuators in active noise control systems. A type of directed combinatorial search, called Tabu Search, is used to select an optimal configuration from a much larger set of candidate locations. The benefit of using an optimized set is demonstrated. The importance of limiting actuator forces to realistic levels when evaluating the cost function is discussed. Results of flight testing an optimized system are presented. Although the technique has been applied primarily to Active Structural Acoustic Control systems, it can be adapted for use in other active noise control implementations.
Stochastic Optimal Control for Series Hybrid Electric Vehicles
Malikopoulos, Andreas
2013-01-01
Increasing demand for improving fuel economy and reducing emissions has stimulated significant research and investment in hybrid propulsion systems. In this paper, we address the problem of optimizing online the supervisory control in a series hybrid configuration by modeling its operation as a controlled Markov chain using the average cost criterion. We treat the stochastic optimal control problem as a dual constrained optimization problem. We show that the control policy that yields higher probability distribution to the states with low cost and lower probability distribution to the states with high cost is an optimal control policy, defined as an equilibrium control policy. We demonstrate the effectiveness of the efficiency of the proposed controller in a series hybrid configuration and compare it with a thermostat-type controller.
A Framework for Optimal Control Allocation with Structural Load Constraints
NASA Technical Reports Server (NTRS)
Frost, Susan A.; Taylor, Brian R.; Jutte, Christine V.; Burken, John J.; Trinh, Khanh V.; Bodson, Marc
2010-01-01
Conventional aircraft generally employ mixing algorithms or lookup tables to determine control surface deflections needed to achieve moments commanded by the flight control system. Control allocation is the problem of converting desired moments into control effector commands. Next generation aircraft may have many multipurpose, redundant control surfaces, adding considerable complexity to the control allocation problem. These issues can be addressed with optimal control allocation. Most optimal control allocation algorithms have control surface position and rate constraints. However, these constraints are insufficient to ensure that the aircraft's structural load limits will not be exceeded by commanded surface deflections. In this paper, a framework is proposed to enable a flight control system with optimal control allocation to incorporate real-time structural load feedback and structural load constraints. A proof of concept simulation that demonstrates the framework in a simulation of a generic transport aircraft is presented.
Control theory based airfoil design for potential flow and a finite volume discretization
NASA Technical Reports Server (NTRS)
Reuther, J.; Jameson, A.
1994-01-01
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.
Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.
Patri, Jean-François; Diard, Julien; Perrier, Pascal
2015-12-01
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way. PMID:26497359
Optimal speech motor control and token-to-token variability: a Bayesian modeling approach.
Patri, Jean-François; Diard, Julien; Perrier, Pascal
2015-12-01
The remarkable capacity of the speech motor system to adapt to various speech conditions is due to an excess of degrees of freedom, which enables producing similar acoustical properties with different sets of control strategies. To explain how the central nervous system selects one of the possible strategies, a common approach, in line with optimal motor control theories, is to model speech motor planning as the solution of an optimality problem based on cost functions. Despite the success of this approach, one of its drawbacks is the intrinsic contradiction between the concept of optimality and the observed experimental intra-speaker token-to-token variability. The present paper proposes an alternative approach by formulating feedforward optimal control in a probabilistic Bayesian modeling framework. This is illustrated by controlling a biomechanical model of the vocal tract for speech production and by comparing it with an existing optimal control model (GEPPETO). The essential elements of this optimal control model are presented first. From them the Bayesian model is constructed in a progressive way. Performance of the Bayesian model is evaluated based on computer simulations and compared to the optimal control model. This approach is shown to be appropriate for solving the speech planning problem while accounting for variability in a principled way.
A criterion for joint optimization of identification and robust control
NASA Technical Reports Server (NTRS)
Bayard, D. S.; Yam, Y.; Mettler, E.
1992-01-01
A criterion for system identification is developed that is consistent with the intended used of the fitted model for modern robust control synthesis. Specifically, a joint optimization problem is posed which simultaneously solves the plant model estimate and control design, so as to optimize robust performance over the set of plants consistent with a specified experimental data set.
Educational Tool for Optimal Controller Tuning Using Evolutionary Strategies
ERIC Educational Resources Information Center
Carmona Morales, D.; Jimenez-Hornero, J. E.; Vazquez, F.; Morilla, F.
2012-01-01
In this paper, an optimal tuning tool is presented for control structures based on multivariable proportional-integral-derivative (PID) control, using genetic algorithms as an alternative to traditional optimization algorithms. From an educational point of view, this tool provides students with the necessary means to consolidate their knowledge on…
Attitude Control Optimization for ROCSAT-2 Operation
NASA Astrophysics Data System (ADS)
Chern, Jeng-Shing; Wu, A.-M.
one revolution. The purpose of this paper is to present the attitude control design optimization such that the maximum solar energy is ingested while minimum maneuvering energy is dissipated. The strategy includes the maneuvering sequence design, the minimization of angular path, the sizing of three magnetic torquers, and the trade-off of the size, number and orientations arrangement of momentum wheels.
Application of modern control theory to the design of optimum aircraft controllers
NASA Technical Reports Server (NTRS)
Power, L. J.
1973-01-01
The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.
Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers
NASA Technical Reports Server (NTRS)
Goodson, Troy D.; Chuang, Jason C. H.; Ledsinger, Laura A.
1996-01-01
This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.
In-flight performance optimization for rotorcraft with redundant controls
NASA Astrophysics Data System (ADS)
Ozdemir, Gurbuz Taha
A conventional helicopter has limits on performance at high speeds because of the limitations of main rotor, such as compressibility issues on advancing side or stall issues on retreating side. Auxiliary lift and thrust components have been suggested to improve performance of the helicopter substantially by reducing the loading on the main rotor. Such a configuration is called the compound rotorcraft. Rotor speed can also be varied to improve helicopter performance. In addition to improved performance, compound rotorcraft and variable RPM can provide a much larger degree of control redundancy. This additional redundancy gives the opportunity to further enhance performance and handling qualities. A flight control system is designed to perform in-flight optimization of redundant control effectors on a compound rotorcraft in order to minimize power required and extend range. This "Fly to Optimal" (FTO) control law is tested in simulation using the GENHEL model. A model of the UH-60, a compound version of the UH-60A with lifting wing and vectored thrust ducted propeller (VTDP), and a generic compound version of the UH-60A with lifting wing and propeller were developed and tested in simulation. A model following dynamic inversion controller is implemented for inner loop control of roll, pitch, yaw, heave, and rotor RPM. An outer loop controller regulates airspeed and flight path during optimization. A Golden Section search method was used to find optimal rotor RPM on a conventional helicopter, where the single redundant control effector is rotor RPM. The FTO builds off of the Adaptive Performance Optimization (APO) method of Gilyard by performing low frequency sweeps on a redundant control for a fixed wing aircraft. A method based on the APO method was used to optimize trim on a compound rotorcraft with several redundant control effectors. The controller can be used to optimize rotor RPM and compound control effectors through flight test or simulations in order to
Optimization and Control of Electric Power Systems
Lesieutre, Bernard C.; Molzahn, Daniel K.
2014-10-17
The analysis and optimization needs for planning and operation of the electric power system are challenging due to the scale and the form of model representations. The connected network spans the continent and the mathematical models are inherently nonlinear. Traditionally, computational limits have necessitated the use of very simplified models for grid analysis, and this has resulted in either less secure operation, or less efficient operation, or both. The research conducted in this project advances techniques for power system optimization problems that will enhance reliable and efficient operation. The results of this work appear in numerous publications and address different application problems include optimal power flow (OPF), unit commitment, demand response, reliability margins, planning, transmission expansion, as well as general tools and algorithms.
Matching trajectory optimization and nonlinear tracking control for HALE
NASA Astrophysics Data System (ADS)
Lee, Sangjong; Jang, Jieun; Ryu, Hyeok; Lee, Kyun Ho
2014-11-01
This paper concerns optimal trajectory generation and nonlinear tracking control for stratospheric airship platform of VIA-200. To compensate for the mismatch between the point-mass model of optimal trajectory and the 6-DOF model of the nonlinear tracking problem, a new matching trajectory optimization approach is proposed. The proposed idea reduces the dissimilarity of both problems and reduces the uncertainties in the nonlinear equations of motion for stratospheric airship. In addition, its refined optimal trajectories yield better results under jet stream conditions during flight. The resultant optimal trajectories of VIA-200 are full three-dimensional ascent flight trajectories reflecting the realistic constraints of flight conditions and airship performance with and without a jet stream. Finally, 6-DOF nonlinear equations of motion are derived, including a moving wind field, and the vectorial backstepping approach is applied. The desirable tracking performance is demonstrated that application of the proposed matching optimization method enables the smooth linkage of trajectory optimization to tracking control problems.
NASA Technical Reports Server (NTRS)
Bernstein, Dennis S.; Rosen, I. Gary
1988-01-01
The finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory is investigated analytically. The approach yields fixed-finite-order controllers which are optimal with respect to high-order approximating finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for a one-dimensional SISO parabolic (heat/diffusion) system using a spline-based Ritz-Galerkin finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2-percent performance degradation over full-order LQG controllers.
Edge orientation for optimizing controllability of complex networks
NASA Astrophysics Data System (ADS)
Xiao, Yan-Dong; Lao, Song-Yang; Hou, Lv-Lin; Bai, Liang
2014-10-01
Recently, as the controllability of complex networks attracts much attention, how to design and optimize the controllability of networks has become a common and urgent problem in the field of controlling complex networks. Previous work focused on the structural perturbation and neglected the role of edge direction to optimize the network controllability. In a recent work [Phys. Rev. Lett. 103, 228702 (2009), 10.1103/PhysRevLett.103.228702], the authors proposed a simple method to enhance the synchronizability of networks by assignment of link direction while keeping network topology unchanged. However, the controllability is fundamentally different from synchronization. In this work, we systematically propose the definition of assigning direction to optimize controllability, which is called the edge orientation for optimal controllability problem (EOOC). To solve the EOOC problem, we construct a switching network and transfer the EOOC problem to find the maximum independent set of the switching network. We prove that the principle of our optimization method meets the sense of unambiguity and optimum simultaneously. Furthermore, the relationship between the degree-degree correlations and EOOC are investigated by experiments. The results show that the disassortativity pattern could weaken the orientation for optimal controllability, while the assortativity pattern has no correlation with EOOC. All the experimental results of this work verify that the network structure determines the network controllability and the optimization effects.
Edge orientation for optimizing controllability of complex networks.
Xiao, Yan-Dong; Lao, Song-Yang; Hou, Lv-Lin; Bai, Liang
2014-10-01
Recently, as the controllability of complex networks attracts much attention, how to design and optimize the controllability of networks has become a common and urgent problem in the field of controlling complex networks. Previous work focused on the structural perturbation and neglected the role of edge direction to optimize the network controllability. In a recent work [Phys. Rev. Lett. 103, 228702 (2009)], the authors proposed a simple method to enhance the synchronizability of networks by assignment of link direction while keeping network topology unchanged. However, the controllability is fundamentally different from synchronization. In this work, we systematically propose the definition of assigning direction to optimize controllability, which is called the edge orientation for optimal controllability problem (EOOC). To solve the EOOC problem, we construct a switching network and transfer the EOOC problem to find the maximum independent set of the switching network. We prove that the principle of our optimization method meets the sense of unambiguity and optimum simultaneously. Furthermore, the relationship between the degree-degree correlations and EOOC are investigated by experiments. The results show that the disassortativity pattern could weaken the orientation for optimal controllability, while the assortativity pattern has no correlation with EOOC. All the experimental results of this work verify that the network structure determines the network controllability and the optimization effects. PMID:25375546
Information spread in networks: Games, optimal control, and stabilization
NASA Astrophysics Data System (ADS)
Khanafer, Ali
This thesis focuses on designing efficient mechanisms for controlling information spread in networks. We consider two models for information spread. The first one is the well-known distributed averaging dynamics. The second model is a nonlinear one that describes virus spread in computer and biological networks. We seek to design optimal, robust, and stabilizing controllers under practical constraints. For distributed averaging networks, we study the interaction between a network designer and an adversary. We consider two types of attacks on the network. In Attack-I, the adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's Maximum Principle (MP) seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Further, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for the underlying zero-sum game. In Attack-II, the designer and the adversary are both capable of altering the measurements of all nodes in the network by injecting global signals. We impose two constraints on both players: a power constraint and an energy constraint. We assume that the available energy to each player is not sufficient to operate at maximum power throughout the horizon of the game. We show the existence of an SPE and derive the optimal strategies in closed form for this attack scenario. As an alternative to the "network designer vs. adversary" framework, we investigate the possibility of stabilizing unknown network diffusion processes using a distributed mechanism, where the uncertainty is due to an attack
Alternative Solutions for Optimization Problems in Generalizability Theory.
ERIC Educational Resources Information Center
Sanders, Piet F.
1992-01-01
Presents solutions for the problem of maximizing the generalizability coefficient under a budget constraint. Shows that the Cauchy-Schwarz inequality can be applied to derive optimal continuous solutions for the number of conditions of each facet. Illustrates the formal similarity between optimization problems in survey sampling and…
Exact optimal solution for a class of dual control problems
NASA Astrophysics Data System (ADS)
Cao, Suping; Qian, Fucai; Wang, Xiaomei
2016-07-01
This paper considers a discrete-time stochastic optimal control problem for which only measurement equation is partially observed with unknown constant parameters taking value in a finite set of stochastic systems. Because of the fact that the cost-to-go function at each stage contains variance and the non-separability of the variance is so complicated that the dynamic programming cannot be successfully applied, the optimal solution has not been found. In this paper, a new approach to the optimal solution is proposed by embedding the original non-separable problem into a separable auxiliary problem. The theoretical condition on which the optimal solution of the original problem can be attained from a set of solutions of the auxiliary problem is established. In addition, the optimality of the interchanging algorithm is proved and the analytical solution of the optimal control is also obtained. The performance of this controller is illustrated with a simple example.
A mathematical basis for the design and design optimization of adaptive trusses in precision control
NASA Technical Reports Server (NTRS)
Das, S. K.; Utku, S.; Chen, G.-S.; Wada, B. K.
1991-01-01
A mathematical basis for the optimal design of adaptive trusses to be used in supporting precision equipment is provided. The general theory of adaptive structures is introduced, and the global optimization problem of placing a limited number, q, of actuators, so as to maximally achieve precision control and provide prestress, is stated. Two serialized optimization problems, namely, optimal actuator placement for prestress and optimal actuator placement for precision control, are addressed. In the case of prestressing, the computation of a 'desired' prestress is discussed, the interaction between actuators and redundants in conveying the prestress is shown in its mathematical form, and a methodology for arriving at the optimal placement of actuators and additional redundants is discussed. With regard to precision control, an optimal placement scheme (for q actuators) for maximum 'authority' over the precision points is suggested. The results of the two serialized optimization problems are combined to give a suboptimal solution to the global optimization problem. A method for improving this suboptimal actuator placement scheme by iteration is presented.
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Anderson, D.R.
1975-01-01
Optimal exploitation strategies were studied for an animal population in a Markovian (stochastic, serially correlated) environment. This is a general case and encompasses a number of important special cases as simplifications. Extensive empirical data on the Mallard (Anas platyrhynchos) were used as an example of general theory. The number of small ponds on the central breeding grounds was used as an index to the state of the environment. A general mathematical model was formulated to provide a synthesis of the existing literature, estimates of parameters developed from an analysis of data, and hypotheses regarding the specific effect of exploitation on total survival. The literature and analysis of data were inconclusive concerning the effect of exploitation on survival. Therefore, two hypotheses were explored: (1) exploitation mortality represents a largely additive form of mortality, and (2) exploitation mortality is compensatory with other forms of mortality, at least to some threshold level. Models incorporating these two hypotheses were formulated as stochastic dynamic programming models and optimal exploitation strategies were derived numerically on a digital computer. Optimal exploitation strategies were found to exist under the rather general conditions. Direct feedback control was an integral component in the optimal decision-making process. Optimal exploitation was found to be substantially different depending upon the hypothesis regarding the effect of exploitation on the population. If we assume that exploitation is largely an additive force of mortality in Mallards, then optimal exploitation decisions are a convex function of the size of the breeding population and a linear or slight concave function of the environmental conditions. Under the hypothesis of compensatory mortality forces, optimal exploitation decisions are approximately linearly related to the size of the Mallard breeding population. Dynamic programming is suggested as a very general
Optimal control for a tuberculosis model with undetected cases in Cameroon
NASA Astrophysics Data System (ADS)
Moualeu, D. P.; Weiser, M.; Ehrig, R.; Deuflhard, P.
2015-03-01
This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population, Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods. It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80% in 10 years.
Polyhedral Interpolation for Optimal Reaction Control System Jet Selection
NASA Technical Reports Server (NTRS)
Gefert, Leon P.; Wright, Theodore
2014-01-01
An efficient algorithm is described for interpolating optimal values for spacecraft Reaction Control System jet firing duty cycles. The algorithm uses the symmetrical geometry of the optimal solution to reduce the number of calculations and data storage requirements to a level that enables implementation on the small real time flight control systems used in spacecraft. The process minimizes acceleration direction errors, maximizes control authority, and minimizes fuel consumption.
A Riccati approach for constrained linear quadratic optimal control
NASA Astrophysics Data System (ADS)
Sideris, Athanasios; Rodriguez, Luis A.
2011-02-01
An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.
A task control theory of mirror-touch synesthesia.
Heyes, Cecilia; Catmur, Caroline
2015-01-01
Ward and Banissy's illuminating discussion of mirror-touch synesthesia (MTS) encourages research testing two alternatives to Threshold Theory: Their own Self-Other Theory, and "Task Control Theory". MTS may be due to abnormal mirror activity plus a domain-general, rather than a specifically social, impairment in the ability to privilege processing of task-relevant over task-irrelevant information.
Frequency domain synthesis of optimal inputs for adaptive identification and control
NASA Technical Reports Server (NTRS)
Fu, Li-Chen; Sastry, Shankar
1987-01-01
The input design problem of selecting appropriate inputs for use in SISO adaptive identification and model reference adaptive control algorithms is considered. Averaging theory is used to characterize the optimal inputs in the frequency domain. The design problem is formulated as an optimization problem which maximizes the smallest eigenvalue of the average information matrix over power constrained signals, and the global optimal solution is obtained using a convergent numerical algorithm. A bound on the frequency search range required in the design algorithm has been determined in terms of the desired performance.
Optimal control design that accounts for model mismatch errors
Kim, T.J.; Hull, D.G.
1995-02-01
A new technique is presented in this paper that reduces the complexity of state differential equations while accounting for modeling assumptions. The mismatch controls are defined as the differences between the model equations and the true state equations. The performance index of the optimal control problem is formulated with a set of tuning parameters that are user-selected to tune the control solution in order to achieve the best results. Computer simulations demonstrate that the tuned control law outperforms the untuned controller and produces results that are comparable to a numerically-determined, piecewise-linear optimal controller.
Control strategy optimization of HVAC plants
Facci, Andrea Luigi; Zanfardino, Antonella; Martini, Fabrizio; Pirozzi, Salvatore; Ubertini, Stefano
2015-03-10
In this paper we present a methodology to optimize the operating conditions of heating, ventilation and air conditioning (HVAC) plants to achieve a higher energy efficiency in use. Semi-empiric numerical models of the plant components are used to predict their performances as a function of their set-point and the environmental and occupied space conditions. The optimization is performed through a graph-based algorithm that finds the set-points of the system components that minimize energy consumption and/or energy costs, while matching the user energy demands. The resulting model can be used with systems of almost any complexity, featuring both HVAC components and energy systems, and is sufficiently fast to make it applicable to real-time setting.
Optimal control of Atlantic population Canada geese
Hauser, C.E.; Runge, M.C.; Cooch, E.G.; Johnson, F.A.; Harvey, W.F.
2007-01-01
Management of Canada geese (Branta canadensis) can be a balance between providing sustained harvest opportunity while not allowing populations to become overabundant and cause damage. In this paper, we focus on the Atlantic population of Canada geese and use stochastic dynamic programming to determine the optimal harvest strategy over a range of plausible models for population dynamics. There is evidence to suggest that the population exhibits significant age structure, and it is possible to reconstruct age structure from surveys. Consequently the harvest strategy is a function of the age composition, as well as the abundance, of the population. The objective is to maximize harvest while maintaining the number of breeding adults in the population between specified upper and lower limits. In addition, the total harvest capacity is limited and there is uncertainty about the strength of density-dependence. We find that under a density-independent model, harvest is maximized by maintaining the breeding population at the highest acceptable abundance. However if harvest capacity is limited, then the optimal long-term breeding population size is lower than the highest acceptable level, to reduce the risk of the population growing to an unacceptably large size. Under the proposed density-dependent model, harvest is maximized by maintaining the breeding population at an intermediate level between the bounds on acceptable population size; limits to harvest capacity have little effect on the optimal long-term population size. It is clear that the strength of density-dependence and constraints on harvest significantly affect the optimal harvest strategy for this population. Model discrimination might be achieved in the long term, while continuing to meet management goals, by adopting an adaptive management strategy.
Optimization of plasma diagnostics using Bayesian probability theory
NASA Astrophysics Data System (ADS)
Dreier, H.; Fischer, R.; Dinklage, A.; Hirsch, M.; Kornejew, P.
2006-11-01
The diagnostic set-up for Wendelstein 7-X, a magnetic fusion device presently under construction, is currently in the design process to optimize the outcome under given technical constraints. Compared to traditional design approaches, Bayesian Experimental Design (BED) allows to optimize with respect to physical motivated design criterions. It aims to find the optimal design by maximizing an expected utility function that quantifies the goals of the experiment. The expectation marginalizes over the uncertain physical parameters and the possible values of future data. The approach presented here bases on maximization of an information measure (Kullback-Leibler entropy). As an example, the optimization of an infrared multichannel interferometer is shown in detail. Design aspects like the impact of technical restrictions are discussed.
NASA Astrophysics Data System (ADS)
Bergmann, Michel; Cordier, Laurent; Brancher, Jean-Pierre
2005-09-01
In this paper we investigate the optimal control approach for the active control and drag optimization of incompressible viscous flow past circular cylinders. The control function is the time angular velocity of the rotating cylinder. The wake flow is solved in the laminar regime (Re=200) with a finite-element method. Due to the CPU and memory costs related to the optimal control theory, a proper orthogonal decomposition (POD) reduced-order model (ROM) is used as the state equation. The key enablers to an accurate and robust POD ROM are the introduction of a time-dependent eddy-viscosity estimated for each POD mode as the solution of an auxiliary optimization problem and the use of a snapshot ensemble for POD based on chirp-forced transients. Since the POD basis represents only velocities, we minimize a drag-related cost functional characteristic of the wake unsteadiness. The optimization problem is solved using Lagrange multipliers to enforce the constraints. 25% of relative drag reduction is found when the Navier-Stokes equations are controlled using a harmonic control function deduced from the optimal solution determined with the POD ROM. Earlier numerical studies concerning mean drag reduction are confirmed: it is shown, in particular, that without a sufficient penalization of the control input, our approach is energetically inefficient. The main result is that cost-reduction factors of 100 and 760 are obtained for the CPU time and the memory, respectively. Finally, limits of the performance of our approach are discussed.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Optimal Control Modification for Time-Scale Separated Systems
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.
2012-01-01
Recently a new optimal control modification has been introduced that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. This modification is based on an optimal control formulation to minimize the L2 norm of the tracking error. The optimal control modification adaptive law results in a stable adaptation in the presence of a large adaptive gain. This study examines the optimal control modification adaptive law in the context of a system with a time scale separation resulting from a fast plant with a slow actuator. A singular perturbation analysis is performed to derive a modification to the adaptive law by transforming the original system into a reduced-order system in slow time. A model matching conditions in the transformed time coordinate results in an increase in the actuator command that effectively compensate for the slow actuator dynamics. Simulations demonstrate effectiveness of the method.
A duality framework for stochastic optimal control of complex systems
Malikopoulos, Andreas A.
2016-01-01
In this study, we address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations having constraints consistent with those studied here, our results imply that the Pareto control policy may be of value when we seek to derive online the optimal control policy in complex systems.
Optimal control of a harmonic oscillator: Economic interpretations
NASA Astrophysics Data System (ADS)
Janová, Jitka; Hampel, David
2013-10-01
Optimal control is a popular technique for modelling and solving the dynamic decision problems in economics. A standard interpretation of the criteria function and Lagrange multipliers in the profit maximization problem is well known. On a particular example, we aim to a deeper understanding of the possible economic interpretations of further mathematical and solution features of the optimal control problem: we focus on the solution of the optimal control problem for harmonic oscillator serving as a model for Phillips business cycle. We discuss the economic interpretations of arising mathematical objects with respect to well known reasoning for these in other problems.
Time dependent optimal switching controls in online selling models
Bradonjic, Milan; Cohen, Albert
2010-01-01
We present a method to incorporate dishonesty in online selling via a stochastic optimal control problem. In our framework, the seller wishes to maximize her average wealth level W at a fixed time T of her choosing. The corresponding Hamilton-Jacobi-Bellmann (HJB) equation is analyzed for a basic case. For more general models, the admissible control set is restricted to a jump process that switches between extreme values. We propose a new approach, where the optimal control problem is reduced to a multivariable optimization problem.
Multi-host transmission dynamics of schistosomiasis and its optimal control.
Ding, Chunxiao; Qiu, Zhipeng; Zhu, Huaiping
2015-10-01
In this paper we formulate a dynamical model to study the transmission dynamics of schistosomiasis in humans and snails. We also incorporate bovines in the model to study their impact on transmission and controlling the spread of Schistosoma japonicum in humans in China. The dynamics of the model is rigorously analyzed by using the theory of dynamical systems. The theoretical results show that the disease free equilibrium is globally asymptotically stable if R0 < 1, and if R0 > 1 the system has only one positive equilibrium. The local stability of the unique positive equilibrium is investigated and sufficient conditions are also provided for the global stability of the positive equilibrium. The optimal control theory are further applied to the model to study the corresponding optimal control problem. Both analytical and numerical results suggest that: (a) the infected bovines play an important role in the spread of schistosomiasis among humans, and killing the infected bovines will be useful to prevent transmission of schistosomiasis among humans; (b) optimal control strategy performs better than the constant controls in reducing the prevalence of the infected human and the cost for implementing optimal control is much less than that for constant controls; and
Datta, Saurav; Biswas, Ajay; Bhaumik, Swapan; Majumdar, Gautam
2011-01-17
Multi-objective optimization problem has been solved in order to estimate an optimal process environment consisting of optimal parametric combination to achieve desired quality indicators (related to bead geometry) of submerged arc weld of mild steel. The quality indicators selected in the study were bead height, penetration depth, bead width and percentage dilution. Taguchi method followed by utility concept has been adopted to evaluate the optimal process condition achieving multiple objective requirements of the desired quality weld.
Optimal actuator location of minimum norm controls for heat equation with general controlled domain
NASA Astrophysics Data System (ADS)
Guo, Bao-Zhu; Xu, Yashan; Yang, Dong-Hui
2016-09-01
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L2 (Ω × (0 , T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks.
Coupled Low-thrust Trajectory and System Optimization via Multi-Objective Hybrid Optimal Control
NASA Technical Reports Server (NTRS)
Vavrina, Matthew A.; Englander, Jacob Aldo; Ghosh, Alexander R.
2015-01-01
The optimization of low-thrust trajectories is tightly coupled with the spacecraft hardware. Trading trajectory characteristics with system parameters ton identify viable solutions and determine mission sensitivities across discrete hardware configurations is labor intensive. Local independent optimization runs can sample the design space, but a global exploration that resolves the relationships between the system variables across multiple objectives enables a full mapping of the optimal solution space. A multi-objective, hybrid optimal control algorithm is formulated using a multi-objective genetic algorithm as an outer loop systems optimizer around a global trajectory optimizer. The coupled problem is solved simultaneously to generate Pareto-optimal solutions in a single execution. The automated approach is demonstrated on two boulder return missions.
Optimal Control of the Parametric Oscillator
ERIC Educational Resources Information Center
Andresen, B.; Hoffmann, K. H.; Nulton, J.; Tsirlin, A.; Salamon, P.
2011-01-01
We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy E[subscript T] from a given initial state (q[subscript i], p[subscript i]) by controlling its frequency [omega], [omega][subscript min] less than or equal to [omega] less than or equal to [omega][subscript max]. A brief synopsis…
Understanding Product Optimization: Kinetic versus Thermodynamic Control.
ERIC Educational Resources Information Center
Lin, King-Chuen
1988-01-01
Discusses the concept of kinetic versus thermodynamic control of reactions. Explains on the undergraduate level (1) the role of kinetic and thermodynamic control in kinetic equations, (2) the influence of concentration and temperature upon the reaction, and (3) the application of factors one and two to synthetic chemistry. (MVL)
Theory of automatic control of airplanes
NASA Technical Reports Server (NTRS)
Weiss, Herbert K
1939-01-01
Methods of automatically controlling the airplane are reviewed. Equations for the controlled motion including inertia effects of the control are developed and methods of investigating the stability of the resulting fifth and higher order equations are presented. The equations for longitudinal and lateral motion with both ideal and non-ideal controls are developed in dimensionless form in terms of control parameters based on simple dynamic tests of the isolated control unit.
Optimized synthesis of concurrently checked controllers
Leveugle, R.; Saucier, G. )
1990-04-01
Dedicated controllers (or FSM's) with concurrent checking capabilities are of prime importance in highly dependable applications. This paper presents a new method for introducing on-line test facilities in a controller with a very low overhead. This on-line test consists in detecting illegal paths in the control flow graph. These illegal paths may be due either to permanent faults or to transient errors. The state code flow is compacted through polynomial division. An implicit justifying signature method is applied at the state code level and ensures identical signatures before each join node of the control flow graph. The signatures are then independent of the path followed previously in the graph and the comparison to reference data is greatly facilitated. This property is obtained by a clever state assignment, nearly without area overhead. The controllers can then be checked by signature analysis, either by a built-in monitor or by an external checker.
Stability analysis and optimal control of an epidemic model with awareness programs by media.
Misra, A K; Sharma, Anupama; Shukla, J B
2015-12-01
The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown. PMID:26551557
Stability analysis and optimal control of an epidemic model with awareness programs by media.
Misra, A K; Sharma, Anupama; Shukla, J B
2015-12-01
The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown.
Relationships between digital signal processing and control and estimation theory
NASA Technical Reports Server (NTRS)
Willsky, A. S.
1978-01-01
Research directions in the fields of digital signal processing and modern control and estimation theory are discussed. Stability theory, linear prediction and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing are considered in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the disciplines.
A Numerical Optimization Approach for Tuning Fuzzy Logic Controllers
NASA Technical Reports Server (NTRS)
Woodard, Stanley E.; Garg, Devendra P.
1998-01-01
This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science instrument line-of-sight pointing control is used to demonstrate results.
OPTIMIZATION OF INTEGRATED URBAN WET-WEATHER CONTROL STRATEGIES
An optimization method for urban wet weather control (WWC) strategies is presented. The developed optimization model can be used to determine the most cost-effective strategies for the combination of centralized storage-release systems and distributed on-site WWC alternatives. T...
Shape Optimization for Trailing Edge Noise Control
NASA Astrophysics Data System (ADS)
Marsden, Alison; Wang, Meng; Mohammadi, Bijan; Moin, Parviz
2001-11-01
Noise generated by turbulent boundary layers near the trailing edge of lifting surfaces continues to pose a challenge for many applications. In this study, we explore noise reduction strategies through shape optimization. A gradient based shape design method is formulated and implemented for use with large eddy simulation of the flow over an airfoil. The cost function gradient is calculated using the method of incomplete sensitivities (Mohammadi and Pironneau 2001 ph Applied shape Optimization for Fluids, Oxford Univ. Press). This method has the advantage that effects of geometry changes on the flow field can be neglected when computing the gradient of the cost function, making it far more cost effective than solving the full adjoint problem. Validation studies are presented for a model problem of the unsteady laminar flow over an acoustically compact airfoil. A section of the surface is allowed to deform and the cost function is derived based on aeroacoustic theroy. Rapid convergence of the trailing-edge shape and significant reduction of the noise due to vortex shedding and wake instability have been achieved. The addition of constraints and issues of extension to fully turbulent flows past an acoustically noncompact airfoil are also discussed.
Novel multireceiver communication systems configurations based on optimal estimation theory
NASA Technical Reports Server (NTRS)
Kumar, Rajendra
1992-01-01
A novel multireceiver configuration for carrier arraying and/or signal arraying is presented. The proposed configuration is obtained by formulating the carrier and/or signal arraying problem as an optimal estimation problem, and it consists of two stages. The first stage optimally estimates various phase processes received at different receivers with coupled phase-locked loops wherein the individual loops acquire and track their respective receivers' phase processes but are aided by each other in an optimal manner via LF error signals. The proposed configuration results in the minimization of the the effective radio loss at the combiner output, and thus maximization of energy per bit to noise power spectral density ratio is achieved. A novel adaptive algorithm for the estimator of the signal model parameters when these are not known a priori is also presented.
Ramezanpour, HR; Setayeshi, S; Akbari, ME
2011-01-01
Background Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. Methods In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. Results The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. Conclusion In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems. PMID:26322192
Cost benefit theory and optimal design of gene regulation functions
NASA Astrophysics Data System (ADS)
Kalisky, Tomer; Dekel, Erez; Alon, Uri
2007-12-01
Cells respond to the environment by regulating the expression of genes according to environmental signals. The relation between the input signal level and the expression of the gene is called the gene regulation function. It is of interest to understand the shape of a gene regulation function in terms of the environment in which it has evolved and the basic constraints of biological systems. Here we address this by presenting a cost-benefit theory for gene regulation functions that takes into account temporally varying inputs in the environment and stochastic noise in the biological components. We apply this theory to the well-studied lac operon of E. coli. The present theory explains the shape of this regulation function in terms of temporal variation of the input signals, and of minimizing the deleterious effect of cell-cell variability in regulatory protein levels. We also apply the theory to understand the evolutionary tradeoffs in setting the number of regulatory proteins and for selection of feed-forward loops in genetic circuits. The present cost-benefit theory can be used to understand the shape of other gene regulatory functions in terms of environment and noise constraints.
Bridging developmental systems theory and evolutionary psychology using dynamic optimization.
Frankenhuis, Willem E; Panchanathan, Karthik; Clark Barrett, H
2013-07-01
Interactions between evolutionary psychologists and developmental systems theorists have been largely antagonistic. This is unfortunate because potential synergies between the two approaches remain unexplored. This article presents a method that may help to bridge the divide, and that has proven fruitful in biology: dynamic optimization. Dynamic optimization integrates developmental systems theorists' focus on dynamics and contingency with the 'design stance' of evolutionary psychology. It provides a theoretical framework as well as a set of tools for exploring the properties of developmental systems that natural selection might favor, given particular evolutionary ecologies. We also discuss limitations of the approach.
ERIC Educational Resources Information Center
Boman, John H., IV; Krohn, Marvin D.; Gibson, Chris L.; Stogner, John M.
2012-01-01
While associations with deviant peers are well understood to impact individual development, less is understood about the relationship between friendship quality and delinquency. Two criminological theories--social control theory and self-control theory--are able to offer an explanation for the latter relationship. Social control and self-control…
Information spread in networks: Games, optimal control, and stabilization
NASA Astrophysics Data System (ADS)
Khanafer, Ali
This thesis focuses on designing efficient mechanisms for controlling information spread in networks. We consider two models for information spread. The first one is the well-known distributed averaging dynamics. The second model is a nonlinear one that describes virus spread in computer and biological networks. We seek to design optimal, robust, and stabilizing controllers under practical constraints. For distributed averaging networks, we study the interaction between a network designer and an adversary. We consider two types of attacks on the network. In Attack-I, the adversary strategically disconnects a set of links to prevent the nodes from reaching consensus. Meanwhile, the network designer assists the nodes in reaching consensus by changing the weights of a limited number of links in the network. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. Although the canonical equations provided by the Pontryagin's Maximum Principle (MP) seem to be intractable, we provide an alternative characterization for the optimal strategies that makes connection to potential theory. Further, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for the underlying zero-sum game. In Attack-II, the designer and the adversary are both capable of altering the measurements of all nodes in the network by injecting global signals. We impose two constraints on both players: a power constraint and an energy constraint. We assume that the available energy to each player is not sufficient to operate at maximum power throughout the horizon of the game. We show the existence of an SPE and derive the optimal strategies in closed form for this attack scenario. As an alternative to the "network designer vs. adversary" framework, we investigate the possibility of stabilizing unknown network diffusion processes using a distributed mechanism, where the uncertainty is due to an attack
Optimal control studies of solar heating systems
Winn, C B
1980-01-01
In the past few years fuel prices have seen steady increases. Also, the supply of fuel has been on the decline. Because of these two problems there has been an increase in the number of solar heated buildings. Since conventional fuel prices are increasing and as a solar heating system represents a high capital cost it is desirable to obtain the maximum performance from a solar heating system. The control scheme that is used in a solar heated building has an effect on the performance of the solar system. The best control scheme possible would, of course, be desired. This report deals with the control problems of a solar heated building. The first of these problems is to control the inside temperature of the building and to minimize the fuel consumption. This problem applies to both solar and conventionally heated buildings. The second problem considered is to control the collector fluid flow to maximize the difference between the useful energy collected and the energy required to pump the fluid. The third problem is to control the enclosure temperature of a building which has two sources of heat, one solar and the other conventional.
Optimal False Discovery Rate Control for Dependent Data.
Xie, Jichun; Cai, T Tony; Maris, John; Li, Hongzhe
2011-01-01
This paper considers the problem of optimal false discovery rate control when the test statistics are dependent. An optimal joint oracle procedure, which minimizes the false non-discovery rate subject to a constraint on the false discovery rate is developed. A data-driven marginal plug-in procedure is then proposed to approximate the optimal joint procedure for multivariate normal data. It is shown that the marginal procedure is asymptotically optimal for multivariate normal data with a short-range dependent covariance structure. Numerical results show that the marginal procedure controls false discovery rate and leads to a smaller false non-discovery rate than several commonly used p-value based false discovery rate controlling methods. The procedure is illustrated by an application to a genome-wide association study of neuroblastoma and it identifies a few more genetic variants that are potentially associated with neuroblastoma than several p-value-based false discovery rate controlling procedures.
Optimization theory fails to predict performance of pigeons in a two-response situation.
Mazur, J E
1981-11-13
Optimization theory states that organisms behave in a way that maximizes reinforcement or "value." In a two-response situation, pigeons' response proportions approximately equaled reinforcement proportions, even when this behavior pattern substantially decreased the rate of reinforcement. Optimization or reinforcement maximization was not supported as the basic mechanism underlying choice behavior.
The Role of Optimism in the Interpersonal-Psychological Theory of Suicidal Behavior
ERIC Educational Resources Information Center
Rasmussen, Kathy A.; Wingate, LaRicka R.
2011-01-01
A possible relationship between Joiner's (2005) interpersonal-psychological theory of suicidal behavior and optimism was investigated by examining the ability of optimism to act as a moderator of perceived burdensomeness, thwarted belongingness, and acquired capability to engage in self-injury in the prediction of suicidal ideation. Results…
Multi-Objective Optimization of Green EDM: An Integrated Theory
NASA Astrophysics Data System (ADS)
Jagadish; Ray, A.
2015-01-01
Electrical Discharge Machining (EDM) generates toxic substances, results in serious occupational health, and environmental issues, which influence the process parameters of EDM. These process parameters are multi-response parameters. The aim of this research is to solve the multi-response optimization problems and selection of optimum process parameters of green EDM using an integrated methodology comprising of entropy and Grey Relational Analysis (GRA). In this work, initially, an experiment was performed using Taguchi experimental technique. Thereafter, Entropy-GRA has been used to convert the multi-response parameters into single response parameter. Finally, the ranking of the parameter decides the best experimental set up and optimizes the input process parameters. In this work, Entropy method has been used to extract the precise value of each of the output parameters, which influences the gray relational grades for finding the optimal experimental set up. The justification of optimal input process parameters has been made using Analysis of Variance (ANOVA) analysis. An attempt has been made to compare the proposed methodology with the Fuzzy-TOPSIS and Taguchi-VIKOR methodology. The numerical result shows that the optimum process parameters are peak current (4.5 A), pulse duration (261 μs), dielectric level (80 mm) and flushing pressure (0.3 kg/cm2).
Bridging Developmental Systems Theory and Evolutionary Psychology Using Dynamic Optimization
ERIC Educational Resources Information Center
Frankenhuis, Willem E.; Panchanathan, Karthik; Clark Barrett, H.
2013-01-01
Interactions between evolutionary psychologists and developmental systems theorists have been largely antagonistic. This is unfortunate because potential synergies between the two approaches remain unexplored. This article presents a method that may help to bridge the divide, and that has proven fruitful in biology: dynamic optimization. Dynamic…
Using Chemicals to Optimize Conformance Control in Fractured Reservoirs
Seright, Randall S.; Liang, Jenn-Tai; Schrader, Richard; Hagstrom II, John; Wang, Ying; Kumar, Ananad; Wavrik, Kathryn
2001-10-29
This report describes work performed during the third and final year of the project, Using Chemicals to Optimize Conformance Control in Fractured Reservoirs. This research project had three objectives. The first objective was to develop a capability to predict and optimize the ability of gels to reduce permeability to water more than that to oil or gas. The second objective was to develop procedures for optimizing blocking agent placement in wells where hydraulic fractures cause channeling problems. The third objective was to develop procedures to optimize blocking agent placement in naturally fractured reservoirs.
Optimal second order sliding mode control for linear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-11-01
In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.
Cost-effectiveness analysis of optimal control measures for tuberculosis.
Rodrigues, Paula; Silva, Cristiana J; Torres, Delfim F M
2014-10-01
We propose and analyze an optimal control problem where the control system is a mathematical model for tuberculosis that considers reinfection. The control functions represent the fraction of early latent and persistent latent individuals that are treated. Our aim was to study how these control measures should be implemented, for a certain time period, in order to reduce the number of active infected individuals, while minimizing the interventions implementation costs. The optimal intervention is compared along different epidemiological scenarios, by varying the transmission coefficient. The impact of variation of the risk of reinfection, as a result of acquired immunity to a previous infection for treated individuals on the optimal controls and associated solutions, is analyzed. A cost-effectiveness analysis is done, to compare the application of each one of the control measures, separately or in combination.
Case Study: Optimality Theory and the Assessment and Treatment of Phonological Disorders.
ERIC Educational Resources Information Center
Barlow, Jessica A.
2001-01-01
A case study of a 3-year-old with a phonological disorder is used to demonstrate the application of optimality theory to the assessment and treatment. A tutorial of the theory is provided and then several prototypical error patterns evident in the child's productions are analyzed within the framework. (Contains references.) (Author/CR)
NASA Technical Reports Server (NTRS)
Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.
1979-01-01
A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.
Can price controls induce optimal physician behavior?
Wedig, G; Mitchell, J B; Cromwell, J
1989-01-01
Recently, budget-conscious policymakers have shifted their attention to the physician services market and have begun to consider a wide variety of price regulatory schemes for moderating expenditures in this market. In a recent article in this journal, Feldman and Sloan warned that price controls on physician services may cause undesirable declines in service quality, independent of their budgetary ramifications. Our aim in this article is to reconsider the effects of price controls in the broader context of insurance coverage and moral hazard. Our ultimate goal is to assess the benefits of price controls independent of specific assumptions about the controversial issues of demand inducement and income targeting. Using a simple extension of the Feldman/Sloan model, we find that price controls can be and almost certainly are welfare-improving as long as consumers are sufficiently well insured, regardless of where one stands on the inducement issue. The salutary effects of price controls, on the other hand, can be compromised by income-targeting behavior on the part of physicians. We also introduce evidence from Medicare's recent fee freeze to evaluate the possibility of income-targeting behavior empirically. While formal studies of income targeting suggest that its magnitude is small in cross-section, we warn that its effects may be larger over time; this is what our descriptive evidence suggests. We conclude that more dramatic short-term progress on physician fee inflation will require stronger measures, such as putting physicians at risk for consumer expenditures.
NASA Technical Reports Server (NTRS)
Boland, J. S., III
1973-01-01
The conventional six-engine reaction control jet relay attitude control law with deadband is shown to be a good linear approximation to a weighted time-fuel optimal control law. Techniques for evaluating the value of the relative weighting between time and fuel for a particular relay control law is studied along with techniques to interrelate other parameters for the two control laws. Vehicle attitude control laws employing control moment gyros are then investigated. Steering laws obtained from the expression for the reaction torque of the gyro configuration are compared to a total optimal attitude control law that is derived from optimal linear regulator theory. This total optimal attitude control law has computational disadvantages in the solving of the matrix Riccati equation. Several computational algorithms for solving the matrix Riccati equation are investigated with respect to accuracy, computational storage requirements, and computational speed.
Malikopoulos, Andreas
2015-01-01
The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion. Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.
Malikopoulos, Andreas
2015-01-01
The increasing urgency to extract additional efficiency from hybrid propulsion systems has led to the development of advanced power management control algorithms. In this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV operation as a controlled Markov chain and we show that the control policy yielding the Pareto optimal solution minimizes online the long-run expected average cost per unit time criterion. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.more » Both solutions achieved the same cumulative fuel consumption demonstrating that the online Pareto control policy is an optimal control policy.« less
Information fusion based optimal control for large civil aircraft system.
Zhen, Ziyang; Jiang, Ju; Wang, Xinhua; Gao, Chen
2015-03-01
Wind disturbance has a great influence on landing security of Large Civil Aircraft. Through simulation research and engineering experience, it can be found that PID control is not good enough to solve the problem of restraining the wind disturbance. This paper focuses on anti-wind attitude control for Large Civil Aircraft in landing phase. In order to improve the riding comfort and the flight security, an information fusion based optimal control strategy is presented to restrain the wind in landing phase for maintaining attitudes and airspeed. Data of Boeing707 is used to establish a nonlinear mode with total variables of Large Civil Aircraft, and then two linear models are obtained which are divided into longitudinal and lateral equations. Based on engineering experience, the longitudinal channel adopts PID control and C inner control to keep longitudinal attitude constant, and applies autothrottle system for keeping airspeed constant, while an information fusion based optimal regulator in the lateral control channel is designed to achieve lateral attitude holding. According to information fusion estimation, by fusing hard constraint information of system dynamic equations and the soft constraint information of performance index function, optimal estimation of the control sequence is derived. Based on this, an information fusion state regulator is deduced for discrete time linear system with disturbance. The simulation results of nonlinear model of aircraft indicate that the information fusion optimal control is better than traditional PID control, LQR control and LQR control with integral action, in anti-wind disturbance performance in the landing phase.
Preconception optimization of glycaemic control in diabetes.
Islam, Najmul
2016-09-01
The prevalence of Diabetes Mellitus is increasing worldwide. In developing countries 25% of adult females with diabetes are in the reproductive age. Thus in developing countries increased number of pregnancies are complicated by diabetes. Uncontrolled diabetes in pregnancy is associated with increased risk for both mother and foetus. These risks can be minimized by good control of diabetes before and during pregnancy. Management in the preconception period is discussed in this review article. Detailed management involves general advice of lifestyle modification followed by specific details of screening for complications of diabetes. Changes in the drugs for both glycaemic control and other co-morbid conditions are discussed. The recommended insulin regimen in the preconception period and monitoring of glycaemic control by self-monitoring of blood glucose (SMBG) and HbA1C has also been highlighted.
Preconception optimization of glycaemic control in diabetes.
Islam, Najmul
2016-09-01
The prevalence of Diabetes Mellitus is increasing worldwide. In developing countries 25% of adult females with diabetes are in the reproductive age. Thus in developing countries increased number of pregnancies are complicated by diabetes. Uncontrolled diabetes in pregnancy is associated with increased risk for both mother and foetus. These risks can be minimized by good control of diabetes before and during pregnancy. Management in the preconception period is discussed in this review article. Detailed management involves general advice of lifestyle modification followed by specific details of screening for complications of diabetes. Changes in the drugs for both glycaemic control and other co-morbid conditions are discussed. The recommended insulin regimen in the preconception period and monitoring of glycaemic control by self-monitoring of blood glucose (SMBG) and HbA1C has also been highlighted. PMID:27582143
Multiobjective optimization design of a fractional order PID controller for a gun control system.
Gao, Qiang; Chen, Jilin; Wang, Li; Xu, Shiqing; Hou, Yuanlong
2013-01-01
Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.
Multidimensional optimal droop control for wind resources in DC microgrids
NASA Astrophysics Data System (ADS)
Bunker, Kaitlyn J.
Two important and upcoming technologies, microgrids and electricity generation from wind resources, are increasingly being combined. Various control strategies can be implemented, and droop control provides a simple option without requiring communication between microgrid components. Eliminating the single source of potential failure around the communication system is especially important in remote, islanded microgrids, which are considered in this work. However, traditional droop control does not allow the microgrid to utilize much of the power available from the wind. This dissertation presents a novel droop control strategy, which implements a droop surface in higher dimension than the traditional strategy. The droop control relationship then depends on two variables: the dc microgrid bus voltage, and the wind speed at the current time. An approach for optimizing this droop control surface in order to meet a given objective, for example utilizing all of the power available from a wind resource, is proposed and demonstrated. Various cases are used to test the proposed optimal high dimension droop control method, and demonstrate its function. First, the use of linear multidimensional droop control without optimization is demonstrated through simulation. Next, an optimal high dimension droop control surface is implemented with a simple dc microgrid containing two sources and one load. Various cases for changing load and wind speed are investigated using simulation and hardware-in-the-loop techniques. Optimal multidimensional droop control is demonstrated with a wind resource in a full dc microgrid example, containing an energy storage device as well as multiple sources and loads. Finally, the optimal high dimension droop control method is applied with a solar resource, and using a load model developed for a military patrol base application. The operation of the proposed control is again investigated using simulation and hardware-in-the-loop techniques.
Proper Orthogonal Decomposition in Optimal Control of Fluids
NASA Technical Reports Server (NTRS)
Ravindran, S. S.
1999-01-01
In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The POD allows extraction of certain optimal set of basis functions, perhaps few, from a computational or experimental data-base through an eigenvalue analysis. The solution is then obtained as a linear combination of these optimal set of basis functions by means of Galerkin projection. This makes it attractive for optimal control and estimation of systems governed by partial differential equations. We here use it in active control of fluid flows governed by the Navier-Stokes equations. We show that the resulting reduced order model can be very efficient for the computations of optimization and control problems in unsteady flows. Finally, implementational issues and numerical experiments are presented for simulations and optimal control of fluid flow through channels.
Optimal control of hopper unloading on collection conveyor
Bernshtein, A.I.
1987-11-01
This article describes a computer simulation and control approach for optimizing the configuration of a hopper-belt conveyor system for the excavation of coal from underground mine workings. The purpose of the approach is to optimize the placement of hoppers along the conveyor route for maximum load capacity and optimal load distribution. The simulation is based on linear programming and has been implemented to control hopper loading and unloading in the Krasnoarmeiskaya mine No. 1 of the Krasnoarmeiskugol' Coal Production Association. Input criteria are given.
Mechanisms of Molecular Response in the Optimal Control of Photoisomerization
Dietzek, Benjamin; Brueggemann, Ben; Pascher, Torbjoern; Yartsev, Arkady
2006-12-22
We report on adaptive feedback control of photoinduced barrierless isomerization of 1,1'-diethyl-2,2'-cyanine in solution. We compare the effect of different fitness parameters and show that optimal control of the absolute yield of isomerization (photoisomer concentration versus excitation photons) can be achieved, while the relative isomerization yield (photoisomer concentration versus number of relaxed excited-state molecules) is unaffected by adaptive feedback control. The temporal structure of the optimized excitation pulses allows one to draw clear mechanistic conclusions showing the critical importance of coherent nuclear motion for the control of isomerization.
Reproducibility, Controllability, and Optimization of Lenr Experiments
NASA Astrophysics Data System (ADS)
Nagel, David J.
2006-02-01
Low-energy nuclear reaction (LENR) measurements are significantly and increasingly reproducible. Practical control of the production of energy or materials by LENR has yet to be demonstrated. Minimization of costly inputs and maximization of desired outputs of LENR remain for future developments.
Linear stochastic optimal control and estimation
NASA Technical Reports Server (NTRS)
Geyser, L. C.; Lehtinen, F. K. B.
1976-01-01
Digital program has been written to solve the LSOCE problem by using a time-domain formulation. LSOCE problem is defined as that of designing controls for linear time-invariant system which is disturbed by white noise in such a way as to minimize quadratic performance index.
Reengineering for optimized control of DC networks
NASA Astrophysics Data System (ADS)
Vintea, Adela; Schiopu, Paul
2015-02-01
The management of the Independent Power Grids is the global body/structure with flexible technological support for Command-Control-Communications and Informatized Management having the responsibility for providing the conditions and information (the informational flux of decision) for the decision-maker aiming at predictable and harmonic administration of the situations (crises) and for generating the harmonic situations (results).
Microstructurally Controlled Composites with Optimal Elastodynamic Properties
NASA Astrophysics Data System (ADS)
Sadeghi, Hossein
Periodic composites (PCs) are artificial materials with specially designed microstructure to manage stress waves. The objective of this dissertation is to study various techniques for microstructural design of PCs for a desired elastodynamic response. A mixed variational formulation is studied for band structure calculation of PCs. Dynamic homogenization is studied for calculation of the frequency dependent effective properties of PCs. Optimization techniques are used together with mixed variational formulation and dynamic homogenization to make a computational platform for microstructural design of PCs. Several PCs are designed and fabricated, and various tests are performed for experimental verification. First, band-gap in one- and two-dimensional PCs is investigated experimentally. Mixed variational formulation is used to design samples with band-gaps at frequencies convenient to conduct experiment. Samples are fabricated and their transmission coefficient is measured. Experimental data are compared with theoretical results for evaluation of the band structure. Using constituent materials with temperature dependent material properties, it is also shown that band structure of PCs can be tuned by changing the ambient temperature. Furthermore, dynamic homogenization is used to design a one-dimensional PC for acoustic impedance matching. As a result, the reflection of stress waves at the interface of two impedance matched media becomes zero. Samples are fabricated and ultrasound tests are performed to measure the reflection coefficient for experimental verification. In addition, a one-dimensional PC with metamaterial response is designed to achieve a composite with both high stiffness-to-density ratio and high attenuation at low frequency regime. Samples are fabricated and the attenuation coefficient is measured for experimental verification. Moreover, optimal design of PCs for shock wave mitigation is investigated. A genetic algorithm is used to design the
Genetic Algorithm Optimizes Q-LAW Control Parameters
NASA Technical Reports Server (NTRS)
Lee, Seungwon; von Allmen, Paul; Petropoulos, Anastassios; Terrile, Richard
2008-01-01
A document discusses a multi-objective, genetic algorithm designed to optimize Lyapunov feedback control law (Q-law) parameters in order to efficiently find Pareto-optimal solutions for low-thrust trajectories for electronic propulsion systems. These would be propellant-optimal solutions for a given flight time, or flight time optimal solutions for a given propellant requirement. The approximate solutions are used as good initial solutions for high-fidelity optimization tools. When the good initial solutions are used, the high-fidelity optimization tools quickly converge to a locally optimal solution near the initial solution. Q-law control parameters are represented as real-valued genes in the genetic algorithm. The performances of the Q-law control parameters are evaluated in the multi-objective space (flight time vs. propellant mass) and sorted by the non-dominated sorting method that assigns a better fitness value to the solutions that are dominated by a fewer number of other solutions. With the ranking result, the genetic algorithm encourages the solutions with higher fitness values to participate in the reproduction process, improving the solutions in the evolution process. The population of solutions converges to the Pareto front that is permitted within the Q-law control parameter space.
Hydro- abrasive jet machining modeling for computer control and optimization
NASA Astrophysics Data System (ADS)
Groppetti, R.; Jovane, F.
1993-06-01
Use of hydro-abrasive jet machining (HAJM) for machining a wide variety of materials—metals, poly-mers, ceramics, fiber-reinforced composites, metal-matrix composites, and bonded or hybridized mate-rials—primarily for two- and three-dimensional cutting and also for drilling, turning, milling, and deburring, has been reported. However, the potential of this innovative process has not been explored fully. This article discusses process control, integration, and optimization of HAJM to establish a plat-form for the implementation of real-time adaptive control constraint (ACC), adaptive control optimiza-tion (ACO), and CAD/CAM integration. It presents the approach followed and the main results obtained during the development, implementation, automation, and integration of a HAJM cell and its computer-ized controller. After a critical analysis of the process variables and models reported in the literature to identify process variables and to define a process model suitable for HAJM real-time control and optimi-zation, to correlate process variables and parameters with machining results, and to avoid expensive and time-consuming experiments for determination of the optimal machining conditions, a process predic-tion and optimization model was identified and implemented. Then, the configuration of the HAJM cell, architecture, and multiprogramming operation of the controller in terms of monitoring, control, process result prediction, and process condition optimization were analyzed. This prediction and optimization model for selection of optimal machining conditions using multi-objective programming was analyzed. Based on the definition of an economy function and a productivity function, with suitable constraints relevant to required machining quality, required kerfing depth, and available resources, the model was applied to test cases based on experimental results.
Formal optimization of hovering performance using free wake lifting surface theory
NASA Technical Reports Server (NTRS)
Chung, S. Y.
1986-01-01
Free wake techniques for performance prediction and optimization of hovering rotor are discussed. The influence functions due to vortex ring, vortex cylinder, and source or vortex sheets are presented. The vortex core sizes of rotor wake vortices are calculated and their importance is discussed. Lifting body theory for finite thickness body is developed for pressure calculation, and hence performance prediction of hovering rotors. Numerical optimization technique based on free wake lifting line theory is presented and discussed. It is demonstrated that formal optimization can be used with the implicit and nonlinear objective or cost function such as the performance of hovering rotors as used in this report.
Theory of the optimally coupled Q-switched laser
NASA Technical Reports Server (NTRS)
Degnan, John J.
1989-01-01
The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.
Design of turbofan engine controls using output feedback regulator theory
NASA Technical Reports Server (NTRS)
Merrill, W. C.
1977-01-01
A multivariable control design procedure based on output feedback regulator (OFR) theory is applied to the F100 turbofan engine. Results for the OFR design are compared to a design based on linear quadratic regulator (LQR) theory. The OFR feedback control is designed in the full order state space and thus eliminates any need for model reduction techniques. Using the performance measure and control structure of the LQR design, an equivalent OFR feedback control is obtained. The flexibility of the OFR as a control design procedure is demonstrated, and differing feedback control structures are evaluated.
Propulsion control and control theory: A new research focus
NASA Technical Reports Server (NTRS)
Zeller, J. R.
1980-01-01
Technological developments necessary for the implementation of advanced digital control concepts for aircraft propulsion are identified and discussed. Developments associated with the replacement analog controllers with digital control systems, sensors and actuators, and control modes and software are reported.
Adaptive control based on retrospective cost optimization
NASA Technical Reports Server (NTRS)
Santillo, Mario A. (Inventor); Bernstein, Dennis S. (Inventor)
2012-01-01
A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.
Optimizing wind turbine control system parameters
NASA Astrophysics Data System (ADS)
Schluter, Larry L.; Vachon, William A.
1993-05-01
The impending expiration of the levelized period in the Interim Standard Offer Number 4 (ISO4) utility contracts for purchasing wind-generated power in California mandates, more than ever, that windplants be operated in a cost-effective manner. Operating plans and approaches are needed that maximize the net revenue from wind parks--after accounting for operation and maintenance costs. This paper describes a design tool that makes it possible to tailor a control system of a wind turbine (WT) to maximize energy production while minimizing the financial consequences of fatigue damage to key structural components. Plans for code enhancements to include expert systems and fuzzy logic are discussed, and typical results are presented in which the code is applied to study the controls of a generic Danish 15-m horizontal axis wind turbine (HAWT).
Optimizing wind turbine control system parameters
Schluter, L.L.; Vachon, W.A.
1993-08-01
The impending expiration of the levelized period in the Interim Standard Offer Number 4 (ISO4) utility contracts for purchasing wind-generated power in California mandates, more than ever, that windplants be operated in a cost-effective manner. Operating plans and approaches are needed that maximize the net revenue from wind parks--after accounting for operation and maintenance costs. This paper describes a design tool that makes it possible to tailor a control system of a wind turbine (WT) to maximize energy production while minimizing the financial consequences of fatigue damage to key structural components. Plans for code enhancements to include expert systems and fuzzy logic are discussed, and typical results are presented in which the code is applied to study the controls of a generic Danish 15-m horizontal axis wind turbine (HAWT).
Integrated structure/control law design by multilevel optimization
NASA Technical Reports Server (NTRS)
Gilbert, Michael G.; Schmidt, David K.
1989-01-01
A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.
Optimizing and controlling the operation of heat-exchanger networks
Aguilera, N.; Marchetti, J.L.
1998-05-01
A procedure was developed for on-line optimization and control systems of heat-exchanger networks, which features a two-level control structure, one for a constant configuration control system and the other for a supervisor on-line optimizer. The coordination between levels is achieved by adjusting the formulation of the optimization problem to meet requirements of the adopted control system. The general goal is always to work without losing stream temperature targets while keeping the highest energy integration. The operation constraints used for heat-exchanger and utility units emphasize the computation of heat-exchanger duties rather than intermediate stream temperatures. This simplifies the modeling task and provides clear links with the limits of the manipulated variables. The optimal condition is determined using LP or NLP, depending on the final problem formulation. Degrees of freedom for optimization and equation constraints for considering simple and multiple bypasses are rigorously discussed. An example used shows how the optimization problem can be adjusted to a specific network design, its expected operating space, and the control configuration. Dynamic simulations also show benefits and limitations of this procedure.
Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory
NASA Technical Reports Server (NTRS)
Dees, Patrick D.; Zwack, Matthew R.; Edwards, Stephen; Steffens, Michael
2016-01-01
It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information
Optimally Controlled Flexible Fuel Powertrain System
Duncan Sheppard; Bruce Woodrow; Paul Kilmurray; Simon Thwaite
2011-06-30
A multi phase program was undertaken with the stated goal of using advanced design and development tools to create a unique combination of existing technologies to create a powertrain system specification that allowed minimal increase of volumetric fuel consumption when operating on E85 relative to gasoline. Although on an energy basis gasoline / ethanol blends typically return similar fuel economy to straight gasoline, because of its lower energy density (gasoline ~ 31.8MJ/l and ethanol ~ 21.1MJ/l) the volume based fuel economy of gasoline / ethanol blends are typically considerably worse. This project was able to define an initial engine specification envelope, develop specific hardware for the application, and test that hardware in both single and multi-cylinder test engines to verify the ability of the specified powertrain to deliver reduced E85 fuel consumption. Finally, the results from the engine testing were used in a vehicle drive cycle analysis tool to define a final vehicle level fuel economy result. During the course of the project, it was identified that the technologies utilized to improve fuel economy on E85 also enabled improved fuel economy when operating on gasoline. However, the E85 fueled powertrain provided improved vehicle performance when compared to the gasoline fueled powertrain due to the improved high load performance of the E85 fuel. Relative to the baseline comparator engine and considering current market fuels, the volumetric fuel consumption penalty when running on E85 with the fully optimized project powertrain specification was reduced significantly. This result shows that alternative fuels can be utilized in high percentages while maintaining or improving vehicle performance and with minimal or positive impact on total cost of ownership to the end consumer. The justification for this project was two-fold. In order to reduce the US dependence on crude oil, much of which is imported, the US Environmental Protection Agency (EPA
NASA Astrophysics Data System (ADS)
Paasche, H.; Tronicke, J.
2012-04-01
In many near surface geophysical applications multiple tomographic data sets are routinely acquired to explore subsurface structures and parameters. Linking the model generation process of multi-method geophysical data sets can significantly reduce ambiguities in geophysical data analysis and model interpretation. Most geophysical inversion approaches rely on local search optimization methods used to find an optimal model in the vicinity of a user-given starting model. The final solution may critically depend on the initial model. Alternatively, global optimization (GO) methods have been used to invert geophysical data. They explore the solution space in more detail and determine the optimal model independently from the starting model. Additionally, they can be used to find sets of optimal models allowing a further analysis of model parameter uncertainties. Here we employ particle swarm optimization (PSO) to realize the global optimization of tomographic data. PSO is an emergent methods based on swarm intelligence characterized by fast and robust convergence towards optimal solutions. The fundamental principle of PSO is inspired by nature, since the algorithm mimics the behavior of a flock of birds searching food in a search space. In PSO, a number of particles cruise a multi-dimensional solution space striving to find optimal model solutions explaining the acquired data. The particles communicate their positions and success and direct their movement according to the position of the currently most successful particle of the swarm. The success of a particle, i.e. the quality of the currently found model by a particle, must be uniquely quantifiable to identify the swarm leader. When jointly inverting disparate data sets, the optimization solution has to satisfy multiple optimization objectives, at least one for each data set. Unique determination of the most successful particle currently leading the swarm is not possible. Instead, only statements about the Pareto
Lyapunov optimal feedback control of a nonlinear inverted pendulum
NASA Technical Reports Server (NTRS)
Grantham, W. J.; Anderson, M. J.
1989-01-01
Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
OCTBEC—A Matlab toolbox for optimal quantum control of Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Hohenester, Ulrich
2014-01-01
OCTBEC is a Matlab toolbox designed for optimal quantum control, within the framework of optimal control theory (OCT), of Bose-Einstein condensates (BEC). The systems we have in mind are ultracold atoms in confined geometries, where the dynamics takes place in one or two spatial dimensions, and the confinement potential can be controlled by some external parameters. Typical experimental realizations are atom chips, where the currents running through the wires produce magnetic fields that allow to trap and manipulate nearby atoms. The toolbox provides a variety of Matlab classes for simulations based on the Gross-Pitaevskii equation, the multi-configurational Hartree method for bosons, and on generic few-mode models, as well as optimization problems. These classes can be easily combined, which has the advantage that one can adapt the simulation programs flexibly for various applications.
Near-time-optimal control for quantum systems
NASA Astrophysics Data System (ADS)
Chen, Qi-Ming; Wu, Re-Bing; Zhang, Tian-Ming; Rabitz, Herschel
2015-12-01
For a quantum system controlled by an external field, time-optimal control is referred to as the shortest-time-duration control that can still permit maximizing an objective function J , which is especially a desirable goal for engineering quantum dynamics against decoherence effects. However, since rigorously finding a time-optimal control is usually very difficult and in many circumstances the control is only required to be sufficiently short and precise, one can design algorithms seeking such suboptimal control solutions for much reduced computational effort. In this paper, we propose an iterative algorithm for finding near-time-optimal control in a high level set (i.e., the set of controls that achieves the same value of J ) that can be arbitrarily close to the global optima. The algorithm proceeds seeking to decrease the time duration T while the value of J remains invariant, until J leaves the level-set value; the deviation of J due to numerical errors is corrected by gradient climbing that brings the search back to the level-set J value. Since the level set is very close to the maximum value of J , the resulting control solution is nearly time optimal with manageable precision. Numerical examples demonstrate the effectiveness and general applicability of the algorithm.
Robust Optimal Adaptive Control Method with Large Adaptive Gain
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.
2009-01-01
In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.
NASA Astrophysics Data System (ADS)
Debiane, L.; Ivorra, B.; Mohammadi, B.; Nicoud, F.; Poinsot, T.; Ern, A.; Pitsch, H.
2006-02-01
Controlling flame shapes and emissions is a major objective for all combustion engineers. Considering the complexity of reacting flows, novel optimization methods are required: this paper explores the application of control theory for partial differential equations to combustion. Both flame temperature and pollutant levels are optimized in a laminar Bunsen burner computed with complex chemistry using a recursive semi-deterministic global optimization algorithm. In order to keep the computational time low, the optimization procedure is coupled with mesh adaptation and incomplete gradient techniques.
An optimized buffer controlled data compression system
NASA Technical Reports Server (NTRS)
Dosik, P. H.; Schwartz, M.
1974-01-01
The digital data compression system considered uses a buffer controlled aperture algorithm which minimizes the mean-squared error between the reconstructed receiver output and transmitter input. The data compression technique selected is based on the zero-order floating aperture prediction rule. It is assumed that the statistics of the input data are initially uniformly distributed, stationary, and first-order Markov. The problem is solved for stationary data. An approach is presented for extending the results to slowly varying uniformly distributed nonstationary Markov data.
Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures
NASA Astrophysics Data System (ADS)
Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin
2012-08-01
Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.
Polynomial method for PLL controller optimization.
Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu
2011-01-01
The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach. PMID:22163973
Efficient frequency conversion based on local optimization theory
NASA Astrophysics Data System (ADS)
Xu, Lei; Chen, Changshui; Zhao, Xiangyang; Liu, Tuo; Hu, Hui
2015-12-01
We discuss theoretically a robustness of the difference frequency conversion method and demonstrate it by numerical simulation. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance called ‘local optimization’, can keep the intermediate frequency fixed and make the counterintuitive ordering emerge automatically. Here we show an efficient frequency conversion in two-process three wave mixing (TWM). And because the local optimization method is a well-defined, automated computational procedure, we think it would be very useful in the efficient conversion of complicated multi-process TWM, which is a difficult subject in STIRAP.
Theory of optimal weighting of data to detect climatic change
NASA Technical Reports Server (NTRS)
Bell, T. L.
1986-01-01
A search for climatic change predicted by climate models can easily yield unconvincing results because of 'climatic noise,' the inherent, unpredictable variability of time-average atmospheric data. A weighted average of data that maximizes the probability of detecting predicted climatic change is presented. To obtain the optimal weights, an estimate of the covariance matrix of the data from a prior data set is needed. This introduces additional sampling error into the method. This is presently taken into account. A form of the weighted average is found whose probability distribution is independent of the true (but unknown) covariance statistics of the data and of the climate model prediction.
Exploring quantum control landscapes: Topology, features, and optimization scaling
Moore, Katharine W.; Rabitz, Herschel
2011-07-15
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states N ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of suboptimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9% on careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension N. This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as N increases.
A task control theory of mirror-touch synesthesia.
Heyes, Cecilia; Catmur, Caroline
2015-01-01
Ward and Banissy's illuminating discussion of mirror-touch synesthesia (MTS) encourages research testing two alternatives to Threshold Theory: Their own Self-Other Theory, and "Task Control Theory". MTS may be due to abnormal mirror activity plus a domain-general, rather than a specifically social, impairment in the ability to privilege processing of task-relevant over task-irrelevant information. PMID:26114543
Random matrix theory and portfolio optimization in Moroccan stock exchange
NASA Astrophysics Data System (ADS)
El Alaoui, Marwane
2015-09-01
In this work, we use random matrix theory to analyze eigenvalues and see if there is a presence of pertinent information by using Marčenko-Pastur distribution. Thus, we study cross-correlation among stocks of Casablanca Stock Exchange. Moreover, we clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. We also analyze eigenvectors components distributions and their degree of deviations by computing the inverse participation ratio. This analysis is a way to understand the correlation structure among stocks of Casablanca Stock Exchange portfolio.
Transportation optimization with fuzzy trapezoidal numbers based on possibility theory.
He, Dayi; Li, Ran; Huang, Qi; Lei, Ping
2014-01-01
In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.
Theory of the optimally coupled Q-switched laser
Degnan, J.J.
1989-02-01
The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions. This greatly complicates the optimization of real devices. In this paper, we demonstrate that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters (which include the optimum reflectivity, output energy, extraction efficiency, pulsewidth, peak power, etc.) can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (non-useful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.
Theory of optimal information transmission in E. coli chemotaxis pathway
NASA Astrophysics Data System (ADS)
Micali, Gabriele; Endres, Robert G.
Bacteria live in complex microenvironments where they need to make critical decisions fast and reliably. These decisions are inherently affected by noise at all levels of the signaling pathway, and cells are often modeled as an input-output device that transmits extracellular stimuli (input) to internal proteins (channel), which determine the final behavior (output). Increasing the amount of transmitted information between input and output allows cells to better infer extracellular stimuli and respond accordingly. However, in contrast to electronic devices, the separation into input, channel, and output is not always clear in biological systems. Output might feed back into the input, and the channel, made by proteins, normally interacts with the input. Furthermore, a biological channel is affected by mutations and can change under evolutionary pressure. Here, we present a novel approach to maximize information transmission: given cell-external and internal noise, we analytically identify both input distributions and input-output relations that optimally transmit information. Using E. coli chemotaxis as an example, we conclude that its pathway is compatible with an optimal information transmission device despite the ultrasensitive rotary motors.
OPTIMIZATION OF DECENTRALIZED BMP CONTROLS IN URBAN AREAS
This paper will present an overview of a recently completed project for the US EPA entitled, Optimization of Urban Wet-weather Flow Control Systems. The focus of this effort is on techniques that are suitable for evaluating decentralized BMP controls. The four major components ...
OPTIMIZATION OF DECENTRALIZED BMP CONTROLS IN URBAN AREAS
This paper will present an overview of a recently completed project for the US EPA entitled Optimization of Urban Wet-weather Flow Control Systems. The focus of this effort is on techniques that are suitable for evaluating decentralized BMP controls. The four major components o...
Sensitivity Analysis and Optimal Control of Anthroponotic Cutaneous Leishmania
Zamir, Muhammad; Zaman, Gul; Alshomrani, Ali Saleh
2016-01-01
This paper is focused on the transmission dynamics and optimal control of Anthroponotic Cutaneous Leishmania. The threshold condition R0 for initial transmission of infection is obtained by next generation method. Biological sense of the threshold condition is investigated and discussed in detail. The sensitivity analysis of the reproduction number is presented and the most sensitive parameters are high lighted. On the basis of sensitivity analysis, some control strategies are introduced in the model. These strategies positively reduce the effect of the parameters with high sensitivity indices, on the initial transmission. Finally, an optimal control strategy is presented by taking into account the cost associated with control strategies. It is also shown that an optimal control exists for the proposed control problem. The goal of optimal control problem is to minimize, the cost associated with control strategies and the chances of infectious humans, exposed humans and vector population to become infected. Numerical simulations are carried out with the help of Runge-Kutta fourth order procedure. PMID:27505634
Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control
Masiero, Federica
2005-03-15
Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations.
Optimal Control of a Dengue Epidemic Model with Vaccination
NASA Astrophysics Data System (ADS)
Rodrigues, Helena Sofia; Teresa, M.; Monteiro, T.; Torres, Delfim F. M.
2011-09-01
We present a SIR+ASI epidemic model to describe the interaction between human and dengue fever mosquito populations. A control strategy in the form of vaccination, to decrease the number of infected individuals, is used. An optimal control approach is applied in order to find the best way to fight the disease.
Recursive multibody dynamics and discrete-time optimal control
NASA Technical Reports Server (NTRS)
Deleuterio, G. M. T.; Damaren, C. J.
1989-01-01
A recursive algorithm is developed for the solution of the simulation dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal control problem. For each relevant quantity in the multibody dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.
Optimization of an Aeroservoelastic Wing with Distributed Multiple Control Surfaces
NASA Technical Reports Server (NTRS)
Stanford, Bret K.
2015-01-01
This paper considers the aeroelastic optimization of a subsonic transport wingbox under a variety of static and dynamic aeroelastic constraints. Three types of design variables are utilized: structural variables (skin thickness, stiffener details), the quasi-steady deflection scheduling of a series of control surfaces distributed along the trailing edge for maneuver load alleviation and trim attainment, and the design details of an LQR controller, which commands oscillatory hinge moments into those same control surfaces. Optimization problems are solved where a closed loop flutter constraint is forced to satisfy the required flight margin, and mass reduction benefits are realized by relaxing the open loop flutter requirements.
Optimal member damper controller design for large space structures
NASA Technical Reports Server (NTRS)
Joshi, S. M.; Groom, N. J.
1980-01-01
Consideration is given to the selection of velocity feedback gains for individual dampers for the members of a structurally controlled large flexible space structure. The problem is formulated as an optimal output feedback regulator problem, and necessary conditions are derived for minimizing a quadratic performance function. The diagonal nature of the gain matrix is taken into account, along with knowledge of noise covariances. It is pointed out that the method presented offers a systematic approach to the design of a class of controllers for enhancing structural damping, which have significant potential if used in conjunction with a reduced-order optimal controller for rigid-body modes and selected structural modes.
Solving the optimal attention allocation problem in manual control
NASA Technical Reports Server (NTRS)
Kleinman, D. L.
1976-01-01
Within the context of the optimal control model of human response, analytic expressions for the gradients of closed-loop performance metrics with respect to human operator attention allocation are derived. These derivatives serve as the basis for a gradient algorithm that determines the optimal attention that a human should allocate among several display indicators in a steady-state manual control task. Application of the human modeling techniques are made to study the hover control task for a CH-46 VTOL flight tested by NASA.
State-Constrained Optimal Control Problems of Impulsive Differential Equations
Forcadel, Nicolas; Rao Zhiping Zidani, Hasnaa
2013-08-01
The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
Topology of classical molecular optimal control landscapes in phase space
NASA Astrophysics Data System (ADS)
Joe-Wong, Carlee; Ho, Tak-San; Long, Ruixing; Rabitz, Herschel; Wu, Rebing
2013-03-01
Optimal control of molecular dynamics is commonly expressed from a quantum mechanical perspective. However, in most contexts the preponderance of molecular dynamics studies utilize classical mechanical models. This paper treats laser-driven optimal control of molecular dynamics in a classical framework. We consider the objective of steering a molecular system from an initial point in phase space to a target point, subject to the dynamic constraint of Hamilton's equations. The classical control landscape corresponding to this objective is a functional of the control field, and the topology of the landscape is analyzed through its gradient and Hessian with respect to the control. Under specific assumptions on the regularity of the control fields, the classical control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating the presence of an inherent degree of robustness to control noise. Extensive numerical simulations are performed to illustrate the theoretical principles on (a) a model diatomic molecule, (b) two coupled Morse oscillators, and (c) a chaotic system with a coupled quartic oscillator, confirming the absence of traps in the classical control landscape. We compare the classical formulation with the mathematically analogous quantum state-to-state transition probability control landscape.
Topology of classical molecular optimal control landscapes in phase space.
Joe-Wong, Carlee; Ho, Tak-San; Long, Ruixing; Rabitz, Herschel; Wu, Rebing
2013-03-28
Optimal control of molecular dynamics is commonly expressed from a quantum mechanical perspective. However, in most contexts the preponderance of molecular dynamics studies utilize classical mechanical models. This paper treats laser-driven optimal control of molecular dynamics in a classical framework. We consider the objective of steering a molecular system from an initial point in phase space to a target point, subject to the dynamic constraint of Hamilton's equations. The classical control landscape corresponding to this objective is a functional of the control field, and the topology of the landscape is analyzed through its gradient and Hessian with respect to the control. Under specific assumptions on the regularity of the control fields, the classical control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating the presence of an inherent degree of robustness to control noise. Extensive numerical simulations are performed to illustrate the theoretical principles on (a) a model diatomic molecule, (b) two coupled Morse oscillators, and (c) a chaotic system with a coupled quartic oscillator, confirming the absence of traps in the classical control landscape. We compare the classical formulation with the mathematically analogous quantum state-to-state transition probability control landscape.
Optimal control methods for rapidly time-varying Hamiltonians
Motzoi, F.; Merkel, S. T.; Wilhelm, F. K.; Gambetta, J. M.
2011-08-15
In this article, we develop a numerical method to find optimal control pulses that accounts for the separation of timescales between the variation of the input control fields and the applied Hamiltonian. In traditional numerical optimization methods, these timescales are treated as being the same. While this approximation has had much success, in applications where the input controls are filtered substantially or mixed with a fast carrier, the resulting optimized pulses have little relation to the applied physical fields. Our technique remains numerically efficient in that the dimension of our search space is only dependent on the variation of the input control fields, while our simulation of the quantum evolution is accurate on the timescale of the fast variation in the applied Hamiltonian.
Intermittent control: a computational theory of human control.
Gawthrop, Peter; Loram, Ian; Lakie, Martin; Gollee, Henrik
2011-02-01
The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as "continuous observation, intermittent action". Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.
The Application of Layer Theory to Design: The Control Layer
ERIC Educational Resources Information Center
Gibbons, Andrew S.; Langton, Matthew B.
2016-01-01
A theory of design layers proposed by Gibbons ("An Architectural Approach to Instructional Design." Routledge, New York, 2014) asserts that each layer of an instructional design is related to a body of theory closely associated with the concerns of that particular layer. This study focuses on one layer, the control layer, examining…
Relationships between digital signal processing and control and estimation theory
NASA Technical Reports Server (NTRS)
Willsky, A. S.
1978-01-01
Research areas associated with digital signal processing and control and estimation theory are identified. Particular attention is given to image processing, system identification problems (parameter identification, linear prediction, least squares, Kalman filtering), stability analyses (the use of the Liapunov theory, frequency domain criteria, passivity), and multiparameter systems, distributed processes, and random fields.
Optimal control of information epidemics modeled as Maki Thompson rumors
NASA Astrophysics Data System (ADS)
Kandhway, Kundan; Kuri, Joy
2014-12-01
We model the spread of information in a homogeneously mixed population using the Maki Thompson rumor model. We formulate an optimal control problem, from the perspective of single campaigner, to maximize the spread of information when the campaign budget is fixed. Control signals, such as advertising in the mass media, attempt to convert ignorants and stiflers into spreaders. We show the existence of a solution to the optimal control problem when the campaigning incurs non-linear costs under the isoperimetric budget constraint. The solution employs Pontryagin's Minimum Principle and a modified version of forward backward sweep technique for numerical computation to accommodate the isoperimetric budget constraint. The techniques developed in this paper are general and can be applied to similar optimal control problems in other areas. We have allowed the spreading rate of the information epidemic to vary over the campaign duration to model practical situations when the interest level of the population in the subject of the campaign changes with time. The shape of the optimal control signal is studied for different model parameters and spreading rate profiles. We have also studied the variation of the optimal campaigning costs with respect to various model parameters. Results indicate that, for some model parameters, significant improvements can be achieved by the optimal strategy compared to the static control strategy. The static strategy respects the same budget constraint as the optimal strategy and has a constant value throughout the campaign horizon. This work finds application in election and social awareness campaigns, product advertising, movie promotion and crowdfunding campaigns.
Optimal control of coupled PDE networks with automated code generation
NASA Astrophysics Data System (ADS)
Papadopoulos, D.
2012-09-01
The purpose of this work is to present a framework for the optimal control of coupled PDE networks. A coupled PDE network is a system of partial differential equations coupled together. Such systems can be represented as a directed graph. A domain specific language (DSL)—an extension of the DOT language—is used for the description of such a coupled PDE network. The adjoint equations and the gradient, required for its optimal control, are computed with the help of a computer algebra system (CAS). Automated code generation techniques have been used for the generation of the PDE systems of both the direct and the adjoint equations. Both the direct and adjoint equations are solved with the standard finite element method. Finally, for the numerical optimization of the system standard optimization techniques are used such as BFGS and Newton conjugate gradient.
Thermodynamic framework for discrete optimal control in multiphase flow systems
NASA Astrophysics Data System (ADS)
Sieniutycz, Stanislaw
1999-08-01
Bellman's method of dynamic programming is used to synthesize diverse optimization approaches to active (work producing) and inactive (entropy generating) multiphase flow systems. Thermal machines, optimally controlled unit operations, nonlinear heat conduction, spontaneous relaxation processes, and self-propagating wave fronts are all shown to satisfy a discrete Hamilton-Jacobi-Bellman equation and a corresponding discrete optimization algorithm of Pontryagin's type, with the maximum principle for a Hamiltonian. The extremal structures are always canonical. A common unifying criterion is set for all considered systems, which is the criterion of a minimum generated entropy. It is shown that constraints can modify the entropy functionals in a different way for each group of the processes considered; thus the resulting structures of these functionals may differ significantly. Practical conclusions are formulated regarding the energy savings and energy policy in optimally controlled systems.
Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.
2012-01-01
This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.
Exploring the complexity of quantum control optimization trajectories.
Nanduri, Arun; Shir, Ofer M; Donovan, Ashley; Ho, Tak-San; Rabitz, Herschel
2015-01-01
The control of quantum system dynamics is generally performed by seeking a suitable applied field. The physical objective as a functional of the field forms the quantum control landscape, whose topology, under certain conditions, has been shown to contain no critical point suboptimal traps, thereby enabling effective searches for fields that give the global maximum of the objective. This paper addresses the structure of the landscape as a complement to topological critical point features. Recent work showed that landscape structure is highly favorable for optimization of state-to-state transition probabilities, in that gradient-based control trajectories to the global maximum value are nearly straight paths. The landscape structure is codified in the metric R ≥ 1.0, defined as the ratio of the length of the control trajectory to the Euclidean distance between the initial and optimal controls. A value of R = 1 would indicate an exactly straight trajectory to the optimal observable value. This paper extends the state-to-state transition probability results to the quantum ensemble and unitary transformation control landscapes. Again, nearly straight trajectories predominate, and we demonstrate that R can take values approaching 1.0 with high precision. However, the interplay of optimization trajectories with critical saddle submanifolds is found to influence landscape structure. A fundamental relationship necessary for perfectly straight gradient-based control trajectories is derived, wherein the gradient on the quantum control landscape must be an eigenfunction of the Hessian. This relation is an indicator of landscape structure and may provide a means to identify physical conditions when control trajectories can achieve perfect linearity. The collective favorable landscape topology and structure provide a foundation to understand why optimal quantum control can be readily achieved.
Optimized Reactive Power Compensation Using Fuzzy Logic Controller
NASA Astrophysics Data System (ADS)
George, S.; Mini, K. N.; Supriya, K.
2015-03-01
Reactive power flow in a long transmission line plays a vital role in power transfer capability and voltage stability in power system. Traditionally, shunt connected compensators are used to control reactive power in long transmission line. Thyristor controlled reactor is used to control reactive power under lightly loaded condition. By controlling firing angle of thyristor, it is possible to control reactive power in the transmission lines. However, thyristor controlled reactor will inject harmonic current into the system. An attempt to reduce reactive power injection will increase harmonic distortion in the line current and vice versa. Thus, there is a trade-off between reactive power injection and harmonics in current. By optimally controlling the reactive power injection, harmonics in current can be brought within the specified limit. In this paper, a Fuzzy Logic Controller is implemented to obtain optimal control of reactive power of the compensator to maintain voltage and harmonic in current within the limits. An algorithm which optimizes the firing angle in each fuzzy subset by calculating the rank of feasible firing angles is proposed for the construction of rules in Fuzzy Logic Controller. The novelty of the algorithm is that it uses a simple error formula for the calculation of the rank of the feasible firing angles in each fuzzy subset.
Optimal Robust Motion Controller Design Using Multiobjective Genetic Algorithm
Svečko, Rajko
2014-01-01
This paper describes the use of a multiobjective genetic algorithm for robust motion controller design. Motion controller structure is based on a disturbance observer in an RIC framework. The RIC approach is presented in the form with internal and external feedback loops, in which an internal disturbance rejection controller and an external performance controller must be synthesised. This paper involves novel objectives for robustness and performance assessments for such an approach. Objective functions for the robustness property of RIC are based on simple even polynomials with nonnegativity conditions. Regional pole placement method is presented with the aims of controllers' structures simplification and their additional arbitrary selection. Regional pole placement involves arbitrary selection of central polynomials for both loops, with additional admissible region of the optimized pole location. Polynomial deviation between selected and optimized polynomials is measured with derived performance objective functions. A multiobjective function is composed of different unrelated criteria such as robust stability, controllers' stability, and time-performance indexes of closed loops. The design of controllers and multiobjective optimization procedure involve a set of the objectives, which are optimized simultaneously with a genetic algorithm—differential evolution. PMID:24987749
Optimal robust motion controller design using multiobjective genetic algorithm.
Sarjaš, Andrej; Svečko, Rajko; Chowdhury, Amor
2014-01-01
This paper describes the use of a multiobjective genetic algorithm for robust motion controller design. Motion controller structure is based on a disturbance observer in an RIC framework. The RIC approach is presented in the form with internal and external feedback loops, in which an internal disturbance rejection controller and an external performance controller must be synthesised. This paper involves novel objectives for robustness and performance assessments for such an approach. Objective functions for the robustness property of RIC are based on simple even polynomials with nonnegativity conditions. Regional pole placement method is presented with the aims of controllers' structures simplification and their additional arbitrary selection. Regional pole placement involves arbitrary selection of central polynomials for both loops, with additional admissible region of the optimized pole location. Polynomial deviation between selected and optimized polynomials is measured with derived performance objective functions. A multiobjective function is composed of different unrelated criteria such as robust stability, controllers' stability, and time-performance indexes of closed loops. The design of controllers and multiobjective optimization procedure involve a set of the objectives, which are optimized simultaneously with a genetic algorithm-differential evolution. PMID:24987749
Efficient algorithms for the laboratory discovery of optimal quantum controls
NASA Astrophysics Data System (ADS)
Turinici, Gabriel; Le Bris, Claude; Rabitz, Herschel
2004-07-01
The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.
Solving bi-objective optimal control problems with rectangular framing
NASA Astrophysics Data System (ADS)
Wijaya, Karunia Putra; Götz, Thomas
2016-06-01
Optimization problems, e.g. arising from epidemiology models, often ask for solutions minimizing multi-criteria objective functions. In this paper we discuss a novel approach for solving bi-objective optimal control problems. The set of non-dominated points is constructed via a decreasing sequence of rectangles. Particular attention is paid to a problem with disconnected set of non-dominated points. Several examples from epidemiology are investigated and show the applicability of the method.
Optimizing laser pulses to control photoinduced states of matter
NASA Astrophysics Data System (ADS)
Hwang, Bin; Duxbury, P. M.
2016-10-01
We present a computational approach to optimal laser pulse shaping directed at accessing novel photoinduced states of matter. Results are illustrated for a simple charge-density wave (CDW) model where the targeted effect is CDW melting and negative temperature states. Optimal control is implemented using the Krotov method applied to nonequilibrium tight-binding Hamiltonians where the laser pulse is introduced using the Peierls substitution, and we demonstrate monotonic convergence for this class of problem.
Approximate optimal tracking control for near-surface AUVs with wave disturbances
NASA Astrophysics Data System (ADS)
Yang, Qing; Su, Hao; Tang, Gongyou
2016-10-01
This paper considers the optimal trajectory tracking control problem for near-surface autonomous underwater vehicles (AUVs) in the presence of wave disturbances. An approximate optimal tracking control (AOTC) approach is proposed. Firstly, a six-degrees-of-freedom (six-DOF) AUV model with its body-fixed coordinate system is decoupled and simplified and then a nonlinear control model of AUVs in the vertical plane is given. Also, an exosystem model of wave disturbances is constructed based on Hirom approximation formula. Secondly, the time-parameterized desired trajectory which is tracked by the AUV's system is represented by the exosystem. Then, the coupled two-point boundary value (TPBV) problem of optimal tracking control for AUVs is derived from the theory of quadratic optimal control. By using a recently developed successive approximation approach to construct sequences, the coupled TPBV problem is transformed into a problem of solving two decoupled linear differential sequences of state vectors and adjoint vectors. By iteratively solving the two equation sequences, the AOTC law is obtained, which consists of a nonlinear optimal feedback item, an expected output tracking item, a feedforward disturbances rejection item, and a nonlinear compensatory term. Furthermore, a wave disturbances observer model is designed in order to solve the physically realizable problem. Simulation is carried out by using the Remote Environmental Unit (REMUS) AUV model to demonstrate the effectiveness of the proposed algorithm.
Optimal periodic control for spacecraft pointing and attitude determination
NASA Technical Reports Server (NTRS)
Pittelkau, Mark E.
1993-01-01
A new approach to autonomous magnetic roll/yaw control of polar-orbiting, nadir-pointing momentum bias spacecraft is considered as the baseline attitude control system for the next Tiros series. It is shown that the roll/yaw dynamics with magnetic control are periodically time varying. An optimal periodic control law is then developed. The control design features a state estimator that estimates attitude, attitude rate, and environmental torque disturbances from Earth sensor and sun sensor measurements; no gyros are needed. The state estimator doubles as a dynamic attitude determination and prediction function. In addition to improved performance, the optimal controller allows a much smaller momentum bias than would otherwise be necessary. Simulation results are given.
Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers
NASA Technical Reports Server (NTRS)
Crassidis, John L.; Vadali, Srinivas R.; Markley, F. Landis
1999-01-01
An optimal control approach using variable-structure (sliding-mode) tracking for large angle spacecraft maneuvers is presented. The approach expands upon a previously derived regulation result using a quaternion parameterization for the kinematic equations of motion. This parameterization is used since it is free of singularities. The main contribution of this paper is the utilization of a simple term in the control law that produces a maneuver to the reference attitude trajectory in the shortest distance. Also, a multiplicative error quaternion between the desired and actual attitude is used to derive the control law. Sliding-mode switching surfaces are derived using an optimal-control analysis. Control laws are given using either external torque commands or reaction wheel commands. Global asymptotic stability is shown for both cases using a Lyapunov analysis. Simulation results are shown which use the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft.
Optimization in Hardy space and the problem of controller optimization (Review)
NASA Astrophysics Data System (ADS)
Larin, V. B.
1992-02-01
Problems related to optimization in Hardy space H2 are examined with particular reference to approaches based on the Wiener-Kolmogorov and Wiener-Hopf methods. The existing parametrization procedures for sets of stabilizing controllers are compared. The use of the LQG approach and H2 optimization in applied problems is discussed using specific examples. Consideration is also given to the solution of the Riccati algebraic equation and factorization of matrix polynomials.
NASA Astrophysics Data System (ADS)
Kapur, P. K.; Pham, Hoang; Chanda, Udayan; Kumar, Vijay
2013-09-01
Allocation of efforts to a software development project during the testing phase is a multifaceted task for software managers. The challenges become stiffer when the nature of the development process is considered in the dynamic environment. Many software reliability growth models have been proposed in last decade to minimise the total testing-effort expenditures, but mostly under static assumption. The main purpose of this article is to investigate an optimal resource allocation plan to minimise the cost of software during the testing and operational phase under dynamic condition. An elaborate optimisation policy based on the optimal control theory is proposed and numerical examples are illustrated. This article also studies the optimal resource allocation problems for various conditions by examining the behaviour of the model parameters and also suggests policy for the optimal release time of the software. The experimental results greatly help us to identify the contribution of each selected parameter and its weight.
A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour
NASA Technical Reports Server (NTRS)
Leyland, Jane Anne
1996-01-01
Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.
Advanced launch system trajectory optimization using suboptimal control
NASA Technical Reports Server (NTRS)
Shaver, Douglas A.; Hull, David G.
1993-01-01
The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations.
Optimal control of switched linear systems based on Migrant Particle Swarm Optimization algorithm
NASA Astrophysics Data System (ADS)
Xie, Fuqiang; Wang, Yongji; Zheng, Zongzhun; Li, Chuanfeng
2009-10-01
The optimal control problem for switched linear systems with internally forced switching has more constraints than with externally forced switching. Heavy computations and slow convergence in solving this problem is a major obstacle. In this paper we describe a new approach for solving this problem, which is called Migrant Particle Swarm Optimization (Migrant PSO). Imitating the behavior of a flock of migrant birds, the Migrant PSO applies naturally to both continuous and discrete spaces, in which definitive optimization algorithm and stochastic search method are combined. The efficacy of the proposed algorithm is illustrated via a numerical example.
NASA Astrophysics Data System (ADS)
Yan, Zuomao; Lu, Fangxia
2016-08-01
In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.
ERIC Educational Resources Information Center
Cook, Desmond L.
This document, one of a series of reports examining the possible contribution of other disciplines to evaluation methodology, describes the major elements of general systems theory (GST), cybernetics theory (CT) and management control theory (MCT). The author suggests that MCT encapsulates major concerns of evaluation since it reveals that…
Damage control resuscitation: history, theory and technique
Ball, Chad G.
2014-01-01
Damage control resuscitation (DCR) represents the natural evolution of the initial concept of damage control surgery. It currently includes early blood product transfusion, immediate arrest and/or temporization of ongoing hemorrhage (i.e., temporary intravascular shunts and/or balloon tamponade) as well as restoration of blood volume and physiologic/hematologic stability. As a result, DCR addresses the early coagulopathy of trauma, avoids massive crystalloid resuscitation and leaves the peritoneal cavity open when a patient approaches physiologic exhaustion without improvement. This concept also applies to severe injuries within anatomical transition zones as well as extremities. This review will discuss each of these concepts in detail. PMID:24461267
Optimal control, investment and utilization schemes for energy storage under uncertainty
NASA Astrophysics Data System (ADS)
Mirhosseini, Niloufar Sadat
Energy storage has the potential to offer new means for added flexibility on the electricity systems. This flexibility can be used in a number of ways, including adding value towards asset management, power quality and reliability, integration of renewable resources and energy bill savings for the end users. However, uncertainty about system states and volatility in system dynamics can complicate the question of when to invest in energy storage and how best to manage and utilize it. This work proposes models to address different problems associated with energy storage within a microgrid, including optimal control, investment, and utilization. Electric load, renewable resources output, storage technology cost and electricity day-ahead and spot prices are the factors that bring uncertainty to the problem. A number of analytical methodologies have been adopted to develop the aforementioned models. Model Predictive Control and discretized dynamic programming, along with a new decomposition algorithm are used to develop optimal control schemes for energy storage for two different levels of renewable penetration. Real option theory and Monte Carlo simulation, coupled with an optimal control approach, are used to obtain optimal incremental investment decisions, considering multiple sources of uncertainty. Two stage stochastic programming is used to develop a novel and holistic methodology, including utilization of energy storage within a microgrid, in order to optimally interact with energy market. Energy storage can contribute in terms of value generation and risk reduction for the microgrid. The integration of the models developed here are the basis for a framework which extends from long term investments in storage capacity to short term operational control (charge/discharge) of storage within a microgrid. In particular, the following practical goals are achieved: (i) optimal investment on storage capacity over time to maximize savings during normal and emergency
An optimal performance control scheme for a 3D crane
NASA Astrophysics Data System (ADS)
Maghsoudi, Mohammad Javad; Mohamed, Z.; Husain, A. R.; Tokhi, M. O.
2016-01-01
This paper presents an optimal performance control scheme for control of a three dimensional (3D) crane system including a Zero Vibration shaper which considers two control objectives concurrently. The control objectives are fast and accurate positioning of a trolley and minimum sway of a payload. A complete mathematical model of a lab-scaled 3D crane is simulated in Simulink. With a specific cost function the proposed controller is designed to cater both control objectives similar to a skilled operator. Simulation and experimental studies on a 3D crane show that the proposed controller has better performance as compared to a sequentially tuned PID-PID anti swing controller. The controller provides better position response with satisfactory payload sway in both rail and trolley responses. Experiments with different payloads and cable lengths show that the proposed controller is robust to changes in payload with satisfactory responses.
Force control of a tri-layer conducting polymer actuator using optimized fuzzy logic control
NASA Astrophysics Data System (ADS)
Itik, Mehmet; Sabetghadam, Mohammadreza; Alici, Gursel
2014-12-01
Conducting polymers actuators (CPAs) are potential candidates for replacing conventional actuators in various fields, such as robotics and biomedical engineering, due to their advantageous properties, which includes their low cost, light weight, low actuation voltage and biocompatibility. As these actuators are very suitable for use in micro-nano manipulation and in injection devices in which the magnitude of the force applied to the target is of crucial importance, the force generated by CPAs needs to be accurately controlled. In this paper, a fuzzy logic (FL) controller with a Mamdani inference system is designed to control the blocking force of a trilayer CPA with polypyrrole electrodes, which operates in air. The particle swarm optimization (PSO) method is employed to optimize the controller’s membership function parameters and therefore enhance the performance of the FL controller. An adaptive neuro-fuzzy inference system model, which can capture the nonlinear dynamics of the actuator, is utilized in the optimization process. The optimized Mamdani FL controller is then implemented on the CPA experimentally, and its performance is compared with a non-optimized fuzzy controller as well as with those obtained from a conventional PID controller. The results presented indicate that the blocking force at the tip of the CPA can be effectively controlled by the optimized FL controller, which shows excellent transient and steady state characteristics but increases the control voltage compared to the non-optimized fuzzy controllers.
Momentary maximizing and optimal foraging theories of performance on concurrent VR schedules.
MacDonall, James S; Goodell, Jon; Juliano, Anthony
2006-06-01
Optimal foraging theory proposes that animals obtain the highest rate of reinforcers for the least effort and momentary maximizing theory proposes that animals make the response that at that instant is most likely to be reinforced. While each theory may account for matching on concurrent schedules, the data supporting each theory are weak. Two experiments assessed these theories by considering concurrent choice as consisting of two pairs of stay and switch schedules. Symmetrical arrangements, which are equivalent to standard concurrent schedules, maintained behavior described by the generalized matching law. Weighted arrangements, in which the programmed rate of earning reinforcers was always greater at one alternative, maintained behavior that was biased towards the weighted alternative, yet the bias was less than that predicted by optimal foraging theory. Asymmetrical arrangements, in which the stay and switch schedules operating at an alternative are the same, maintained behavior that favored one alternative, even though momentary maximizing predicted indifference. The generalized matching law poorly described each rat's pooled data from all conditions but these data were described by an equation based on the stay and switch reinforcers earned per-visit and included elements of optimal foraging and momentary maximizing theories of choice.
Multi-objective optimization for model predictive control.
Wojsznis, Willy; Mehta, Ashish; Wojsznis, Peter; Thiele, Dirk; Blevins, Terry
2007-06-01
This paper presents a technique of multi-objective optimization for Model Predictive Control (MPC) where the optimization has three levels of the objective function, in order of priority: handling constraints, maximizing economics, and maintaining control. The greatest weights are assigned dynamically to control or constraint variables that are predicted to be out of their limits. The weights assigned for economics have to out-weigh those assigned for control objectives. Control variables (CV) can be controlled at fixed targets or within one- or two-sided ranges around the targets. Manipulated Variables (MV) can have assigned targets too, which may be predefined values or current actual values. This MV functionality is extremely useful when economic objectives are not defined for some or all the MVs. To achieve this complex operation, handle process outputs predicted to go out of limits, and have a guaranteed solution for any condition, the technique makes use of the priority structure, penalties on slack variables, and redefinition of the constraint and control model. An engineering implementation of this approach is shown in the MPC embedded in an industrial control system. The optimization and control of a distillation column, the standard Shell heavy oil fractionator (HOF) problem, is adequately achieved with this MPC. PMID:17382946
A duality framework for stochastic optimal control of complex systems
Malikopoulos, Andreas A.
2016-01-01
In this study, we address the problem of minimizing the long-run expected average cost of a complex system consisting of interactive subsystems. We formulate a multiobjective optimization problem of the one-stage expected costs of the subsystems and provide a duality framework to prove that the control policy yielding the Pareto optimal solution minimizes the average cost criterion of the system. We provide the conditions of existence and a geometric interpretation of the solution. For practical situations having constraints consistent with those studied here, our results imply that the Pareto control policy may be of value when we seek to derivemore » online the optimal control policy in complex systems.« less
Optimal Control for Coupled Near-Field/Far-Field Domains
NASA Astrophysics Data System (ADS)
Chen, Guoquan; Collis, S. Scott; Ghayour, Kaveh; Heinkenschloss, Matthias
2002-11-01
A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier--Stokes solver coupled with a far-field wave equation using a discontinuous Galerkin formulation. In this approach, the coupling of near-field and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinear flow effects and noise sources. For optimal control, gradient formation is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. The formulation and implementation of the state and adjoint problems will be presented along with preliminary results. This computational framework will be applied in the future to study optimal boundary control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing.
Single step optimization of manipulator maneuvers with variable structure control
NASA Technical Reports Server (NTRS)
Chen, N.; Dwyer, T. A. W., III
1987-01-01
One step ahead optimization has been recently proposed for spacecraft attitude maneuvers as well as for robot manipulator maneuvers. Such a technique yields a discrete time control algorithm implementable as a sequence of state-dependent, quadratic programming problems for acceleration optimization. Its sensitivity to model accuracy, for the required inversion of the system dynamics, is shown in this paper to be alleviated by a fast variable structure control correction, acting between the sampling intervals of the slow one step ahead discrete time acceleration command generation algorithm. The slow and fast looping concept chosen follows that recently proposed for optimal aiming strategies with variable structure control. Accelerations required by the VSC correction are reserved during the slow one step ahead command generation so that the ability to overshoot the sliding surface is guaranteed.
Motor Control Theories and Their Applications
Latash, Mark L.; Levin, Mindy F.; Scholz, John P.; Schöner, Gregor
2010-01-01
Summary We describe several influential hypotheses in the field of motor control including the equilibrium-point (referent configuration) hypothesis, the uncontrolled manifold hypothesis, and the idea of synergies based on the principle of motor abundance. The equilibrium-point hypothesis is based on the idea of control with thresholds for activation of neuronal pools; it provides a framework for analysis of both voluntary and involuntary movements. In particular, control of a single muscle can be adequately described with changes in the threshold of motor unit recruitment during slow muscle stretch (threshold of the tonic stretch reflex). Unlike the ideas of internal models, the equilibrium-point hypothesis does not assume neural computations of mechanical variables. The uncontrolled manifold hypothesis is based on the dynamic system approach to movements; it offers a toolbox to analyze synergic changes within redundant sets of elements related to stabilization of potentially important performance variables. The referent configuration hypothesis and the principle of abundance can be naturally combined into a single coherent scheme of control of multi-element systems. A body of experimental data on healthy persons and patients with movement disorders are reviewed in support of the mentioned hypotheses. In particular, movement disorders associated with spasticity are considered as consequences of an impaired ability to shift threshold of the tonic stretch reflex within the whole normal range. Technical details and applications of the mentioned hypotheses to studies of motor learning are described. We view the mentioned hypotheses as the most promising ones in the field of motor control, based on a solid physical and neurophysiological foundation. PMID:20944446
Derivative Trade Optimizing Model Utilizing GP Based on Behavioral Finance Theory
NASA Astrophysics Data System (ADS)
Matsumura, Koki; Kawamoto, Masaru
This paper proposed a new technique which makes the strategy trees for the derivative (option) trading investment decision based on the behavioral finance theory and optimizes it using evolutionary computation, in order to achieve high profitability. The strategy tree uses a technical analysis based on a statistical, experienced technique for the investment decision. The trading model is represented by various technical indexes, and the strategy tree is optimized by the genetic programming(GP) which is one of the evolutionary computations. Moreover, this paper proposed a method using the prospect theory based on the behavioral finance theory to set psychological bias for profit and deficit and attempted to select the appropriate strike price of option for the higher investment efficiency. As a result, this technique produced a good result and found the effectiveness of this trading model by the optimized dealings strategy.
A multiple objective optimization approach to quality control
NASA Technical Reports Server (NTRS)
Seaman, Christopher Michael
1991-01-01
The use of product quality as the performance criteria for manufacturing system control is explored. The goal in manufacturing, for economic reasons, is to optimize product quality. The problem is that since quality is a rather nebulous product characteristic, there is seldom an analytic function that can be used as a measure. Therefore standard control approaches, such as optimal control, cannot readily be applied. A second problem with optimizing product quality is that it is typically measured along many dimensions: there are many apsects of quality which must be optimized simultaneously. Very often these different aspects are incommensurate and competing. The concept of optimality must now include accepting tradeoffs among the different quality characteristics. These problems are addressed using multiple objective optimization. It is shown that the quality control problem can be defined as a multiple objective optimization problem. A controller structure is defined using this as the basis. Then, an algorithm is presented which can be used by an operator to interactively find the best operating point. Essentially, the algorithm uses process data to provide the operator with two pieces of information: (1) if it is possible to simultaneously improve all quality criteria, then determine what changes to the process input or controller parameters should be made to do this; and (2) if it is not possible to improve all criteria, and the current operating point is not a desirable one, select a criteria in which a tradeoff should be made, and make input changes to improve all other criteria. The process is not operating at an optimal point in any sense if no tradeoff has to be made to move to a new operating point. This algorithm ensures that operating points are optimal in some sense and provides the operator with information about tradeoffs when seeking the best operating point. The multiobjective algorithm was implemented in two different injection molding scenarios
A stochastic optimal feedforward and feedback control methodology for superagility
NASA Technical Reports Server (NTRS)
Halyo, Nesim; Direskeneli, Haldun; Taylor, Deborah B.
1992-01-01
A new control design methodology is developed: Stochastic Optimal Feedforward and Feedback Technology (SOFFT). Traditional design techniques optimize a single cost function (which expresses the design objectives) to obtain both the feedforward and feedback control laws. This approach places conflicting demands on the control law such as fast tracking versus noise atttenuation/disturbance rejection. In the SOFFT approach, two cost functions are defined. The feedforward control law is designed to optimize one cost function, the feedback optimizes the other. By separating the design objectives and decoupling the feedforward and feedback design processes, both objectives can be achieved fully. A new measure of command tracking performance, Z-plots, is also developed. By analyzing these plots at off-nominal conditions, the sensitivity or robustness of the system in tracking commands can be predicted. Z-plots provide an important tool for designing robust control systems. The Variable-Gain SOFFT methodology was used to design a flight control system for the F/A-18 aircraft. It is shown that SOFFT can be used to expand the operating regime and provide greater performance (flying/handling qualities) throughout the extended flight regime. This work was performed under the NASA SBIR program. ICS plans to market the software developed as a new module in its commercial CACSD software package: ACET.
Multidisciplinary optimization of controlled space structures with global sensitivity equations
NASA Technical Reports Server (NTRS)
Padula, Sharon L.; James, Benjamin B.; Graves, Philip C.; Woodard, Stanley E.
1991-01-01
A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.
Quadratic Optimization in the Problems of Active Control of Sound
NASA Technical Reports Server (NTRS)
Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).
Random matrix theory for portfolio optimization: a stability approach
NASA Astrophysics Data System (ADS)
Sharifi, S.; Crane, M.; Shamaie, A.; Ruskin, H.
2004-04-01
We apply random matrix theory (RMT) to an empirically measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally, we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C that has many advantages, from the stability point of view, over the existing method of cleaning.
An inverter/controller subsystem optimized for photovoltaic applications
NASA Technical Reports Server (NTRS)
Pickrell, R. L.; Osullivan, G.; Merrill, W. C.
1978-01-01
Conversion of solar array dc power to ac power stimulated the specification, design, and simulation testing of an inverter/controller subsystem tailored to the photovoltaic power source characteristics. Optimization of the inverter/controller design is discussed as part of an overall photovoltaic power system designed for maximum energy extraction from the solar array. The special design requirements for the inverter/ controller include: a power system controller (PSC) to control continuously the solar array operating point at the maximum power level based on variable solar insolation and cell temperatures; and an inverter designed for high efficiency at rated load and low losses at light loadings to conserve energy.
The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter
NASA Technical Reports Server (NTRS)
Townsend, Barbara K.
1986-01-01
A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.
Torque-based optimal acceleration control for electric vehicle
NASA Astrophysics Data System (ADS)
Lu, Dongbin; Ouyang, Minggao
2014-03-01
The existing research of the acceleration control mainly focuses on an optimization of the velocity trajectory with respect to a criterion formulation that weights acceleration time and fuel consumption. The minimum-fuel acceleration problem in conventional vehicle has been solved by Pontryagin's maximum principle and dynamic programming algorithm, respectively. The acceleration control with minimum energy consumption for battery electric vehicle(EV) has not been reported. In this paper, the permanent magnet synchronous motor(PMSM) is controlled by the field oriented control(FOC) method and the electric drive system for the EV(including the PMSM, the inverter and the battery) is modeled to favor over a detailed consumption map. The analytical algorithm is proposed to analyze the optimal acceleration control and the optimal torque versus speed curve in the acceleration process is obtained. Considering the acceleration time, a penalty function is introduced to realize a fast vehicle speed tracking. The optimal acceleration control is also addressed with dynamic programming(DP). This method can solve the optimal acceleration problem with precise time constraint, but it consumes a large amount of computation time. The EV used in simulation and experiment is a four-wheel hub motor drive electric vehicle. The simulation and experimental results show that the required battery energy has little difference between the acceleration control solved by analytical algorithm and that solved by DP, and is greatly reduced comparing with the constant pedal opening acceleration. The proposed analytical and DP algorithms can minimize the energy consumption in EV's acceleration process and the analytical algorithm is easy to be implemented in real-time control.
Control design variable linking for optimization of structural/control systems
NASA Technical Reports Server (NTRS)
Jin, I. M.; Schmit, L. A.
1991-01-01
In this study a method is presented to integrate the design space of structural/control system optimization problems in the case of state feedback control. Conventional structural sizing variables and elements of the feedback gain matrix are both treated as strictly independent design variables in the optimization by extending design variable linking concepts to the control gains. Examples which involve a variety of behavior constraints, including dynamic transient response and control force limits, are effectively solved by using the method presented.
Optimizing Locomotion Controllers Using Biologically-Based Actuators and Objectives
Wang, Jack M.; Hamner, Samuel R.; Delp, Scott L.; Koltun, Vladlen
2015-01-01
We present a technique for automatically synthesizing walking and running controllers for physically-simulated 3D humanoid characters. The sagittal hip, knee, and ankle degrees-of-freedom are actuated using a set of eight Hill-type musculotendon models in each leg, with biologically-motivated control laws. The parameters of these control laws are set by an optimization procedure that satisfies a number of locomotion task terms while minimizing a biological model of metabolic energy expenditure. We show that the use of biologically-based actuators and objectives measurably increases the realism of gaits generated by locomotion controllers that operate without the use of motion capture data, and that metabolic energy expenditure provides a simple and unifying measurement of effort that can be used for both walking and running control optimization. PMID:26251560
Fuel optimal control of an experimental multi-mode system
NASA Technical Reports Server (NTRS)
Redmond, J.; Mayer, J. L.; Silverberg, L.
1992-01-01
In this paper, the dynamic characteristics associated with the fuel optimal control of a harmonic oscillator are utilized in the development of a near fuel optimal feedback control strategy for spacecraft vibration suppression. In this scheme, single level thrust actuators are governed by recursive computations of the standard deviations of displacement and velocity at the actuator's locations. The algorithm was tested on an experimental structure possessing a significant number of flexible body modes. The structure's response to both single and multiple mode excitation is presented.
Optimal control of underactuated mechanical systems: A geometric approach
NASA Astrophysics Data System (ADS)
Colombo, Leonardo; Martín De Diego, David; Zuccalli, Marcela
2010-08-01
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics of the optimal control problem. These developments will allow us to develop a new class of geometric integrators based on discrete variational calculus.
Optimal placement of active elements in control augmented structural synthesis
NASA Technical Reports Server (NTRS)
Sepulveda, A. E.; Jin, I. M.; Schmit, L. A., Jr.
1992-01-01
A methodology for structural/control synthesis is presented in which the optimal location of active members is treated in terms of (0,1) variables. Structural member sizes, control gains and (0,1) placement variables are treated simultaneously as design variables. Optimization is carried out by generating and solving a sequence of explicit approximate problems using a branch and bound strategy. Intermediate design variable and intermediate response quantity concepts are used to enhance the quality of the approximate design problems. Numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.
Optimal control of quaternion propagation errors in spacecraft navigation
NASA Technical Reports Server (NTRS)
Vathsal, S.
1986-01-01
Optimal control techniques are used to drive the numerical error (truncation, roundoff, commutation) in computing the quaternion vector to zero. The normalization of the quaternion is carried out by appropriate choice of a performance index, which can be optimized. The error equations are derived from Friedland's (1978) theoretical development, and a matrix Riccati equation results for the computation of the gain matrix. Simulation results show that a high precision of the order of 10 to the -12th can be obtained using this technique in meeting the q(T)q=1 constraint. The performance of the estimator in the presence of the feedback control that maintains the normalization, is studied.
Control and structural optimization for maneuvering large spacecraft
NASA Technical Reports Server (NTRS)
Chun, H. M.; Turner, J. D.; Yu, C. C.
1990-01-01
Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment.
Occupant-responsive optimal control of smart facade systems
NASA Astrophysics Data System (ADS)
Park, Cheol-Soo
Windows provide occupants with daylight, direct sunlight, visual contact with the outside and a feeling of openness. Windows enable the use of daylighting and offer occupants a outside view. Glazing may also cause a number of problems: undesired heat gain/loss in winter. An over-lit window can cause glare, which is another major complaint by occupants. Furthermore, cold or hot window surfaces induce asymmetric thermal radiation which can result in thermal discomfort. To reduce the potential problems of window systems, double skin facades and airflow window systems have been introduced in the 1970s. They typically contain interstitial louvers and ventilation openings. The current problem with double skin facades and airflow windows is that their operation requires adequate dynamic control to reach their expected performance. Many studies have recognized that only an optimal control enables these systems to truly act as active energy savers and indoor environment controllers. However, an adequate solution for this dynamic optimization problem has thus far not been developed. The primary objective of this study is to develop occupant responsive optimal control of smart facade systems. The control could be implemented as a smart controller that operates the motorized Venetian blind system and the opening ratio of ventilation openings. The objective of the control is to combine the benefits of large windows with low energy demands for heating and cooling, while keeping visual well-being and thermal comfort at an optimal level. The control uses a simulation model with an embedded optimization routine that allows occupant interaction via the Web. An occupant can access the smart controller from a standard browser and choose a pre-defined mode (energy saving mode, visual comfort mode, thermal comfort mode, default mode, nighttime mode) or set a preferred mode (user-override mode) by moving preference sliders on the screen. The most prominent feature of these systems is the
Optimal control for stochastic systems with polynomial chaos
NASA Astrophysics Data System (ADS)
Gallagher, David James
Assuring robustness of control system performance against model uncertainty is a significant component of control design. Current methods for developing a robust controller, however, are typically either too conservative or too computationally expensive. This thesis uses generalized polynomial chaos alongside finite-horizon optimal control as a new method of robust control design for a stochastic system. Since the equations for the mean and variance of the response can be expressed in terms of coefficients from a polynomial chaos expansion, optimizing a polynomial chaos expansion can be used to optimize the mean and variance, thus providing robust responses in a stochastic system. This thesis first provides a review of the concepts and literature then the rationale as well as the derivation of the proposed robust control method. Three examples are given to show the effectiveness of the new control method and are discussed. In particular, the final example demonstrates the applicability of using polynomial chaos to provide robust control for a stochastic soft landing problem.
Automated design of multiphase space missions using hybrid optimal control
NASA Astrophysics Data System (ADS)
Chilan, Christian Miguel
A modern space mission is assembled from multiple phases or events such as impulsive maneuvers, coast arcs, thrust arcs and planetary flybys. Traditionally, a mission planner would resort to intuition and experience to develop a sequence of events for the multiphase mission and to find the space trajectory that minimizes propellant use by solving the associated continuous optimal control problem. This strategy, however, will most likely yield a sub-optimal solution, as the problem is sophisticated for several reasons. For example, the number of events in the optimal mission structure is not known a priori and the system equations of motion change depending on what event is current. In this work a framework for the automated design of multiphase space missions is presented using hybrid optimal control (HOC). The method developed uses two nested loops: an outer-loop that handles the discrete dynamics and finds the optimal mission structure in terms of the categorical variables, and an inner-loop that performs the optimization of the corresponding continuous-time dynamical system and obtains the required control history. Genetic algorithms (GA) and direct transcription with nonlinear programming (NLP) are introduced as methods of solution for the outer-loop and inner-loop problems, respectively. Automation of the inner-loop, continuous optimal control problem solver, required two new technologies. The first is a method for the automated construction of the NLP problems resulting from the use of a direct solver for systems with different structures, including different numbers of categorical events. The method assembles modules, consisting of parameters and constraints appropriate to each event, sequentially according to the given mission structure. The other new technology is for a robust initial guess generator required by the inner-loop NLP problem solver. Two new methods were developed for cases including low-thrust trajectories. The first method, based on GA
Optimization and Control of Cyber-Physical Vehicle Systems.
Bradley, Justin M; Atkins, Ella M
2015-01-01
A cyber-physical system (CPS) is composed of tightly-integrated computation, communication and physical elements. Medical devices, buildings, mobile devices, robots, transportation and energy systems can benefit from CPS co-design and optimization techniques. Cyber-physical vehicle systems (CPVSs) are rapidly advancing due to progress in real-time computing, control and artificial intelligence. Multidisciplinary or multi-objective design optimization maximizes CPS efficiency, capability and safety, while online regulation enables the vehicle to be responsive to disturbances, modeling errors and uncertainties. CPVS optimization occurs at design-time and at run-time. This paper surveys the run-time cooperative optimization or co-optimization of cyber and physical systems, which have historically been considered separately. A run-time CPVS is also cooperatively regulated or co-regulated when cyber and physical resources are utilized in a manner that is responsive to both cyber and physical system requirements. This paper surveys research that considers both cyber and physical resources in co-optimization and co-regulation schemes with applications to mobile robotic and vehicle systems. Time-varying sampling patterns, sensor scheduling, anytime control, feedback scheduling, task and motion planning and resource sharing are examined. PMID:26378541
Optimization and Control of Cyber-Physical Vehicle Systems.
Bradley, Justin M; Atkins, Ella M
2015-09-11
A cyber-physical system (CPS) is composed of tightly-integrated computation, communication and physical elements. Medical devices, buildings, mobile devices, robots, transportation and energy systems can benefit from CPS co-design and optimization techniques. Cyber-physical vehicle systems (CPVSs) are rapidly advancing due to progress in real-time computing, control and artificial intelligence. Multidisciplinary or multi-objective design optimization maximizes CPS efficiency, capability and safety, while online regulation enables the vehicle to be responsive to disturbances, modeling errors and uncertainties. CPVS optimization occurs at design-time and at run-time. This paper surveys the run-time cooperative optimization or co-optimization of cyber and physical systems, which have historically been considered separately. A run-time CPVS is also cooperatively regulated or co-regulated when cyber and physical resources are utilized in a manner that is responsive to both cyber and physical system requirements. This paper surveys research that considers both cyber and physical resources in co-optimization and co-regulation schemes with applications to mobile robotic and vehicle systems. Time-varying sampling patterns, sensor scheduling, anytime control, feedback scheduling, task and motion planning and resource sharing are examined.
Optimization and Control of Cyber-Physical Vehicle Systems
Bradley, Justin M.; Atkins, Ella M.
2015-01-01
A cyber-physical system (CPS) is composed of tightly-integrated computation, communication and physical elements. Medical devices, buildings, mobile devices, robots, transportation and energy systems can benefit from CPS co-design and optimization techniques. Cyber-physical vehicle systems (CPVSs) are rapidly advancing due to progress in real-time computing, control and artificial intelligence. Multidisciplinary or multi-objective design optimization maximizes CPS efficiency, capability and safety, while online regulation enables the vehicle to be responsive to disturbances, modeling errors and uncertainties. CPVS optimization occurs at design-time and at run-time. This paper surveys the run-time cooperative optimization or co-optimization of cyber and physical systems, which have historically been considered separately. A run-time CPVS is also cooperatively regulated or co-regulated when cyber and physical resources are utilized in a manner that is responsive to both cyber and physical system requirements. This paper surveys research that considers both cyber and physical resources in co-optimization and co-regulation schemes with applications to mobile robotic and vehicle systems. Time-varying sampling patterns, sensor scheduling, anytime control, feedback scheduling, task and motion planning and resource sharing are examined. PMID:26378541
Neural network based optimal control of HVAC&R systems
NASA Astrophysics Data System (ADS)
Ning, Min
Heating, Ventilation, Air-Conditioning and Refrigeration (HVAC&R) systems have wide applications in providing a desired indoor environment for different types of buildings. It is well acknowledged that 30%-40% of the total energy generated is consumed by buildings and HVAC&R systems alone account for more than 50% of the building energy consumption. Low operational efficiency especially under partial load conditions and poor control are part of reasons for such high energy consumption. To improve energy efficiency, HVAC&R systems should be properly operated to maintain a comfortable and healthy indoor environment under dynamic ambient and indoor conditions with the least energy consumption. This research focuses on the optimal operation of HVAC&R systems. The optimization problem is formulated and solved to find the optimal set points for the chilled water supply temperature, discharge air temperature and AHU (air handling unit) fan static pressure such that the indoor environment is maintained with the least chiller and fan energy consumption. To achieve this objective, a dynamic system model is developed first to simulate the system behavior under different control schemes and operating conditions. The system model is modular in structure, which includes a water-cooled vapor compression chiller model and a two-zone VAV system model. A fuzzy-set based extended transformation approach is then applied to investigate the uncertainties of this model caused by uncertain parameters and the sensitivities of the control inputs with respect to the interested model outputs. A multi-layer feed forward neural network is constructed and trained in unsupervised mode to minimize the cost function which is comprised of overall energy cost and penalty cost when one or more constraints are violated. After training, the network is implemented as a supervisory controller to compute the optimal settings for the system. In order to implement the optimal set points predicted by the
An application of modern control theory to an elastic spacecraft
NASA Technical Reports Server (NTRS)
Larson, V.; Likins, P. W.
1976-01-01
Results are presented to illustrate the application of established procedures of linear, quadratic, Gaussian optimal estimation and control to a spacecraft with dynamically significant elastic appendages. Interpretations are provided in both time domain and frequency domain, and conclusions are drawn for a wide class of problems of flexible spacecraft attitude control.
A control-theory model for human decision-making
NASA Technical Reports Server (NTRS)
Levison, W. H.; Tanner, R. B.
1971-01-01
A model for human decision making is an adaptation of an optimal control model for pilot/vehicle systems. The models for decision and control both contain concepts of time delay, observation noise, optimal prediction, and optimal estimation. The decision making model was intended for situations in which the human bases his decision on his estimate of the state of a linear plant. Experiments are described for the following task situations: (a) single decision tasks, (b) two-decision tasks, and (c) simultaneous manual control and decision making. Using fixed values for model parameters, single-task and two-task decision performance can be predicted to within an accuracy of 10 percent. Agreement is less good for the simultaneous decision and control situation.
Using Chemicals to Optimize Conformance Control in Fractured Reservoirs
Seright, Randall S.; Liang, Jenn-Tai; Schrader, Richard; Hagstrom II, John; Liu, Jin; Wavrik, Kathryn
1999-09-27
This report describes work performed during the first year of the project, ''Using Chemicals to Optimize Conformance Control in Fractured Reservoirs.'' This research project has three objectives. The first objective is to develop a capability to predict and optimize the ability of gels to reduce permeability to water more than that to oil or gas. The second objective is to develop procedures for optimizing blocking agent placement in wells where hydraulic fractures cause channeling problems. The third objective is to develop procedures to optimize blocking agent placement in naturally fractured reservoirs. This research project consists of three tasks, each of which addresses one of the above objectives. Our work is directed at both injection wells and production wells and at vertical, horizontal, and highly deviated wells.
Computer simulation of control strategies for optimal anaerobic digestion.
Strömberg, S; Possfelt, M O; Liu, J
2013-01-01
Three previously published control strategies for anaerobic digestion were implemented in Simulink/Matlab using Anaerobic Digestion Model No. 1 (ADM1) to model the biological process. The controllers' performance were then simulated and evaluated based on their responses from five different types of process scenarios i.e. start-up and steady state performance as well as disturbances from concentration, pH and ammonia in the inflow. Of the three evaluated control strategies, the extremum-seeking variable gain controller gave the best overall performance. However, a proportional feedback controller based on the pH-level, used as a reference case in the evaluation, proved to give as good results as the extremum-seeking variable gain controller but with a lower wear on the pump. It was therefore concluded that a fast proportional control of the reactor pH is a key element for optimally controlling a low-buffering anaerobic digestion process.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
NASA Technical Reports Server (NTRS)
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
NASA Astrophysics Data System (ADS)
Ross, Steven M.
A method is presented to couple and solve the optimal control and the optimal estimation problems simultaneously, allowing systems with bearing-only sensors to maneuver to obtain observability for relative navigation without unnecessarily detracting from a primary mission. A fundamentally new approach to trajectory optimization and the dual control problem is presented, constraining polynomial approximations of the Fisher Information Matrix to provide an information gradient and allow prescription of the level of future estimation certainty required for mission accomplishment. Disturbances, modeling deficiencies, and corrupted measurements are addressed recursively using Radau pseudospectral collocation methods and sequential quadratic programming for the optimal path and an Unscented Kalman Filter for the target position estimate. The underlying real-time optimal control (RTOC) algorithm is developed, specifically addressing limitations of current techniques that lose error integration. The resulting guidance method can be applied to any bearing-only system, such as submarines using passive sonar, anti-radiation missiles, or small UAVs seeking to land on power lines for energy harvesting. System integration, variable timing methods, and discontinuity management techniques are provided for actual hardware implementation. Validation is accomplished with both simulation and flight test, autonomously landing a quadrotor helicopter on a wire.
Laboratory transferability of optimally shaped laser pulses for quantum control.
Moore Tibbetts, Katharine; Xing, Xi; Rabitz, Herschel
2014-02-21
Optimal control experiments can readily identify effective shaped laser pulses, or "photonic reagents," that achieve a wide variety of objectives. An important additional practical desire is for photonic reagent prescriptions to produce good, if not optimal, objective yields when transferred to a different system or laboratory. Building on general experience in chemistry, the hope is that transferred photonic reagent prescriptions may remain functional even though all features of a shaped pulse profile at the sample typically cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments. First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found to still produce near optimal yields on the second laser system. Third, transferring a collection of photonic reagents optimized on the first laser system to the second laser system reproduced systematic trends in photoproduct yields upon interaction with the homologous chemical family. These three transfers of photonic reagents are demonstrated to be successful upon paying reasonable attention to overall laser system characteristics. The ability to transfer photonic reagents from one laser system to another is analogous to well-established utilitarian operating procedures with traditional chemical reagents. The practical implications of the present results for experimental quantum control are discussed. PMID:24559348
Laboratory transferability of optimally shaped laser pulses for quantum control
NASA Astrophysics Data System (ADS)
Moore Tibbetts, Katharine; Xing, Xi; Rabitz, Herschel
2014-02-01
Optimal control experiments can readily identify effective shaped laser pulses, or "photonic reagents," that achieve a wide variety of objectives. An important additional practical desire is for photonic reagent prescriptions to produce good, if not optimal, objective yields when transferred to a different system or laboratory. Building on general experience in chemistry, the hope is that transferred photonic reagent prescriptions may remain functional even though all features of a shaped pulse profile at the sample typically cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments. First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found to still produce near optimal yields on the second laser system. Third, transferring a collection of photonic reagents optimized on the first laser system to the second laser system reproduced systematic trends in photoproduct yields upon interaction with the homologous chemical family. These three transfers of photonic reagents are demonstrated to be successful upon paying reasonable attention to overall laser system characteristics. The ability to transfer photonic reagents from one laser system to another is analogous to well-established utilitarian operating procedures with traditional chemical reagents. The practical implications of the present results for experimental quantum control are discussed.
Control system design for spacecraft formation flying: Theory and experiment
NASA Astrophysics Data System (ADS)
Robertson, Andrew Dunbar
Spacecraft formation flying is an enabling technology for many future space science missions, such as separated spacecraft interferometers (SSI). However the sensing, control and coordination of such instruments pose many new design challenges. SSI missions will require precise relative sensing and control, fuel-efficient, fuel-balanced operation to maximize mission life and group-level autonomy to reduce operations costs. Enabling these new formation flying capabilities requires precise relative sensing and estimation, enhanced control capabilities such as cooperative control (multiple independent spacecraft acting together), group-level formation management and informed design of a system architecture to manage distributed sensing and control-system resources. This research defines an end-to-end control system, including the key elements unique to the formation flying problem: cooperative control, relative sensing, coordination, and the control-system architecture. A new control-system design optimizes performance under typical spacecraft constraints (e.g., on-off actuators, finite fuel, limited computation power, limited contact with ground control, etc.). Standard control techniques have been extended, and new ones synthesized to meet these goals. In designing this control system, several contributions have been made to the field of spacecraft formation flying control including: an analytic two-vehicle fuel-time-optimal cooperative control algorithm, a fast numeric multi-vehicle, optimal cooperative control algorithm that can be used as a feedforward or a feedback controller, a fleet-level coordinator for autonomous fuel balancing, validation of GPS-based relative sensing for formation flying, and trade studies of the relative control and relative-estimation-architecture design problems. These research contributions are mapped to possible applications for three spacecraft formation flying missions currently in development. The lessons learned from this research
Optimal Control of a Parabolic Equation with Dynamic Boundary Condition
Hoemberg, D. Krumbiegel, K.; Rehberg, J.
2013-02-15
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.
Learning the Optimal Control of Coordinated Eye and Head Movements
Saeb, Sohrab; Weber, Cornelius; Triesch, Jochen
2011-01-01
Various optimality principles have been proposed to explain the characteristics of coordinated eye and head movements during visual orienting behavior. At the same time, researchers have suggested several neural models to underly the generation of saccades, but these do not include online learning as a mechanism of optimization. Here, we suggest an open-loop neural controller with a local adaptation mechanism that minimizes a proposed cost function. Simulations show that the characteristics of coordinated eye and head movements generated by this model match the experimental data in many aspects, including the relationship between amplitude, duration and peak velocity in head-restrained and the relative contribution of eye and head to the total gaze shift in head-free conditions. Our model is a first step towards bringing together an optimality principle and an incremental local learning mechanism into a unified control scheme for coordinated eye and head movements. PMID:22072953
NASA Technical Reports Server (NTRS)
Riedel, S. A.
1979-01-01
A method by which modern and classical control theory techniques may be integrated in a synergistic fashion and used in the design of practical flight control systems is presented. A general procedure is developed, and several illustrative examples are included. Emphasis is placed not only on the synthesis of the design, but on the assessment of the results as well. The first step is to establish the differences, distinguishing characteristics and connections between the modern and classical control theory approaches. Ultimately, this uncovers a relationship between bandwidth goals familiar in classical control and cost function weights in the equivalent optimal system. In order to obtain a practical optimal solution, it is also necessary to formulate the problem very carefully, and each choice of state, measurement and output variable must be judiciously considered. Once design goals are established and problem formulation completed, the control system is synthesized in a straightforward manner. Three steps are involved: filter-observer solution, regulator solution, and the combination of those two into the controller. Assessment of the controller permits and examination and expansion of the synthesis results.
Stochastic Maximum Principle for Optimal Control of SPDEs
Fuhrman, Marco; Hu, Ying; Tessitore, Gianmario
2013-10-15
We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form that allows direct applications to a large class of controlled stochastic parabolic equations. We allow for a diffusion coefficient dependent on the control parameter, and the space of control actions is general, so that in particular we need to introduce two adjoint processes. The second adjoint process takes values in a suitable space of operators on L{sup 4}.
Health benefit modelling and optimization of vehicular pollution control strategies
NASA Astrophysics Data System (ADS)
Sonawane, Nayan V.; Patil, Rashmi S.; Sethi, Virendra
2012-12-01
This study asserts that the evaluation of pollution reduction strategies should be approached on the basis of health benefits. The framework presented could be used for decision making on the basis of cost effectiveness when the strategies are applied concurrently. Several vehicular pollution control strategies have been proposed in literature for effective management of urban air pollution. The effectiveness of these strategies has been mostly studied as a one at a time approach on the basis of change in pollution concentration. The adequacy and practicality of such an approach is studied in the present work. Also, the assessment of respective benefits of these strategies has been carried out when they are implemented simultaneously. An integrated model has been developed which can be used as a tool for optimal prioritization of various pollution management strategies. The model estimates health benefits associated with specific control strategies. ISC-AERMOD View has been used to provide the cause-effect relation between control options and change in ambient air quality. BenMAP, developed by U.S. EPA, has been applied for estimation of health and economic benefits associated with various management strategies. Valuation of health benefits has been done for impact indicators of premature mortality, hospital admissions and respiratory syndrome. An optimization model has been developed to maximize overall social benefits with determination of optimized percentage implementations for multiple strategies. The model has been applied for sub-urban region of Mumbai city for vehicular sector. Several control scenarios have been considered like revised emission standards, electric, CNG, LPG and hybrid vehicles. Reduction in concentration and resultant health benefits for the pollutants CO, NOx and particulate matter are estimated for different control scenarios. Finally, an optimization model has been applied to determine optimized percentage implementation of specific
Improved Sensitivity Relations in State Constrained Optimal Control
Bettiol, Piernicola; Frankowska, Hélène; Vinter, Richard B.
2015-04-15
Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjoint state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because
Optimal control by least squares support vector machines.
Suykens, J A; Vandewalle, J; De Moor, B
2001-01-01
Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LS-SVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are considered. The problem is formulated in such a way that it incorporates the N-stage optimal control problem as well as a least squares support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. An alternative formulation as a constrained nonlinear optimization problem in less unknowns is given, together with a method for imposing local stability in the LS-SVM control scheme. The results are discussed for support vector machines with radial basis function kernel. Advantages of LS-SVM control are that no number of hidden units has to be determined for the controller and that no centers have to be specified for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with defining a regular grid for the centers in classical radial basis function networks. This is at the expense of taking the trajectory of state variables as additional unknowns in the optimization problem, while classical neural network approaches typically lead to parametric optimization problems. In the SVM methodology the number of unknowns equals the number of training data, while in the primal space the number of unknowns can be infinite dimensional. The method is illustrated both on stabilization and tracking problems including examples on swinging up an inverted pendulum with local stabilization at the endpoint and a tracking problem for a ball and beam system.
Optimal control of molecular motion expressed through quantum fluid dynamics
NASA Astrophysics Data System (ADS)
Dey, Bijoy K.; Rabitz, Herschel; Askar, Attila
2000-04-01
A quantum fluid-dynamic (QFD) control formulation is presented for optimally manipulating atomic and molecular systems. In QFD the control quantum system is expressed in terms of the probability density ρ and the quantum current j. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid-dynamical variables. The QFD approach is illustrated for manipulation of the ground electronic state dynamics of HCl induced by an external electric field.
A Connection between Singular Stochastic Control and Optimal Stopping
Espen Benth, Fred Reikvam, Kristin
2003-12-15
We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.
The Relationship between Pupil Control Ideology and Academic Optimism
ERIC Educational Resources Information Center
Gilbert, Michael J.
2012-01-01
This study investigates the relationship between pupil control ideology and academic optimism. Information was generated through responses to a questionnaire emailed to teachers in two school districts in Central New Jersey. The districts were categorized GH, as determined by the State's district factor grouping. The research concludes that…
Time optimal control of pendulum-cart system
Turnau, A.; Korytowski, A.
1994-12-31
We consider the synthesis of time optimal control which steers a pendulum hinged to a cart to a given state (e.g., the upright position), starting from arbitrary initial conditions. The control of the pendulum can system has attracted attention of many authors because of its relatively simple structure and at the same time, nontrivial nonlinearity. Various heuristic approaches combined with 1q stabilization in the vicinity of the target state were used to swing the pendulum up to the upright position and to keep it there. However, time-optimality was not achieved. We construct the time optimal control using a sequence of fixed horizon problems in which the norms of terminal states are minimized. The problems with fixed horizons are solved numerically by means of gradient optimization, with gradients determined from the solution of adjoint equations. Due to embedding the synthesis algorithms in the Matlab - Simulink environment, it is possible to track and visualize the control process as well as the results of simulation experiments.
Optimizing a mobile robot control system using GPU acceleration
NASA Astrophysics Data System (ADS)
Tuck, Nat; McGuinness, Michael; Martin, Fred
2012-01-01
This paper describes our attempt to optimize a robot control program for the Intelligent Ground Vehicle Competition (IGVC) by running computationally intensive portions of the system on a commodity graphics processing unit (GPU). The IGVC Autonomous Challenge requires a control program that performs a number of different computationally intensive tasks ranging from computer vision to path planning. For the 2011 competition our Robot Operating System (ROS) based control system would not run comfortably on the multicore CPU on our custom robot platform. The process of profiling the ROS control program and selecting appropriate modules for porting to run on a GPU is described. A GPU-targeting compiler, Bacon, is used to speed up development and help optimize the ported modules. The impact of the ported modules on overall performance is discussed. We conclude that GPU optimization can free a significant amount of CPU resources with minimal effort for expensive user-written code, but that replacing heavily-optimized library functions is more difficult, and a much less efficient use of time.
Modern control theory for Army missile guidance
NASA Astrophysics Data System (ADS)
Travassos, R. H.; Levari, H.; Gupta, N. K.
1982-11-01
A Singular perturbation guidance law has been developed for medium-range surface-to-air missiles. This guidance law is a significant extension of a previously developed guidance law for short-range missiles; in medium-range intercepts, the problem of energy management should be addressed in addition to homing guidance. The mathematical formulation has been simplified by introducing separation of time scales. Target Trajectory Estimation: A recursive algorithm for estimation of autoregressive moving average (ARMA) model parameters from noisy samples has been developed. Application of this algorithm to parameter estimation problems has exhibited its fast convergence and unbiasedness in the presence of noise, even with short data records. The algorithm has two versions, a Recursive Maximum Likelihood (RML) form and a Recursive Prediction Error (RPE) form, both of which possess a parallel structure that makes them highly suitable for parallel-processing implementation. Adaptive autopilots: Lattice-form algorithms have been developed for fast, recursive identification and control of time-varying systems. These algorithms have excellent numerical properties and a modular structure that makes them suitable for on-board real-time implementation.
Neural network learning of optimal Kalman prediction and control.
Linsker, Ralph
2008-11-01
Although there are many neural network (NN) algorithms for prediction and for control, and although methods for optimal estimation (including filtering and prediction) and for optimal control in linear systems were provided by Kalman in 1960 (with nonlinear extensions since then), there has been, to my knowledge, no NN algorithm that learns either Kalman prediction or Kalman control (apart from the special case of stationary control). Here we show how optimal Kalman prediction and control (KPC), as well as system identification, can be learned and executed by a recurrent neural network composed of linear-response nodes, using as input only a stream of noisy measurement data. The requirements of KPC appear to impose significant constraints on the allowed NN circuitry and signal flows. The NN architecture implied by these constraints bears certain resemblances to the local-circuit architecture of mammalian cerebral cortex. We discuss these resemblances, as well as caveats that limit our current ability to draw inferences for biological function. It has been suggested that the local cortical circuit (LCC) architecture may perform core functions (as yet unknown) that underlie sensory, motor, and other cortical processing. It is reasonable to conjecture that such functions may include prediction, the estimation or inference of missing or noisy sensory data, and the goal-driven generation of control signals. The resemblances found between the KPC NN architecture and that of the LCC are consistent with this conjecture.
NASA Astrophysics Data System (ADS)
Meng, Fei; Tao, Gang; Zhang, Tao; Hu, Yihuai; Geng, Peng
2015-08-01
Shifting quality is a crucial factor in all parts of the automobile industry. To ensure an optimal gear shifting strategy with best fuel economy for a stepped automatic transmission, the controller should be designed to meet the challenge of lacking of a feedback sensor to measure the relevant variables. This paper focuses on a new kind of automatic transmission using proportional solenoid valve to control the clutch pressure, a speed difference of the clutch based control strategy is designed for the shift control during the inertia phase. First, the mechanical system is shown and the system dynamic model is built. Second, the control strategy is designed based on the characterization analysis of models which are derived from dynamics of the drive line and electro-hydraulic actuator. Then, the controller uses conventional Proportional-Integral-Derivative control theory, and a robust two-degree-of-freedom controller is also carried out to determine the optimal control parameters to further improve the system performance. Finally, the designed control strategy with different controller is implemented on a simulation model. The compared results show that the speed difference of clutch can track the desired trajectory well and improve the shift quality effectively.
Cooperative control theory and integrated flight and propulsion control
NASA Technical Reports Server (NTRS)
Schmidt, David K.; Schierman, John D.
1994-01-01
This report documents the activities and research results obtained under a grant (NAG3-998) from the NASA Lewis Research Center. The focus of the research was the investigation of dynamic interactions between airframe and engines for advanced ASTOVL aircraft configurations, and the analysis of the implications of these interactions on the stability and performance of the airframe and engine control systems. In addition, the need for integrated flight and propulsion control for such aircraft was addressed. The major contribution of this research was the exposition of the fact that airframe and engine interactions could be present, and their effects could include loss of stability and performance of the control systems. Also, the significance of two directional, as opposed to one-directional, coupling was identified and explained. A multi variable stability and performance analysis methodology was developed, and applied to several candidate aircraft configurations. Also exposed was the fact that with interactions present along with some integrated control approaches, the engine command/limiting logic (which represents an important non-linear component of the engine control system) can impact closed-loop airframe/engine system stability. Finally, a brief investigation of control-law synthesis techniques appropriate for the class of systems was pursued, and it was determined that multi variable techniques, included model-following formulations of LQG and/or H (infinity) methods showed promise. However, for practical reasons, decentralized control architectures are preferred, which is an architecture incompatible with these synthesis methods.
Concurrently adjusting interrelated control parameters to achieve optimal engine performance
Jiang, Li; Lee, Donghoon; Yilmaz, Hakan; Stefanopoulou, Anna
2015-12-01
Methods and systems for real-time engine control optimization are provided. A value of an engine performance variable is determined, a value of a first operating condition and a value of a second operating condition of a vehicle engine are detected, and initial values for a first engine control parameter and a second engine control parameter are determined based on the detected first operating condition and the detected second operating condition. The initial values for the first engine control parameter and the second engine control parameter are adjusted based on the determined value of the engine performance variable to cause the engine performance variable to approach a target engine performance variable. In order to cause the engine performance variable to approach the target engine performance variable, adjusting the initial value for the first engine control parameter necessitates a corresponding adjustment of the initial value for the second engine control parameter.
Putting policy theory to work: tobacco control in California.
Blackman, Virginia Schmied
2005-05-01
Policy theory provides a useful lens for nurses evaluating how problems are understood and responded to within the policy arena. This article examines and critiques the agenda-setting model offered by John Kingdon. Furthermore, the theory is applied to the issue of tobacco control in the state of California, suggesting policy solutions and strategies to achieve their placement on the policy agenda. Strategies and techniques that may be useful to nurse policy champions are elucidated.
Gender Assignment in Contemporary Standard Russian: A Comprehensive Analysis in Optimality Theory
ERIC Educational Resources Information Center
Galbreath, Blake Lee Everett
2010-01-01
The purpose of this dissertation is to provide a comprehensive analysis of gender assignment in Contemporary Standard Russian within the framework of Optimality Theory (Prince and Smolensky 1993). The result of the dissertation is the establishment of the phonological, morphological, semantic, and faithfulness constraints necessary to assign…
ERIC Educational Resources Information Center
Whincop, Chris
1996-01-01
This paper identifies a feature of human brain neural nets that may be described as the principle of ease of processing (PEP), and that, it is argued, is the primary force guiding a learner towards a target grammar. It is suggested that the same principle lies at the heart of Optimality Theory, which characterizes the course of language…
Integration of reinforcement learning and optimal decision-making theories of the basal ganglia.
Bogacz, Rafal; Larsen, Tobias
2011-04-01
This article seeks to integrate two sets of theories describing action selection in the basal ganglia: reinforcement learning theories describing learning which actions to select to maximize reward and decision-making theories proposing that the basal ganglia selects actions on the basis of sensory evidence accumulated in the cortex. In particular, we present a model that integrates the actor-critic model of reinforcement learning and a model assuming that the cortico-basal-ganglia circuit implements a statistically optimal decision-making procedure. The values of cortico-striatal weights required for optimal decision making in our model differ from those provided by standard reinforcement learning models. Nevertheless, we show that an actor-critic model converges to the weights required for optimal decision making when biologically realistic limits on synaptic weights are introduced. We also describe the model's predictions concerning reaction times and neural responses during learning, and we discuss directions required for further integration of reinforcement learning and optimal decision-making theories. PMID:21222528
Integration of reinforcement learning and optimal decision-making theories of the basal ganglia.
Bogacz, Rafal; Larsen, Tobias
2011-04-01
This article seeks to integrate two sets of theories describing action selection in the basal ganglia: reinforcement learning theories describing learning which actions to select to maximize reward and decision-making theories proposing that the basal ganglia selects actions on the basis of sensory evidence accumulated in the cortex. In particular, we present a model that integrates the actor-critic model of reinforcement learning and a model assuming that the cortico-basal-ganglia circuit implements a statistically optimal decision-making procedure. The values of cortico-striatal weights required for optimal decision making in our model differ from those provided by standard reinforcement learning models. Nevertheless, we show that an actor-critic model converges to the weights required for optimal decision making when biologically realistic limits on synaptic weights are introduced. We also describe the model's predictions concerning reaction times and neural responses during learning, and we discuss directions required for further integration of reinforcement learning and optimal decision-making theories.
Cooperative control theory and integrated flight and propulsion control
NASA Technical Reports Server (NTRS)
Schmidt, David K.; Schierman, John D.
1995-01-01
The major contribution of this research was the exposition of the fact that airframe and engine interactions could be present, and their effects could include loss of stability and performance of the control systems. Also, the significance of two directional, as opposed to one-directional, coupling was identified and explained. A multivariable stability and performance analysis methodology was developed, and applied to several candidate aircraft configurations. In these example evaluations, the significance of these interactions was underscored. Also exposed was the fact that with interactions present along with some integrated control approaches, the engine command/limiting logic (which represents an important nonlinear component of the engine control system) can impact closed-loop airframe/engine system stability. Finally, a brief investigation of control-law synthesis techniques appropriate for the class of systems was pursued, and it was determined that multivariable techniques, including model-following formulations of LQG and/or H infinity methods, showed promise. However, for practical reasons, decentralized control architectures are preferred, which is an architecture incompatible with these synthesis methods. The major contributions of the second phase of the grant was the development of conditions under which no decentralized controller could achieve closed loop system requirements on stability and/or performance. Sought were conditions that depended only on properties of the plant and the requirement, and independent of any particular control law or synthesis approach. Therefore, they could be applied a priori, before synthesis of a candidate control law. Under this grant, such conditions were found regarding stability, and encouraging initial results were obtained regarding performance.
Optimal control analysis of the dynamic growth behavior of microorganisms.
Mandli, Aravinda R; Modak, Jayant M
2014-12-01
Understanding the growth behavior of microorganisms using modeling and optimization techniques is an active area of research in the fields of biochemical engineering and systems biology. In this paper, we propose a general modeling framework, based on Monod model, to model the growth of microorganisms. Utilizing the general framework, we formulate an optimal control problem with the objective of maximizing a long-term cellular goal and solve it analytically under various constraints for the growth of microorganisms in a two substrate batch environment. We investigate the relation between long term and short term cellular goals and show that the objective of maximizing cellular concentration at a fixed final time is equivalent to maximization of instantaneous growth rate. We then establish the mathematical connection between the generalized framework and optimal and cybernetic modeling frameworks and derive generalized governing dynamic equations for optimal and cybernetic models. We finally illustrate the influence of various constraints in the cybernetic modeling framework on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms.