Optimal Periodic Control Theory.
1980-08-01
are control variables. For many aircraft, this energy state space produces a hodograph which is not convex. The physical explanation for this is that...convexity in the hodograph and preserve an "optimal" steady-state cruise, Schultz and Zagalsky [61 revised the energy state model so that altitude becomes a
AN APPLICATION OF OPTIMAL CONTROL THEORY.
The purpose of this article is to show that optimal control theory can be used to develop a control strategy for a practical system, namely a distillation column. The approach will be to model the complex system with a simple model, use optimal control theory to determine a control strategy for the simple model, and then apply the results to the original system. (Author)
Vehicle dynamics applications of optimal control theory
NASA Astrophysics Data System (ADS)
Sharp, R. S.; Peng, Huei
2011-07-01
The aim of the paper is to survey the various forms of optimal-control theory which have been applied to automotive problems and to present illustrative examples of applications studies, with assessments of the state of the art and of the contributions made through the use of optimal-control ideas. After a short introduction to the topic mentioning several questions to which optimal-control theory has been addressed, brief reviews of automotive-applicable optimal-control theory are given. There are outlines of the Linear Quadratic Regulator, without and with state reconstruction and then with the addition of disturbance preview, the nonlinear regulator or state-dependent-Riccati equation method, general numerical optimal-control theory including indirect and direct methods, model predictive control and robust control. Applications of the theory to active and semi-active suspension design and performance, worst-case manoeuvring, minimum-time manoeuvring and high-quality driving are then discussed in detail. Application sections describe the problem, the theory that has been used, what has been discovered and what remains to be found. The record of optimal-control theory in aiding the understanding of the various issues, in helping with system designs and knowledge of what is possible, and in guiding future research is assessed. Some ideas about future work are included.
AN INTRODUCTION TO OPTIMAL CONTROL THEORY.
The report presents an introduction to some of the concepts and results currently popular in optimal control theory . The introduction is intended...for someone acquainted with ordinary differential equations and real variables, but with no prior knowledge of control theory . The material covered
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 sustainable environmental management.
Shastri, Yogendra; Diwekar, Urmila; Cabezas, Heriberto
2008-07-15
Sustainable ecosystem management aims to promote the structure and operation of the human components of the system while simultaneously ensuring the persistence of the structures and operation of the natural component. Given the complexity of this task owing to the diverse temporal and spatial scales and multidisciplinary interactions, a systems theory approach based on sound mathematical techniques is essential. Two important aspects of this approach are formulation of sustainability-based objectives and development of the management strategies. Fisher information can be used as the basis of a sustainability hypothesis to formulate relevant mathematical objectives for disparate systems, and optimal control theory provides the means to derive time-dependent management strategies. Partial correlation coefficient analysis is an efficient technique to identify the appropriate control variables for policy development. This paper represents a proof of concept for this approach using a model system that includes an ecosystem, humans, a very rudimentary industrial process, and a very simple agricultural system. Formulation and solution of the control problems help in identifying the effective management options which offer guidelines for policies in real systems. The results also emphasize that management using multiple parameters of different nature can be distinctly effective.
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.
Optimization of microstructure development during hot working using control theory
NASA Astrophysics Data System (ADS)
Malas, James C.; Frazier, W. Garth; Medina, Enrique A.; Medeiros, Steven; Mullins, W. M.; Chaudhary, Anil; Venugopal, S.; Irwin, R. Dennis; Srinivasan, Raghavan
1997-09-01
A new approach for controlling microstructure development during hot working processes is proposed. This approach is based on optimal control theory and involves state-space type models for describing the material behavior and the mechanics of the process. The effect of process control parameters such as strain, strain rate, and temperature on important microstructural features can be systematically formulated and then solved as an optimal control problem. This method has been applied to the optimization of grain size and process parameters such as die geometry and ram velocity during the extrusion of plain carbon steel. Experimental results of this investigation show good agreement with those predicted in the design stage.
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...
Optimal control theory--closing the gap between theory and experiment.
von den Hoff, Philipp; Thallmair, Sebastian; Kowalewski, Markus; Siemering, Robert; de Vivie-Riedle, Regina
2012-11-14
Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions.
Combining optimal control theory and molecular dynamics for protein folding.
Arkun, Yaman; Gur, Mert
2012-01-01
A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the Cα atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the Cα atoms. In turn, MD simulation provides an all-atom conformation whose Cα positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the Cα atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization-MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages.
Design of a Helicopter Stability and Control Augmentation System Using Optimal Control Theory.
technique is described for the design of multivariable feedback controllers based upon results in optimal control theory . For a specified performance...helicopter flight envelope. The results show that optimal control theory can be used to design a helicopter stability and control augmentation system
Searching for pathways involving dressed states in optimal control theory.
von den Hoff, Philipp; Kowalewski, Markus; de Vivie-Riedle, Regina
2011-01-01
Selective population of dressed states has been proposed as an alternative control pathway in molecular reaction dynamics [Wollenhaupt et al., J. Photochem. Photobiol. A: Chem., 2006, 180, 248]. In this article we investigate if, and under which conditions, this strong field pathway is included in the search space of optimal control theory. For our calculations we used the proposed example of the potassium dimer, in which the different target states can be reached via dressed states by resonant transition. Especially, we investigate whether the optimization algorithm is able to find the route involving the dressed states although the target state lies out of resonance in the bare state picture.
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.
Acceleration of quantum optimal control theory algorithms with mixing strategies.
Castro, Alberto; Gross, E K U
2009-05-01
We propose the use of mixing strategies to accelerate the convergence of the common iterative algorithms utilized in quantum optimal control theory (QOCT). We show how the nonlinear equations of QOCT can be viewed as a "fixed-point" nonlinear problem. The iterative algorithms for this class of problems may benefit from mixing strategies, as it happens, e.g., in the quest for the ground-state density in Kohn-Sham density-functional theory. We demonstrate, with some numerical examples, how the same mixing schemes utilized in this latter nonlinear problem may significantly accelerate the QOCT iterative procedures.
Quantum optimal control theory applied to transitions in diatomic molecules
NASA Astrophysics Data System (ADS)
Lysebo, Marius; Veseth, Leif
2014-12-01
Quantum optimal control theory is applied to control electric dipole transitions in a real multilevel system. The specific system studied in the present work is comprised of a multitude of hyperfine levels in the electronic ground state of the OH molecule. Spectroscopic constants are used to obtain accurate energy eigenstates and electric dipole matrix elements. The goal is to calculate the optimal time-dependent electric field that yields a maximum of the transition probability for a specified initial and final state. A further important objective was to study the detailed quantum processes that take place during such a prescribed transition in a multilevel system. Two specific transitions are studied in detail. The computed optimal electric fields as well as the paths taken through the multitude of levels reveal quite interesting quantum phenomena.
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.
Function-valued adaptive dynamics and optimal control theory.
Parvinen, Kalle; Heino, Mikko; Dieckmann, Ulf
2013-09-01
In this article we further develop the theory of adaptive dynamics of function-valued traits. Previous work has concentrated on models for which invasion fitness can be written as an integral in which the integrand for each argument value is a function of the strategy value at that argument value only. For this type of models of direct effect, singular strategies can be found using the calculus of variations, with singular strategies needing to satisfy Euler's equation with environmental feedback. In a broader, more mechanistically oriented class of models, the function-valued strategy affects a process described by differential equations, and fitness can be expressed as an integral in which the integrand for each argument value depends both on the strategy and on process variables at that argument value. In general, the calculus of variations cannot help analyzing this much broader class of models. Here we explain how to find singular strategies in this class of process-mediated models using optimal control theory. In particular, we show that singular strategies need to satisfy Pontryagin's maximum principle with environmental feedback. We demonstrate the utility of this approach by studying the evolution of strategies determining seasonal flowering schedules.
Optimal control of ICU patient discharge: from theory to implementation.
Mallor, Fermín; Azcárate, Cristina; Barado, Julio
2015-09-01
This paper deals with the management of scarce health care resources. We consider a control problem in which the objective is to minimize the rate of patient rejection due to service saturation. The scope of decisions is limited, in terms both of the amount of resources to be used, which are supposed to be fixed, and of the patient arrival pattern, which is assumed to be uncontrollable. This means that the only potential areas of control are speed or completeness of service. By means of queuing theory and optimization techniques, we provide a theoretical solution expressed in terms of service rates. In order to make this theoretical analysis useful for the effective control of the healthcare system, however, further steps in the analysis of the solution are required: physicians need flexible and medically-meaningful operative rules for shortening patient length of service to the degree needed to give the service rates dictated by the theoretical analysis. The main contribution of this paper is to discuss how the theoretical solutions can be transformed into effective management rules to guide doctors' decisions. The study examines three types of rules based on intuitive interpretations of the theoretical solution. Rules are evaluated through implementation in a simulation model. We compare the service rates provided by the different policies with those dictated by the theoretical solution. Probabilistic analysis is also included to support rule validity. An Intensive Care Unit is used to illustrate this control problem. The study focuses on the Markovian case before moving on to consider more realistic LoS distributions (Weibull, Lognormal and Phase-type distribution).
Optimization of a photovoltaic pumping system based on the optimal control theory
Betka, A.; Attali, A.
2010-07-15
This paper suggests how an optimal operation of a photovoltaic pumping system based on an induction motor driving a centrifugal pump can be realized. The optimization problem consists in maximizing the daily pumped water quantity via the optimization of the motor efficiency for every operation point. The proposed structure allows at the same time the minimization the machine losses, the field oriented control and the maximum power tracking of the photovoltaic array. This will be attained based on multi-input and multi-output optimal regulator theory. The effectiveness of the proposed algorithm is described by simulation and the obtained results are compared to those of a system working with a constant air gap flux. (author)
Theory and Applications of Optimal Control in Aerospace Systems,
1981-07-01
CONTROL OF LINEAR QUADRATIC SYSTEM. Consider, as a particular case of the general problem defined in section 2, a lineal , system with quadratic cost... LARSON Proceeding of the IFAC Stochastic Control Symposium, Budapest, 1974. [36] G. CAMPION "Optimal control of non-linear stochastic systems by...dynamics, an r-component algebraic (or transcendental) equation representing the output, and an r-component equation representing the observation: dx (t
Optimizing SFR transmutation performance through direct adjoining control theory
NASA Astrophysics Data System (ADS)
Davis, Jeffrey C.
2007-12-01
We have developed the CORTANA code to optimize the transmutation performance of sodium cooled fast reactors (SFRs). We obtain the necessary conditions for optimal fuel and burnable absorber loadings using Pontryagin's maximum principle with a direct adjoining approach to explicitly account for either a flat flux or a power peaking inequality constraint providing a set of coupled system, Euler-Lagrange (E-L), and optimality equations which are iteratively solved with the method of conjugate gradients until no further improvement in the objective function is achieved. To satisfy the inequality constraints throughout the operating cycle, we have implemented a backwards diffusion theory (BDT) to establish a relationship between fuel loading and the relative assembly power distribution during the cycle and systematically eliminate the constraint violations with each conjugate gradient iteration. The CORTANA SFR optimization code uses multi-group, three-dimensional neutron diffusion theory, with a microscopic depletion scheme. We solve the system equations in a quasi-static fashion forward in time from beginning-of-cycle (BOC) to end-of-cycle (EOC), while we solve the E-L equations backwards in time from EOC to BOC, reflecting the adjoint nature of the Lagrange multipliers. A two enrichment-zone SFR problem verifies our formulation, yielding a TRU enrichment distribution nearly identical to that of the reference SFR core in the Generation IV Roadmap. Using a full heavy metal recycling mode, we coupled our optimization methodology with the REBUS-3 equilibrium cycle methodology to optimize an SFR operating as a second tier transmuter. We model the system using a three-dimensional triangular-z finite differencing scheme with full core symmetry and a time-independent 33-group microscopic cross section library. Beginning from a uniform TRU distribution, our CORTANA improves the SFR performance by reducing the maximum relative assembly power from 1.7 to 1.25, minimizes
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.
Shyshlov, Dmytro; Babikov, Dmitri
2012-11-21
In the context of molecular quantum computation the optimal control theory (OCT) is used to obtain shaped laser pulses for high-fidelity control of vibrational qubits. Optimization is done in time domain and the OCT algorithm varies values of electric field in each time step independently, tuning hundreds of thousands of parameters to find one optimal solution. Such flexibility is not available in experiments, where pulse shaping is done in frequency domain and the number of "tuning knobs" is much smaller. The question of possible experimental interpretations of theoretically found OCT solutions arises. In this work we analyze very accurate optimal pulse that we obtained for implementing quantum gate CNOT for the two-qubit system encoded into the exited vibrational states of thiophosgene molecule. Next, we try to alter this pulse by reducing the number of available frequency channels and intentionally introducing systematic and random errors (in frequency domain, by modifying the values of amplitudes and phases of different frequency components). We conclude that a very limited number of frequency components (only 32 in the model of thiophosgene) are really necessary for accurate control of the vibrational two-qubit system, and such pulses can be readily constructed using OCT. If the amplitude and phase errors of different frequency components do not exceed ±3% of the optimal values, one can still achieve accurate transformations of the vibrational two-qubit system, with gate fidelity of CNOT exceeding 0.99.
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.
Gollub, Caroline; Kowalewski, Markus; de Vivie-Riedle, Regina
2008-08-15
We present a modified optimal control scheme based on the Krotov method, which allows for strict limitations on the spectrum of the optimized laser fields. A frequency constraint is introduced and derived mathematically correct, without losing monotonic convergence of the algorithm. The method guarantees a close link to learning loop control experiments and is demonstrated for the challenging control of nonresonant Raman transitions, which are used to implement a set of global quantum gates for molecular vibrational qubits.
Quantum optimal control theory and dynamic coupling in the spin-boson model
Jirari, H.; Poetz, W.
2006-08-15
A Markovian master equation describing the evolution of open quantum systems in the presence of a time-dependent external field is derived within the Bloch-Redfield formalism. It leads to a system-bath interaction which depends on the control field. Optimal control theory is used to select control fields which allow accelerated or decelerated system relaxation, or suppression of relaxation (dissipation) altogether, depending on the dynamics we impose on the quantum system. The control-dissipation correlation and the nonperturbative treatment of the control field are essential for reaching this goal. The optimal control problem is formulated within Pontryagin's minimum principle and the resulting optimal differential system is solved numerically. As an application, we study the dynamics of a spin-boson model in the strong coupling regime under the influence of an external control field. We show how trapping the system in unstable quantum states and transfer of population can be achieved by optimized control of the dissipative quantum system. We also used optimal control theory to find the driving field that generates the quantum Z gate. In several cases studied, we find that the selected optimal field which reduces the purity loss significantly is a multicomponent low-frequency field including higher harmonics, all of which lie below the phonon cutoff frequency. Finally, in the undriven case we present an analytic result for the Lamb shift at zero temperature.
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.
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.
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.
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.
Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory.
Pezeshki, Soroosh; Schreiber, Michael; Kleinekathöfer, Ulrich
2008-04-21
Optimal control theory is used to tailor laser pulses which enhance a femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) spectrum in a certain frequency range. For this aim the optimal control theory has to be applied to a target state distributed in time. Explicit control mechanisms are given for shaping either the Stokes or the probe pulse in the four-wave mixing process. A simple molecule for which highly accurate potential energy surfaces are available, namely molecular iodine, is used to test the procedure. This approach of controlling vibrational motion and delivering higher intensities to certain frequency ranges might also be important for the improvement of CARS microscopy.
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.
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.
Wall Models for Large-Eddy Simulation Based on Optimal Control Theory
2006-06-14
Optimal Control Theory 5b. GRANT NUMBER F49620-03-1-0132 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Parviz Moin, Principal Investigator...C. THIS ABSTRACT OF PAGES Professor Parviz Moin PAGE 300 20b. TELEPHONE NUMBER (Include area code) 650 723-9713 Standard Form 298 (Rev. 8-98...CONTROL THEORY" PERIOD OF PERFORMANCE: 2/15/2003 - 3/31/2006 by Parviz Moin (PI), Jeremy A. Templeton and Meng Wang Program Manager: Rhett Jefferies
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.
APPLICATION OF OPTIMAL CONTROL THEORY TO CARDIO-CIRCULATORY ASSIST DEVICES.
The objective of the investigation is the application of, and where necessary, extension of optimal control theory to the synthesis of controllers for such cardio-circulatory assist devices. In particular, the concept of set of attainability is extended to include linear, periodic, bounded control systems and the maximum principle applied to obtain necessary and sufficient conditions for various problems. In addition to several numerical examples, the results of a large-scale hybrid simulation for a cardiovascular model and particular assist device are presented.
New developments in the application of optimal control theory to therapeutic protocols.
Bayón, L; Otero, J A; Suárez, P M; Tasis, C
2016-02-01
Optimal control theory is one of the most important tools in the development of new therapeutic protocols for treating infections. In this work, we present an algorithm able to deal with high-dimensional problems with bounded controls. The optimal solution is obtained by minimizing a positive-definite treatment cost function. Our method, based on Pontryagin's Minimum Principle and the coordinate cyclic descent method, allows solving problems of varied nature. In this paper, and by way of example, therapeutic enhancement of the immune response to invasion by pathogenic attack is addressed as an optimal control problem. The generic mathematical model used describes the evolution of the disease by means of four non-linear, ordinary differential equations. The model is characterized by the concentration of pathogens, plasma cells, antibodies and a numerical value that indicates the relative characteristic of an organ damaged by disease. From a system theory point of view, drugs can be interpreted as control inputs. Therapies based on separate application of the agents are presented in previous studies. We shall present the more general problem in this paper, considering combined therapies and bounded controls. Finally, we present several numerical simulations.
May, Volkhard; Ambrosek, David; Oppel, Markus; Gonzalez, Leticia
2007-10-14
A systematic approach is presented to describe nonresonant multiphoton transitions, i.e., transitions between two electronic states without the presence of additional intermediate states resonant with the single-photon energy. The method is well suited to describe femtosecond spectroscopic experiments and, in particular, attempts to achieve laser pulse control of molecular dynamics. The obtained effective time-dependent Schroedinger equation includes effective couplings to the radiation field which combine powers of the field strength and effective transition dipole operators between the initial and final states. To arrive at time-local equations our derivation combines the well-known rotating wave approximation with the approximation of slowly varying amplitudes. Under these terms, the optimal control formalism can be readily extended to also account for nonresonant multiphoton events. Exemplary, nonresonant two- and three-photon processes, similar to those occurring in the recent femtosecond pulse-shaping experiments on CpMn(CO){sub 3}, are treated using related ab initio potential energy surfaces.
Isotope selective photoionization of NaK by optimal control: theory and experiment.
Schäfer-Bung, Boris; Bonacić-Koutecký, Vlasta; Sauer, Franziska; Weber, Stefan M; Wöste, Ludger; Lindinger, Albrecht
2006-12-07
We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.
Mishima, K; Yamashita, K
2009-01-21
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on.
NASA Astrophysics Data System (ADS)
Mishima, K.; Yamashita, K.
2009-01-01
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on.
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.
Sustainable ecosystem management using optimal control theory: part 1 (deterministic systems).
Shastri, Y; Diwekar, U
2006-08-07
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.
NASA Astrophysics Data System (ADS)
Paradkar, Aniruddha; Davari, Asad; Feliachi, Ali; Biswas, Tamal
In this paper, the integration of a fuel cell into the power system is treated as a load frequency control (LFC) problem with the fuel cell acting as a load disturbance source. The integration of a fuel cell into the power system results into a change in real power. But changes in real power affect the system frequency. Thus, the integration will result into a change of frequency of the synchronous machines. Hence, we need to design a control scheme for keeping the system in the steady state. An optimal controller based on the disturbance accommodation control (DAC) theory is proposed for this load frequency control problem. For demonstrating the effectiveness of the proposed controller, we have considered a two-area power system with the fuel cell introduced in area 1. The fuel cell is considered as an external disturbance to each subsystem. A mathematical model is derived for each subsystem and based upon these models controllers are designed for keeping each subsystem stable, which in turn stabilizes the overall system. So, the proposed controller is decentralized in nature. To account for the modeling uncertainties, an observer is designed to estimate each subsystem's own and interfacing variables. The controller uses these estimates to optimize a given performance index and allocate generating unit outputs according to the requirements.
NASA Astrophysics Data System (ADS)
Mishima, Kenji; Yamashita, Koichi
2009-03-01
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed-time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. Our theory can not only achieve high transition probabilities but also determine exact temporal duration of the laser pulses. As a demonstration, our theory is applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Using the tailored laser pulses, we discuss the fidelity of entanglement distillation and quantum teleportation. Our method will significantly be useful for the quantum control of non-local interaction such as entangling interaction, and other time-sensitive general quantum dynamics, chemical reactions.
control theory to systems described by partial differential equations. The intent is not to advance the theory of partial differential equations per se. Thus all considerations will be restricted to the more familiar equations of the type which often occur in mathematical physics. Specifically, the distributed parameter systems under consideration are represented by a set of field
Adamson, M W; Morozov, A Y; Kuzenkov, O A
2016-09-01
Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions-a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.
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.
Mishima, K; Yamashita, K
2009-07-07
We develop monotonically convergent free-time and fixed end-point optimal control theory (OCT) in the density-matrix representation to deal with quantum systems showing dissipation. Our theory is more general and flexible for tailoring optimal laser pulses in order to control quantum dynamics with dissipation than the conventional fixed-time and fixed end-point OCT in that the optimal temporal duration of laser pulses can also be optimized exactly. To show the usefulness of our theory, it is applied to the generation and maintenance of the vibrational entanglement of carbon monoxide adsorbed on the copper (100) surface, CO/Cu(100). We demonstrate the numerical results and clarify how to combat vibrational decoherence as much as possible by the tailored shapes of the optimal laser pulses. It is expected that our theory will be general enough to be applied to a variety of dissipative quantum dynamics systems because the decoherence is one of the quantum phenomena sensitive to the temporal duration of the quantum dynamics.
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…
Discrete Variational Optimal Control
NASA Astrophysics Data System (ADS)
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
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.
NASA Astrophysics Data System (ADS)
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.
Skinner, Thomas E; Reiss, Timo O; Luy, Burkhard; Khaneja, Navin; Glaser, Steffen J
2003-07-01
Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.
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.
NASA Astrophysics Data System (ADS)
Nath, Bikram; Mondal, Chandan Kumar
2014-08-01
We have designed and optimised a combined laser pulse using optimal control theory-based adaptive simulated annealing technique for selective vibrational excitations and photo-dissociation. Since proper choice of pulses for specific excitation and dissociation phenomena is very difficult, we have designed a linearly combined pulse for such processes and optimised the different parameters involved in those pulses so that we can get an efficient combined pulse. The technique makes us free from choosing any arbitrary type of pulses and makes a ground to check their suitability. We have also emphasised on how we can improve the performance of simulated annealing technique by introducing an adaptive step length of the different variables during the optimisation processes. We have also pointed out on how we can choose the initial temperature for the optimisation process by introducing heating/cooling step to reduce the annealing steps so that the method becomes cost effective.
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)
Shu, Chuan-Cun; Henriksen, Niels E
2012-01-28
We implement phase-only shaped laser pulses within quantum optimal control theory for laser-molecule interaction. This approach is applied to the indirect photofragmentation dynamics of NaI in the weak-field limit. It is shown that optimized phase-modulated pulses with a fixed frequency distribution can substantially modify transient dissociation probabilities as well as the momentum distribution associated with the relative motion of Na and I.
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.
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.
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.
1979-12-01
OPTIMAL LINEAR CONTROL C.A. HARVEY M.G. SAFO NOV G. STEIN J.C. DOYLE HONEYWELL SYSTEMS & RESEARCH CENTER j 2600 RIDGWAY PARKWAY j [ MINNEAPOLIS...RECIPIENT’S CAT ALC-’ W.IMIJUff’? * J~’ CR2 15-238-4F TP P EI)ŕll * (~ Optimal Linear Control ~iOGRPR UBA m a M.G Lnar o Con_ _ _ _ _ _ R PORT__ _ _ I RE...Characterizations of optimal linear controls have been derived, from which guides for selecting the structure of the control system and the weights in
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.
Sharma, Sitansh; Sharma, Purshotam; Singh, Harjinder; Balint-Kurti, Gabriel G
2009-06-01
Time dependent quantum dynamics and optimal control theory are used for selective vibrational excitation of the N6-H (amino N-H) bond in free adenine and in the adenine-thymine (A-T) base pair. For the N6-H bond in free adenine we have used a one dimensional model while for the hydrogen bond, N6-H(A)...O4(T), present in the A-T base pair, a two mathematical dimensional model is employed. The conjugate gradient method is used for the optimization of the field dependent cost functional. Optimal laser fields are obtained for selective population transfer in both the model systems, which give virtually 100% excitation probability to preselected vibrational levels. The effect of the optimized laser field on the other hydrogen bond, N1(A)...H-N3(T), present in A-T base pair is also investigated.
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.
Porsa, Sina; Lin, Yi-Chung; Pandy, Marcus G
2016-08-01
The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.
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.
Conference on Operator Theory, Wavelet Theory and Control Theory
1993-09-30
Bourbaki 662 (1985-1986). [9] Meyer, Y., Ondelettes et operateurs I, Hermann editeurs des sciences et des arts, 1990. [10] Natanson, I. P., Theory of...OPERATOR THEORY , WAVELET THEORY & CONTROL THEORY (U)F 6. AUTHOR(S) 2304/ES Professor Xingde Dai F49620-93-1-0180 7. PERFORMING ORGANIZATION NAME(S) AND...1STRIBUTION IS UNLIMITED UTL 13. ABSTRACT (Maximum 200 words) The conference on Interaction Between Operator Theory , Wavelet Theory and Control Theory
Optimized joystick controller.
Ding, D; Cooper, R A; Spaeth, D
2004-01-01
The purpose of the study was to develop an optimized joystick control interface for electric powered wheelchairs and thus provide safe and effective control of electric powered wheelchairs to people with severe physical disabilities. The interface enables clinicians to tune joystick parameters for each individual subject through selecting templates, dead zones, and bias axes. In terms of hand tremor usually associated with people with traumatic brain injury, cerebral palsy, and multiple sclerosis, fuzzy logic rules were applied to suppress erratic hand movements and extract the intended motion from the joystick. Simulation results were presented to show the graphical tuning interface as well as the performance of the fuzzy logic controller.
Optimal control concepts in design sensitivity analysis
NASA Technical Reports Server (NTRS)
Belegundu, Ashok D.
1987-01-01
A close link is established between open loop optimal control theory and optimal design by noting certain similarities in the gradient calculations. The resulting benefits include a unified approach, together with physical insights in design sensitivity analysis, and an efficient approach for simultaneous optimal control and design. Both matrix displacement and matrix force methods are considered, and results are presented for dynamic systems, structures, and elasticity problems.
Fault Tolerant Optimal Control.
1982-08-01
i k+l since the cost to be minimized in (D.2.3) increases withXk (for fixed xsk). When we have b k _ x~ ji ] Aj M 2a(j) R(j) x bOk +l x]rkt] -b (j...22, pp. 236-239. 69. D.D.Sworder and L.L. Choi (1976): Stationary Cost Densities for Optimally Controlled Stochastic Systems, IEEE Trans. Automatic
Quantum control implemented as combinatorial optimization.
Strohecker, Traci; Rabitz, Herschel
2010-01-15
Optimal control theory provides a general means for designing controls to manipulate quantum phenomena. Traditional implementation requires solving coupled nonlinear equations to obtain the optimal control solution, whereas this work introduces a combinatorial quantum control (CQC) algorithm to avoid this complexity. The CQC technique uses a predetermined toolkit of small time step propagators in conjunction with combinatorial optimization to identify a proper sequence for the toolkit members. Results indicate that the CQC technique exhibits invariance of search effort to the number of system states and very favorable scaling upon comparison to a standard gradient algorithm, taking into consideration that CQC is easily parallelizable.
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.
CHALLENGES OF MODERN CONTROL THEORY
The fundamental objective of the new scientific discipline called ’ control theory ’ is that of modifying the behavior of a system subject to various...possible contributions of modern control theory to the biomedical domain are briefly indicated.
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.
NASA Technical Reports Server (NTRS)
Allan, Brian; Owens, Lewis
2010-01-01
In support of the Blended-Wing-Body aircraft concept, a new flow control hybrid vane/jet design has been developed for use in a boundary-layer-ingesting (BLI) offset inlet in transonic flows. This inlet flow control is designed to minimize the engine fan-face distortion levels and the first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. This concept represents a potentially enabling technology for quieter and more environmentally friendly transport aircraft. An optimum vane design was found by minimizing the engine fan-face distortion, DC60, and the first five Fourier harmonic half amplitudes, while maximizing the total pressure recovery. The optimal vane design was then used in a BLI inlet wind tunnel experiment at NASA Langley's 0.3-meter transonic cryogenic tunnel. The experimental results demonstrated an 80-percent decrease in DPCPavg, the reduction in the circumferential distortion levels, at an inlet mass flow rate corresponding to the middle of the operational range at the cruise condition. Even though the vanes were designed at a single inlet mass flow rate, they performed very well over the entire inlet mass flow range tested in the wind tunnel experiment with the addition of a small amount of jet flow control. While the circumferential distortion was decreased, the radial distortion on the outer rings at the aerodynamic interface plane (AIP) increased. This was a result of the large boundary layer being distributed from the bottom of the AIP in the baseline case to the outer edges of the AIP when using the vortex generator (VG) vane flow control. Experimental results, as already mentioned, showed an 80-percent reduction of DPCPavg, the circumferential distortion level at the engine fan-face. The hybrid approach leverages strengths of vane and jet flow control devices, increasing inlet performance over a broader operational range with significant reduction in mass flow requirements. Minimal distortion level requirements
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.
Advanced Topics in Control Systems Theory
NASA Astrophysics Data System (ADS)
Lorsa, Antonio; Lamnabhi-Lagarrigue, Françoise; Panteley, Elena
Advanced Topics in Control Systems Theory contains selected contributions written by lecturers at the third (annual) Formation d'Automatique de Paris (FAP) (Graduate Control School in Paris). Following on from the lecture notes from the second FAP (Volume 311 in the same series) it is addressed to graduate students and researchers in control theory with topics touching on a variety of areas of interest to the control community such as nonlinear optimal control, observer design, stability analysis and structural properties of linear systems.
Relaxed controls and the convergence of optimal control algorithms
NASA Technical Reports Server (NTRS)
Williamson, L. J.; Polak, E.
1976-01-01
This paper presents a framework for the study of the convergence properties of optimal control algorithms and illustrates its use by means of two examples. The framework consists of an algorithm prototype with a convergence theorem, together with some results in relaxed controls theory.
Trajectory Control and Optimization for Responsive Spacecraft
2012-03-22
36 3.2.2 Controlling the Position of the Spacecraft Within the Orbit . . 37 vi Page 3.2.3 Thrust-coast Duty...focuses on methods for performing minimum time in-plane maneuvers. The optimal control problem for an orbiting spacecraft perturbed by a small, constant...focuses on feedback control methods for performing in-plane maneuvers. Lyapunov theory is applied to the nonlinear equations of motion for an orbiting space
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 Control of Electrodynamic Tethers
2008-06-01
method.46 Even though the derivation that produced Eq. (11) required integration over a hypothetical integer number of revolutions, the optimizer ... approach to multi-revolution, long time scale optimal control of an electrodynamic tether is investigated for a tethered satellite system in Low Earth...time scale approach is used to capture the effects of the Earth’s rotating tilted magnetic field. Optimal control solutions are achieved using a
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…
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
Asymptotic controllability and optimal control
NASA Astrophysics Data System (ADS)
Motta, M.; Rampazzo, F.
We consider a control problem where the state must approach asymptotically a target C while paying an integral cost with a non-negative Lagrangian l. The dynamics f is just continuous, and no assumptions are made on the zero level set of the Lagrangian l. Through an inequality involving a positive number p and a Minimum Restraint FunctionU=U(x) - a special type of Control Lyapunov Function - we provide a condition implying that (i) the system is asymptotically controllable, and (ii) the value function is bounded by U/p. The result has significant consequences for the uniqueness issue of the corresponding Hamilton-Jacobi equation. Furthermore it may be regarded as a first step in the direction of a feedback construction.
Metacognitive control and optimal learning.
Son, Lisa K; Sethi, Rajiv
2006-07-08
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 function. When the learning curve is concave, optimality requires that items at lower levels of initial competence be allocated greater time. On the other hand, with logistic learning curves, optimal allocations vary with time availability in complex and surprising ways. Hence there are conditions under which optimal strategies will be relatively easy to uncover, and others in which suboptimal time allocation might be expected. The model can therefore be used to address the question of whether and when learners should be able to exercise good metacognitive control in practice.
NASA Astrophysics Data System (ADS)
Guibout, Vincent M.
This dissertation has been motivated by the need for new methods to address complex problems that arise in spacecraft formation design. As a direct result of this motivation, a general methodology for solving two-point boundary value problems for Hamiltonian systems has been found. Using the Hamilton-Jacobi theory in conjunction with the canonical transformation induced by the phase flow, it is shown that generating functions solve two-point boundary value problems. Traditional techniques for addressing these problems are iterative and require an initial guess. The method presented in this dissertation solves boundary value problems at the cost of a single function evaluation, although it requires knowledge of at least one generating function. Properties of this method are presented. Specifically, we show that it includes perturbation theory and generalizes it to nonlinear systems. Most importantly, it predicts the existence of multiple solutions and allows one to recover all of these solutions. To demonstrate the efficiency of this approach, an algorithm for computing the generating functions is proposed and its convergence properties are studied. As the method developed in this work is based on the Hamiltonian structure of the problem, particular attention must be paid to the numerics of the algorithm. To address this, a general framework for studying the discretization of certain dynamical systems is developed. This framework generalizes earlier work on discretization of Lagrangian and Hamiltonian systems on tangent and cotangent bundles respectively. In addition, it provides new insights into some symplectic integrators and leads to a new discrete Hamilton-Jacobi theory. Most importantly, it allows one to discretize optimal control problems. In particular, a discrete maximum principle is presented. This dissertation also investigates applications of the proposed method to solve two-point boundary value problems. In particular, new techniques for designing
Dual approximations in optimal control
NASA Technical Reports Server (NTRS)
Hager, W. W.; Ianculescu, G. D.
1984-01-01
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Theory of coherent control with quantum light
NASA Astrophysics Data System (ADS)
Schlawin, Frank; Buchleitner, Andreas
2017-01-01
We develop a coherent control theory for multimode quantum light. It allows us to examine a fundamental problem in quantum optics: what is the optimal pulse form to drive a two-photon-transition? In formulating the question as a coherent control problem, we show that—and quantify how much—the strong frequency quantum correlations of entangled photons enhance the transition compared to shaped classical pulses. In ensembles of collectively driven two-level systems, such enhancement requires nonvanishing interactions.
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.
Social Control Theory and Delinquency.
ERIC Educational Resources Information Center
Wiatrowski, Michael D.; And Others
1981-01-01
Develops and tests multivariate models of social control theory which simultaneously consider how four bonds to society (attachment, commitment, involvement, and belief) operate in relation to delinquency. Suggests a revised formulation of social control, after adding background factors (measures of social class and ability) to the model.…
H2-optimal control with generalized state-space models for use in control-structure optimization
NASA Technical Reports Server (NTRS)
Wette, Matt
1991-01-01
Several advances are provided solving combined control-structure optimization problems. The author has extended solutions from H2 optimal control theory to the use of generalized state space models. The generalized state space models preserve the sparsity inherent in finite element models and hence provide some promise for handling very large problems. Also, expressions for the gradient of the optimal control cost are derived which use the generalized state space models.
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.
Protecting quantum information with optimal control
NASA Astrophysics Data System (ADS)
Grace, Matthew
Quantum computation (QC) holds the promise of efficiently solving problems which are practically intractable for classical computers. However, realizing this advantage requires the precise control of a quantum information processor (QIP) and effective protection of this processor from the pernicious inuence of decoherence induced by the surrounding environment. Therefore, the ability to generate high-fidelity logical operations in the presence of environmental coupling is crucial. Methods of optimal control are applied to the field of quantum information processing, providing practical solutions for the generation of logical operations and the suppression of undesired environmental effects. The work contained in this dissertation explores important aspects of system and control design. Results obtained in this work (i) illustrate how practical QC can be greatly facilitated by optimal control theory and (ii) reveal interesting physical insights through the discovery of effective control mechanisms. A special design of the physical structure of quantum information systems is formulated which is naturally immune to certain types of decoherence and yields tremendous flexibility in the construction of logical operations for QC. A fundamental component of this design involves encoding the logical basis states of a quantum bit into multiple physical levels of the corresponding quantum system. This design also makes the QIP better suited for the interaction with ultrafast broadband laser fields used in quantum control applications. Numerical simulations demonstrate the utility of this encoding approach for thermally excited quantum systems. Optimization algorithms are developed which generate controls that protect the QIP from the effects of the environment, with or without the weak-coupling or Born approximation, and simultaneously achieve a target objective, e.g., a state-to-state transition or unitary quantum operation. For the optimal control of quantum operations, a
Unifying process control and optimization
Makansi, J.
2005-09-01
About 40% of US generation is now subject to wholesale competition. To intelligently bid into these new markets, real-time prices must be aligned with real-time costs. It is time to integrate the many advanced applications, sensors, and analyzers used for control, automation, and optimization into a system that reflects process and financial objectives. The paper reports several demonstration projects in the USA revealing what is being done in the area of advanced process optimization (by Alliant Energy, American Electric Power, PacifiCorp, Detroit Edison and Tennessee Valley Authority). In addition to these projects US DOE's NETL has funded the plant environment and cost optimization system, PECOS which combines physical models, neural networks and fuzzy logic control to provide operators with least cost setpoints for controllable variables. At Dynegy Inc's Baldwin station in Illinois the DOE is subsidizing a project where real time, closed-loop IT systems will optimize combustion, soot-blowing and SCR performance as well as unit thermal performance and plant economic performance. Commercial products such as Babcock and Wilcox's Flame Doctor, continuous emissions monitoring systems and various real-time predictive monitoring systems are also available. 4 figs.
Gain optimization with nonlinear controls
NASA Technical Reports Server (NTRS)
Slater, G. L.; Kandadai, R. D.
1982-01-01
An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical computation requires only that the specific nonlinearity be considered in the analysis.
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
Transition delay using control theory.
Bagheri, S; Henningson, D S
2011-04-13
This review gives an account of recent research efforts to use feedback control for the delay of laminar-turbulent transition in wall-bounded shear flows. The emphasis is on reducing the growth of small-amplitude disturbances in the boundary layer using numerical simulations and a linear control approach. Starting with the application of classical control theory to two-dimensional perturbations developing in spatially invariant flows, flow control based on control theory has progressed towards more realistic three-dimensional, spatially inhomogeneous flow configurations with localized sensing/actuation. The development of low-dimensional models of the Navier-Stokes equations has played a key role in this progress. Moreover, shortcomings and future challenges, as well as recent experimental advances in this multi-disciplinary field, are discussed.
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
Practical synchronization on complex dynamical networks via optimal pinning control
NASA Astrophysics Data System (ADS)
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.
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.
Pilot-optimal multivariable control synthesis by output feedback
NASA Technical Reports Server (NTRS)
Schmidt, D. K.; Innocenti, M.
1981-01-01
A control system design approach for optimal stability augmentation, systems, using limited state feedback theory with the specific inclusion of the human pilot in the loop is presented. The methodology is especially suitable for application to flight vehicles exhibiting nonconventional dynamic characteristics and for which quantitative handling qualities specifications are not available. The design is based on a correlation between pilot ratings and objective function of the optimal control model of the human pilot. Simultaneous optimization for augmentation and pilot gains are required.
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.
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.
Zhang, Huaguang; Feng, Tao; Yang, Guang-Hong; Liang, Hongjing
2015-07-01
In this paper, the inverse optimal approach is employed to design distributed consensus protocols that guarantee consensus and global optimality with respect to some quadratic performance indexes for identical linear systems on a directed graph. The inverse optimal theory is developed by introducing the notion of partial stability. As a result, the necessary and sufficient conditions for inverse optimality are proposed. By means of the developed inverse optimal theory, the necessary and sufficient conditions are established for globally optimal cooperative control problems on directed graphs. Basic optimal cooperative design procedures are given based on asymptotic properties of the resulting optimal distributed consensus protocols, and the multiagent systems can reach desired consensus performance (convergence rate and damping rate) asymptotically. Finally, two examples are given to illustrate the effectiveness of the proposed methods.
Approximate Newton-type methods via theory of control
NASA Astrophysics Data System (ADS)
Yap, Chui Ying; Leong, Wah June
2014-12-01
In this paper, we investigate the possible use of control theory, particularly theory on optimal control to derive some numerical methods for unconstrained optimization problems. Based upon this control theory, we derive a Levenberg-Marquardt-like method that guarantees greatest descent in a particular search region. The implementation of this method in its original form requires inversion of a non-sparse matrix or equivalently solving a linear system in every iteration. Thus, an approximation of the proposed method via quasi-Newton update is constructed. Numerical results indicate that the new method is more effective and practical.
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.
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…
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
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 overdamped systems
NASA Astrophysics Data System (ADS)
Zulkowski, Patrick R.; DeWeese, Michael R.
2015-09-01
Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles underlying biological processes at the molecular level. Recent work has demonstrated that when a thermodynamic system is driven away from equilibrium then the space of controllable parameters has a Riemannian geometry induced by a generalized inverse diffusion tensor. We derive a simple, compact expression for the inverse diffusion tensor that depends solely on equilibrium information for a broad class of potentials. We use this formula to compute the minimal dissipation for two model systems relevant to small-scale information processing and biological molecular motors. In the first model, we optimally erase a single classical bit of information modeled by an overdamped particle in a smooth double-well potential. In the second model, we find the minimal dissipation of a simple molecular motor model coupled to an optical trap. In both models, we find that the minimal dissipation for the optimal protocol of duration τ is proportional to 1 /τ , as expected, though the dissipation for the erasure model takes a different form than what we found previously for a similar system.
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.
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…
Nonsmooth Optimization Algorithms, System Theory, and Software Tools
1993-04-13
Solving Optimal Control Problems with...and D. Q. Mayne, "A Method of Centers Based on Barrier Functions for Solving Optimal Control Problems with Continuum State and Con- trol Constraints...Barrier Functions for Solving Optimal Control Problems with Continuum State and Con- trol Constraints", SIAMJ. Control and Opt., Vol.31, No. 1. pp
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.
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.
Optimization of structure and control system
NASA Technical Reports Server (NTRS)
Khot, N. S.; Grandhi, Ramana V.
1989-01-01
The objective of this study is the simultaneous design of the structural and control system for space structures. This study is focused on considering the effect of the number and the location of the actuators on the minimum weight of the structure, and the total work done by the actuators for specified constraints and disturbance. The controls approach used is the linear quadratic regulator theory with constant feedback. At the beginning collocated actuators and sensors are provided in all the elements. The actuator doing the least work is removed one at a time, and the structure is optimized for the specified constraints on the closed-loop eigenvalues and the damping parameters. The procedure of eliminating an actuator is continued until an acceptable design satisfying the constraints is obtained. The study draws some conclusions on the trade between the total work done by the actuators, and the optimum weight and the number of actuators.
H-Infinity-Optimal Control for Distributed Parameter Systems
1991-02-28
F. Callier and C.A. Desoer , "An Algebra of Transfer Functions for Distributed Linear Time-Invariant Systems," IEEE Trans. Circuits Syst., Sept. 1978...neeuey and -f by blog* nu"bM) This report describes progress in the development and application of H-infinity-optimal control theory to distributed...parameter systems. This research is intended to develop both theory and algorithms capable of providing realistic control systems for physical plants which
Fuzzy logic control and optimization system
Lou, Xinsheng [West Hartford, CT
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.
Applying new optimization algorithms to more predictive control
Wright, S.J.
1996-03-01
The connections between optimization and control theory have been explored by many researchers and optimization algorithms have been applied with success to optimal control. The rapid pace of developments in model predictive control has given rise to a host of new problems to which optimization has yet to be applied. Concurrently, developments in optimization, and especially in interior-point methods, have produced a new set of algorithms that may be especially helpful in this context. In this paper, we reexamine the relatively simple problem of control of linear processes subject to quadratic objectives and general linear constraints. We show how new algorithms for quadratic programming can be applied efficiently to this problem. The approach extends to several more general problems in straightforward ways.
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.
Linear quadratic optimal control for symmetric systems
NASA Technical Reports Server (NTRS)
Lewis, J. H.; Martin, C. F.
1983-01-01
Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.
Optimal digital redesign of cascaded analogue controllers
NASA Technical Reports Server (NTRS)
Shieh, L. S.; Decrocq, B. B.; Zhang, J. L.
1991-01-01
This paper presents a new, optimal digital redesign technique for finding an optimal cascaded digital controller from the given continuous-time counterpart by minimizing a quadratic performance index. The control gains can be obtained by solving a set of Liapunov equations. The developed optimal cascaded digital controller enables the state and/or outputs of the digitally controlled closed-loop sampled-data system to optimally match those of the original continuous-time closed-loop system at any instant between sampling periods. The developed control law can be implemented using inexpensive and reliable digital electronics with a relatively long sampling period.
Stability and optimal parameters for continuous feedback chaos control.
Kouomou, Y Chembo; Woafo, P
2002-09-01
We investigate the conditions under which an optimal continuous feedback control can be achieved. Chaotic oscillations in the single-well Duffing model, with either a positive or a negative nonlinear stiffness term, are tuned to their related Ritz approximation. The Floquet theory enables the stability analysis of the control. Critical values of the feedback control coefficient fulfilling the optimization criteria are derived. The influence of the chosen target orbit, of the feedback coefficient, and of the onset time of control on its duration is discussed. The analytic approach is confirmed by numerical simulations.
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.
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.
A Fuzzy Logic Optimal Control Law Solution to the CMMCA Tracking Problem
1993-03-01
12 2.4 Differential Game Theory . . . ..... . . . . . . . 16 2.5 Optimal Control Theory. .. ........... . . . . . 19 2.6 Fuzzy...Specifically, this proposal examines dynamic programming, penalty function mothods, differential game theory, and optimal control theory. 2.2 Dynamic...deviations during the end game (8s19,72). Heavner discretized J by converting the integral to a summation and explored several different time steps. Heavner’a
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.
Geometric Computational Mechanics and Optimal Control
2011-12-02
methods. Further methods that depend on global optimization problems are in development and preliminary versions of these results, many of which...de la Sociedad Espanola de Matimatica Aplicada (SeMA), 50, 2010, pp 61-81. K. Flaßkamp, S. Ober-Blöbaum, M. Kobilarov, Solving optimal control...continuous setting. Consequently, globally optimal methods for computing optimal trajectories for vehicles with complex dynamics were developed. The
Optimal control of wind turbines in a turbulent boundary layer
NASA Astrophysics Data System (ADS)
Yilmaz, Ali Emre; Meyers, Johan
2016-11-01
In recent years, optimal control theory was combined with large-eddy simulations to study the optimal control of wind farms and their interaction with the atmospheric boundary layer. The individual turbine's induction factors were dynamically controlled in time with the aim of increasing overall power extraction. In these studies, wind turbines were represented using an actuator disk method. In the current work, we focus on optimal control on a much finer mesh (and a smaller computational domain), representing turbines with an actuator line method. Similar to Refs., optimization is performed using a gradient-based method, and gradients are obtained employing an adjoint formulation. Different cases are investigated, that include a single and a double turbine case both with uniform inflow, and with turbulent-boundary-layer inflow. The authors acknowledge support from the European Research Council (FP7-Ideas, Grant No. 306471).
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…
Lie Algebroids in Classical Mechanics and Optimal Control
NASA Astrophysics Data System (ADS)
Martínez, Eduardo
2007-03-01
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
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.
Optimal control design of pulse shapes as analytic functions.
Skinner, Thomas E; Gershenzon, Naum I
2010-06-01
Representing NMR pulse shapes by analytic functions is widely employed in procedures for optimizing performance. Insights concerning pulse dynamics can be applied to the choice of appropriate functions that target specific performance criteria, focusing the solution search and reducing the space of possible pulse shapes that must be considered to a manageable level. Optimal control theory can accommodate significantly larger parameter spaces and has been able to tackle problems of much larger scope than more traditional optimization methods. However, its numerically generated pulses, as currently constructed, do not readily incorporate the capabilities of particular functional forms, and the pulses are not guaranteed to vary smoothly in time, which can be a problem for faithful implementation on older hardware. An optimal control methodology is derived for generating pulse shapes as simple parameterized functions. It combines the benefits of analytic and numerical protocols in a single powerful algorithm that both complements and enhances existing optimization strategies.
Symmetries in the Optimal Control of Solar Sail Spacecraft
NASA Astrophysics Data System (ADS)
Kim, M.; Hall, C. D.
2005-08-01
The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal trajectories for several interrelated problem families and develop symmetry properties that can be used to simplify the solution-finding process. For the minimum-time planet rendezvous problem we identify different solution branches resulting in multiple solutions to the associated boundary value problem. We solve the optimal control problem via an indirect method using an efficient cascaded computational scheme. The global optimizer uses a technique called Adaptive Simulated Annealing. Newton and Quasi-Newton Methods perform the terminal fine tuning of the optimization parameters.
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.
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.
Linear optimal control of tokamak fusion devices
Kessel, C.E.; Firestone, M.A.; Conn, R.W.
1989-05-01
The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
Optimal control, optimization and asymptotic analysis of Purcell's microswimmer model
NASA Astrophysics Data System (ADS)
Wiezel, Oren; Or, Yizhar
2016-11-01
Purcell's swimmer (1977) is a classic model of a three-link microswimmer that moves by performing periodic shape changes. Becker et al. (2003) showed that the swimmer's direction of net motion is reversed upon increasing the stroke amplitude of joint angles. Tam and Hosoi (2007) used numerical optimization in order to find optimal gaits for maximizing either net displacement or Lighthill's energetic efficiency. In our work, we analytically derive leading-order expressions as well as next-order corrections for both net displacement and energetic efficiency of Purcell's microswimmer. Using these expressions enables us to explicitly show the reversal in direction of motion, as well as obtaining an estimate for the optimal stroke amplitude. We also find the optimal swimmer's geometry for maximizing either displacement or energetic efficiency. Additionally, the gait optimization problem is revisited and analytically formulated as an optimal control system with only two state variables, which can be solved using Pontryagin's maximum principle. It can be shown that the optimal solution must follow a "singular arc". Numerical solution of the boundary value problem is obtained, which exactly reproduces Tam and Hosoi's optimal gait.
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.
Optimal Quantum Control Using Randomized Benchmarking
NASA Astrophysics Data System (ADS)
Kelly, J.; Barends, R.; Campbell, B.; Chen, Y.; Chen, Z.; Chiaro, B.; Dunsworth, A.; Fowler, A. G.; Hoi, I.-C.; Jeffrey, E.; Megrant, A.; Mutus, J.; Neill, C.; O'Malley, P. J. J.; Quintana, C.; Roushan, P.; Sank, D.; Vainsencher, A.; Wenner, J.; White, T. C.; Cleland, A. N.; Martinis, John M.
2014-06-01
We present a method for optimizing quantum control in experimental systems, using a subset of randomized benchmarking measurements to rapidly infer error. This is demonstrated to improve single- and two-qubit gates, minimize gate bleedthrough, where a gate mechanism can cause errors on subsequent gates, and identify control crosstalk in superconducting qubits. This method is able to correct parameters so that control errors no longer dominate and is suitable for automated and closed-loop optimization of experimental systems.
Towards a general theory of optimal testing
NASA Astrophysics Data System (ADS)
Pericchi, Luis R. G.; Pereira, Carlos A. B.
2012-10-01
In Pericchi and Pereira [1] it is argued against the traditional way on which testing is based on fixed significance level, either using p-values (with fixed levels of evidence, like the 5% rule) or α values. We instead, follow an approach put forward by [2], on which an optimal test is chosen by minimizing type I and type II errors. Morris DeGroot in his authoritative book [2], Probability and Statistics 2nd Edition, stated that it is more reasonable to minimize a weighted sum of Type I and Type II error than to specify a value of type I error and then minimize Type II error. He showed it beyond reasonable doubt, but only in the very restrictive scenario of simple VS simple hypothesis, and it is not clear how to generalize it. We propose here a very natural generalization for composite hypothesis, by using general weight functions in the parameter space. This was also the position taken by [3, 4, 5]. We show, in a parallel manner to DeGroot's proof and Pereira's discussion, that the optimal test statistics are Bayes Factors, when the weighting functions are priors with mass on the whole parameter space. On the other hand when the weight functions are point masses in specific parameter values of practical significance, then a procedure is designed for which the sum of Type I error and Type II error in the specified points of practical significance is minimized. This can be seen as bridge between Bayesian Statistics and a new version of Hypothesis testing, more in line with statistical consistency and scientific insight.
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
Optimal magnetic attitude control of small spacecraft
NASA Astrophysics Data System (ADS)
Liang, Jinsong
Spacecraft attitude control, using only magnetic coils, suffers from being unable to apply a torque about the axis defined by the magnetic field of the earth. This lack of controllability results in marginal stability, slow slew maneuvering and convergence to equilibrium positions. Currently available control schemes typically require one or more orbits to finish a large angle attitude maneuver, which severely restricts the application of magnetic control in projects requiring fast attitude maneuvers. In this dissertation, the open-loop time-optimal magnetic control is first presented to show the potential performance increase of the magnetic attitude control method. Nonlinear time-varying models with constrained inputs are considered instead of the linearized model generally used. The results show that time-optimal magnetic attitude control can be considerably faster, than the current available control schemes. The inherent weakness of the open-loop method is its lack of robustness; specifically, its response is sensitive to small changes in the system. Two methods, model predictive control and continuous optimization approach, are presented as closed-loop control strategies to increase the robustness of the time-optimal approach. Simulation results show that these two feedback control schemes effectively improve the robustness of the control system. Finally, magnetic attitude regulation after the time-optimal magnetic control is discussed. The main contribution of this work shows that magnetic attitude control is not necessarily slow, as commonly believed, as long as an appropriate control algorithm is applied. The different time-optimal controllers presented show considerable convergence time reduction for large angle attitude maneuvers; which enables magnetic attitude control to be applied to more time-critical applications.
A note on the adaptive optimal control of ion accelerator facilities
Huang, T. )
1990-06-01
The application of optimal control theory to the computer control system of an ion accelerator facility is presented. The process is shown to consist of mathematical modeling of the underlying process, parameter identification, as well as some design methods of the optimal computer control and the techniques of realizing adaptive control.
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.
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
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
Ant Colony Optimization (ACO) refers to the family of algorithms inspired by the behavior of real ants and used to solve combinatorial problems such as the Traveling Salesman Problem (TSP).Optimal Foraging Theory (OFT) is an evolutionary principle wherein foraging organisms or insect parasites seek ...
Performance investigation of multigrid optimization for DNS-based optimal control problems
NASA Astrophysics Data System (ADS)
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
Optimal energy growth and optimal control in swept Hiemenz flow
NASA Astrophysics Data System (ADS)
Guégan, Alan; Schmid, Peter J.; Huerre, Patrick
2006-11-01
The objective of the study is first to examine the optimal transient growth of Görtler Hämmerlin perturbations in swept Hiemenz flow. This configuration constitutes a model of the flow in the attachment-line boundary layer at the leading-edge of swept wings. The optimal blowing and suction at the wall which minimizes the energy of the optimal perturbations is then determined. An adjoint-based optimization procedure applicable to both problems is devised, which relies on the maximization or minimization of a suitable objective functional. The variational analysis is carried out in the framework of the set of linear partial differential equations governing the chordwise and wall-normal velocity fluctuations. Energy amplifications of up to three orders of magnitude are achieved at low spanwise wavenumbers (k {˜} 0.1) and large sweep Reynolds number (textit{Re} {˜} 2000). Optimal perturbations consist of spanwise travelling chordwise vortices, with a vorticity distribution which is inclined against the sweep. Transient growth arises from the tilting of the vorticity distribution by the spanwise shear via a two-dimensional Orr mechanism acting in the basic flow dividing plane. Two distinct regimes have been identified: for k {≤sssim} 0.25, vortex dipoles are formed which induce large spanwise perturbation velocities; for k {gtrsim} 0.25, dipoles are not observed and only the Orr mechanism remains active. The optimal wall blowing control yields for instance an 80% decrease of the maximum perturbation kinetic energy reached by optimal disturbances at textit{Re} {=} 550 and k {=} 0.25. The optimal wall blowing pattern consists of spanwise travelling waves which follow the naturally occurring vortices and qualitatively act in the same manner as a more simple constant gain feedback control strategy.
Optimal control problems with switching points
NASA Astrophysics Data System (ADS)
Seywald, Hans
1991-09-01
An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.
Parameter optimization in AQM controller design to support TCP traffic
NASA Astrophysics Data System (ADS)
Yang, Wei; Yang, Oliver W.
2004-09-01
TCP congestion control mechanism has been widely investigated and deployed on Internet in preventing congestion collapse. We would like to employ modern control theory to specify quantitatively the control performance of the TCP communication system. In this paper, we make use of a commonly used performance index called the Integral of the Square of the Error (ISE), which is a quantitative measure to gauge the performance of a control system. By applying the ISE performance index into the Proportional-plus-Integral controller based on Pole Placement (PI_PP controller) for active queue management (AQM) in IP routers, we can further tune the parameters for the controller to achieve an optimum control minimizing control errors. We have analyzed the dynamic model of the TCP congestion control under this ISE, and used OPNET simulation tool to verify the derived optimized parameters of the controllers.
Optimized chaos control with simple limiters.
Wagner, C; Stoop, R
2001-01-01
We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor.
Optimal Corrosion Control Treatment Evaluation Technical Recommendations
This document provides technical recommendations that both systems and primacy agencies can use to comply with LCR CCT requirements and effective evaluation and designation of optimal corrosion control treatment (OCCT).
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.
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.
Optimal disturbance rejecting control of hyperbolic systems
NASA Technical Reports Server (NTRS)
Biswas, Saroj K.; Ahmed, N. U.
1994-01-01
Optimal regulation of hyperbolic systems in the presence of unknown disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of the worst possible perturbations are developed. The results also characterize the worst possible disturbance that the system will be able to tolerate before any degradation of the system performance. Numerical results on the control of a vibrating beam are presented.
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
Linear quadratic optimal controller for cable-driven parallel robots
NASA Astrophysics Data System (ADS)
Abdolshah, Saeed; Shojaei Barjuei, Erfan
2015-12-01
In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.
Stochastic Optimal Control and Linear Programming Approach
Buckdahn, R.; Goreac, D.; Quincampoix, M.
2011-04-15
We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.
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…
Minimax D-Optimal Designs for Item Response Theory Models.
ERIC Educational Resources Information Center
Berger, Martjin P. F.; King, C. Y. Joy; Wong, Weng Kee
2000-01-01
Proposed minimax designs for item response theory (IRT) models to overcome the problem of local optimality. Compared minimax designs to sequentially constructed designs for the two parameter logistic model. Results show that minimax designs can be nearly as efficient as sequentially constructed designs. (Author/SLD)
"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…
Kalman meets neuron - the intersection of control theory and neuroscience
NASA Astrophysics Data System (ADS)
Schiff, Steven
2009-03-01
Since the 1950s, we have developed mature theories of modern control theory and computational neuroscience with almost no interaction between these disciplines. With the advent of computationally efficient nonlinear Kalman filtering techniques, along with improved neuroscience models which provide increasingly accurate reconstruction of dynamics in a variety of important normal and disease states in the brain, the prospects for a synergistic interaction between these fields are now strong. I will show recent examples of the use of nonlinear control theory for the assimilation and control of single neuron dynamics, a novel framework for dynamic clamp, the modulation of oscillatory wave dynamics in brain cortex, a control framework for Parkinsonian dynamics and seizures, and the use of optimized parameter model networks to assimilate complex network data.
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.
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)
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.
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.
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.
System Optimization by Periodic Control.
1982-06-01
1979-80 the main thrust was in finding finite step algorithms for the Cesaro average payoffs when the law of motion is completely controlled by one...II be numbered as 1,2,...m and 1,2,...n. Let *ij(s) be the expected Cesaro average income if pure stationary strff9 o 0Ymf!F1P AR*% ’rW by NOTI CE CO
Plasma Flow Control Optimized Airfoil
NASA Astrophysics Data System (ADS)
Voikov, Vladimir; Patel, Mehul
2005-11-01
Recent advances in flow control research have demonstrated that plasma actuators can be efficient in different aerodynamic applications, particularly in providing flight control without conventional moving surfaces. The concept involves the use of a laminar airfoil design that employs a separation ramp at the trailing edge that can be manipulated by a plasma actuator to control lift, similar to trailing-edge flaps. The advantages are lower drag by a combination of the laminar flow design, and elimination of parasitic drag associated with wing-flap junctions. This work involves numerical simulations and experiments on a HSNLF(1)-0213 airfoil. The numerical results are obtained using an unsteady, compressible Navier-Stokes simulation that includes a model for the plasma actuators. The experiments are performed on a 2-D airfoil section that is mounted on a lift-drag force balance. The results demonstrate lift enhancement produced by the plasma actuator that is comparable to a plane flap. They also reveal an optimum actuator unsteady frequency that scales with the length of the separated region and local velocity, and is associated with the generation of a train of spanwise vortices. Other scaling including the effect of Reynolds number is presented.
A Danger-Theory-Based Immune Network Optimization Algorithm
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. PMID:23483853
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.
Charge Optimization Theory for Induced-Fit Ligands
2012-01-01
The design of ligands with high affinity and specificity remains a fundamental challenge in understanding molecular recognition and developing therapeutic interventions. Charge optimization theory addresses this problem by determining ligand charge distributions that produce the most favorable electrostatic contribution to the binding free energy. The theory has been applied to the design of binding specificity as well. However, the formulations described only treat a rigid ligand—one that does not change conformation upon binding. Here, we extend the theory to treat induced-fit ligands for which the unbound ligand conformation may differ from the bound conformation. We develop a thermodynamic pathway analysis for binding contributions relevant to the theory, and we illustrate application of the theory using HIV-1 protease with our previously designed and validated subnanomolar inhibitor. Direct application of rigid charge optimization approaches to nonrigid cases leads to very favorable intramolecular electrostatic interactions that are physically unreasonable, and analysis shows the ligand charge distribution massively stabilizes the preconformed (bound) conformation over the unbound. After analyzing this case, we provide a treatment for the induced-fit ligand charge optimization problem that produces physically realistic results. The key factor is introducing the constraint that the free energy of the unbound ligand conformation be lower or equal to that of the preconformed ligand structure, which corresponds to the notion that the unbound structure is the ground unbound state. Results not only demonstrate the applicability of this methodology to discovering optimized charge distributions in an induced-fit model, but also provide some insights into the energetic consequences of ligand conformational change on binding. Specifically, the results show that, from an electrostatic perspective, induced-fit binding is not an adaptation designed to enhance binding
Optimal control of the sweeping process over polyhedral controlled sets
NASA Astrophysics Data System (ADS)
Colombo, G.; Henrion, R.; Nguyen, D. Hoang; Mordukhovich, B. S.
2016-02-01
The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong W 1 , 2-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.
Control theory and psychopathology: an integrative approach.
Mansell, Warren
2005-06-01
Perceptual control theory (PCT; Powers, 1973) is presented and adapted as a framework to understand the causes, maintenance, and treatment of psychological disorders. PCT provides dynamic, working models based on the principle that goal-directed activity arises from a hierarchy of negative feedback loops that control perception through control of the environment. The theory proposes that psychological distress arises from the unresolved conflict between goals. The present paper integrates PCT, control theory, and self-regulatory approaches to psychopathology and psychotherapy and recent empirical findings, particularly in the field of cognitive therapy. The approach aims to offer fresh insights into the role of goal conflict, automatic processes, imagery, perceptual distortion, and loss of control in psychological disorders. Implications for psychological therapy are discussed, including an integration of the existing work on the assessment of control profiles and the use of assertive versus yielding modes of control.
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.
The synthesis of optimal controls for linear, time-optimal problems with retarded controls.
NASA Technical Reports Server (NTRS)
Banks, H. T.; Jacobs, M. Q.; Latina, M. R.
1971-01-01
Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
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...
Bifurcation and Optimal Stochastic Control.
1982-03-01
as soon as luX InW w’(0) n L nis boundeI. To sir.iplity the notations, we denote by u = 1 . Without loss of n generality we may assume that c l...Stochastic Control. F O R M I II I • Il I i ,iii i, DD I JAP7 1473 EDITION OF I NOV S IS OSOLE’TE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE i(,en bot. EntereJ) DAT FILMEI DIC
Accelerated monotonic convergence of optimal control over quantum dynamics.
Ho, Tak-San; Rabitz, Herschel
2010-08-01
The control of quantum dynamics is often concerned with finding time-dependent optimal control fields that can take a system from an initial state to a final state to attain the desired value of an observable. This paper presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. The formulation is based on a two-point boundary-value quantum control paradigm (TBQCP) expressed as a nonlinear integral equation of the first kind arising from dynamical invariant tracking control. TBQCP is shown to be related to various existing techniques, including local control theory, the Krotov method, and optimal control theory. Several accelerated monotonic convergence schemes for iteratively computing control fields are derived based on TBQCP. Numerical simulations are compared with the Krotov method showing that the new TBQCP schemes are efficient and remain monotonically convergent over a wide range of the iteration step parameters and the control pulse lengths, which is attributable to the trap-free character of the transition probability quantum dynamics control landscape.
Quantitative Robust Control Engineering: Theory and Applications
2006-09-01
1992). Discrete quantitative feedback technique, Capítulo 16 en el libro : Digital Control Systems: theory, hardware, software, 2ª edicion. McGraw...Rasmussen S.J., Garcia-Sanz, M. (2001, 2005), Software de diseño del libro Quantitative Feedback Theory: Fundamentals and Applications. Edición 2ª. CRCPress
Optimal-control theoretic methods for optimization and regulation of distributed parameter systems
NASA Astrophysics Data System (ADS)
Goss, Jennifer Dawn
Optimal control and optimization of distributed parameter systems are discussed in the context of a common control framework. The adjoint method of optimization and the traditional linear quadratic regulator implementation of optimal control both employ adjoint or costate variables in the determination of control variable progression. As well both theories benefit from a reduced order model approximation in their execution. This research aims to draw clear parallels between optimization and optimal control utilizing these similarities. Several applications are presented showing the use of adjoint/costate variables and reduced order models in optimization and optimal control problems. The adjoint method for shape optimization is derived and implemented for the quasi-one-dimensional duct and two variations of a two-dimensional double ramp inlet. All applications are governed by the Euler equations. The quasi-one-dimensional duct is solved first to test the adjoint method and to verify the results against an analytical solution. The method is then adapted to solve the shape optimization of the double ramp inlet. A finite volume solver is tested on the flow equations and then implemented for the corresponding adjoint equations. The gradient of the cost function with respect to the shape parameters is derived based on the computed adjoint variables. The same inlet shape optimization problem is then solved using a reduced order model. The basis functions in the reduced order model are computed using the method of snapshots form of proper orthogonal decomposition. The corresponding weights are derived using an optimization in the design parameter space to match the reduced order model to the original snapshots. A continuous map of these weights in terms of the design variables is obtained via a response surface approximations and artificial neural networks. This map is then utilized in an optimization problem to determine the optimal inlet shape. As in the adjoint method
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
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...
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.
Computational Methods for Design, Control and Optimization
2007-10-01
34scenario" that applies to channel flows ( Poiseuille flows , Couette flow ) and pipe flows . Over the past 75 years many complex "transition theories" have... Simulation of Turbulent Flows , Springer Verlag, 2005. Additional Publications Supported by this Grant 1. J. Borggaard and T. Iliescu, Approximate Deconvolution...rigorous analysis of design algorithms that combine numerical simulation codes, approximate sensitivity calculations and optimization codes. The fundamental
Monotonically convergent optimization in quantum control using Krotov's method.
Reich, Daniel M; Ndong, Mamadou; Koch, Christiane P
2012-03-14
The non-linear optimization method developed by A. Konnov and V. Krotov [Autom. Remote Cont. (Engl. Transl.) 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schrödinger equation [S. E. Sklarz and D. J. Tannor, Phys. Rev. A 66, 053619 (2002)]. Here we show that based on the Konnov-Krotov method, monotonically convergent algorithms are obtained for a large class of quantum control problems. It includes, in addition to nonlinear equations of motion, control problems that are characterized by non-unitary time evolution, nonlinear dependencies of the Hamiltonian on the control, time-dependent targets, and optimization functionals that depend to higher than second order on the time-evolving states. We furthermore show that the nonlinear (second order) contribution can be estimated either analytically or numerically, yielding readily applicable optimization algorithms. We demonstrate monotonic convergence for an optimization functional that is an eighth-degree polynomial in the states. For the "standard" quantum control problem of a convex final-time functional, linear equations of motion and linear dependency of the Hamiltonian on the field, the second-order contribution is not required for monotonic convergence but can be used to speed up convergence. We demonstrate this by comparing the performance of first- and second-order algorithms for two examples.
Optimal control for Rydberg quantum technology building blocks
NASA Astrophysics Data System (ADS)
Müller, Matthias M.; Pichler, Thomas; Montangero, Simone; Calarco, Tommaso
2016-04-01
We consider a platform for quantum technology based on Rydberg atoms in optical lattices where each atom encodes one qubit of information and external lasers can manipulate their state. We demonstrate how optimal control theory enables the functioning of two specific building blocks on this platform: We engineer an optimal protocol to perform a two-qubit phase gate and to transfer the information within the lattice among specific sites. These two elementary operations allow to design very general operations like storage of atoms and entanglement purification as, for example, needed for quantum repeaters.
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.
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.
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.
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.
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.
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.
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.
Optimal, real-time control--colliders
Spencer, J.E.
1991-05-01
With reasonable definitions, optimal control is possible for both classical and quantal systems with new approaches called PISC(Parallel) and NISC(Neural) from analogy with RISC (Reduced Instruction Set Computing). If control equals interaction, observation and comparison to some figure of merit with interaction via external fields, then optimization comes from varying these fields to give design or operating goals. Structural stability can then give us tolerance and design constraints. But simulations use simplified models, are not in real-time and assume fixed or stationary conditions, so optimal control goes far beyond convergence rates of algorithms. It is inseparable from design and this has many implications for colliders. 12 refs., 3 figs.
Quadratic optimal cooperative control synthesis with flight control application
NASA Technical Reports Server (NTRS)
Schmidt, D. K.; Innocenti, M.
1984-01-01
An optimal control-law synthesis approach is presented that involves simultaneous solution for two cooperating controllers operating in parallel. One controller's structure includes stochastic state estimation and linear feedback of the state estimates, while the other controller involves direct linear feedback of selected system output measurements. This structure is shown to be optimal under the constraint of linear feedback of system outputs in one controller. Furthermore, it is appropriate for flight control synthesis where the full-state optimal stochastic controller can be adjusted to be representative of an optimal control model of the human pilot in a stochastic regulation task. The method is experimentally verified in the case of the selection of pitch-damper gain for optimum pitch tracking, where optimum implies the best subjective pilot rating in the task. Finally, results from application of the method to synthesize a controller for a multivariable fighter aircraft are presented, and implications of the results of this method regarding the optimal plant dynamics for tracking are discussed.
Optimal pulse design in quantum control: A unified computational method
Li, Jr-Shin; Ruths, Justin; Yu, Tsyr-Yan; Arthanari, Haribabu; Wagner, Gerhard
2011-01-01
Many key aspects of control of quantum systems involve manipulating a large quantum ensemble exhibiting variation in the value of parameters characterizing the system dynamics. Developing electromagnetic pulses to produce a desired evolution in the presence of such variation is a fundamental and challenging problem in this research area. We present such robust pulse designs as an optimal control problem of a continuum of bilinear systems with a common control function. We map this control problem of infinite dimension to a problem of polynomial approximation employing tools from geometric control theory. We then adopt this new notion and develop a unified computational method for optimal pulse design using ideas from pseudospectral approximations, by which a continuous-time optimal control problem of pulse design can be discretized to a constrained optimization problem with spectral accuracy. Furthermore, this is a highly flexible and efficient numerical method that requires low order of discretization and yields inherently smooth solutions. We demonstrate this method by designing effective broadband π/2 and π pulses with reduced rf energy and pulse duration, which show significant sensitivity enhancement at the edge of the spectrum over conventional pulses in 1D and 2D NMR spectroscopy experiments. PMID:21245345
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.
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.
Lagrange Duality Theory for Convex Control Problems,
to be optimal is also given. The dual variables p and v corresponding to the system dynamics and state constraints are proved to be of bounded ... variation while the multiplier corresponding to the control constraints is proved to lie in 1. Finally, a control and state minimum principle is proved. If
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.
Optimal control of anthracnose using mixed strategies.
Fotsa Mbogne, David Jaures; Thron, Christopher
2015-11-01
In this paper we propose and study a spatial diffusion model for the control of anthracnose disease in a bounded domain. The model is a generalization of the one previously developed in [15]. We use the model to simulate two different types of control strategies against anthracnose disease. Strategies that employ chemical fungicides are modeled using a continuous control function; while strategies that rely on cultivational practices (such as pruning and removal of mummified fruits) are modeled with a control function which is discrete in time (though not in space). For comparative purposes, we perform our analyses for a spatially-averaged model as well as the space-dependent diffusion model. Under weak smoothness conditions on parameters we demonstrate the well-posedness of both models by verifying existence and uniqueness of the solution for the growth inhibition rate for given initial conditions. We also show that the set [0, 1] is positively invariant. We first study control by impulsive strategies, then analyze the simultaneous use of mixed continuous and pulse strategies. In each case we specify a cost functional to be minimized, and we demonstrate the existence of optimal control strategies. In the case of pulse-only strategies, we provide explicit algorithms for finding the optimal control strategies for both the spatially-averaged model and the space-dependent model. We verify the algorithms for both models via simulation, and discuss properties of the optimal solutions.
Optimal control of circular cylinder wakes using long control horizons
NASA Astrophysics Data System (ADS)
Flinois, Thibault L. B.; Colonius, Tim
2015-08-01
The classical problem of suppressing vortex shedding in the wake of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers between 75 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by 19%, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after transients. Unlike open-loop control, the optimal control is shown to maintain a specific phase relationship between the actuation and the shedding in order to stabilize the wake. A comparison is also given between the performance of optimizations for different Reynolds numbers, cost functions, and horizon lengths. It is shown that the long horizons used are necessary in order to stabilize the vortex shedding efficiently.
Optimal control in NMR spectroscopy: numerical implementation in SIMPSON.
Tosner, Zdenek; Vosegaard, Thomas; Kehlet, Cindie; Khaneja, Navin; Glaser, Steffen J; Nielsen, Niels Chr
2009-04-01
We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.
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.
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.
Optimization-based controller design for rotorcraft
NASA Technical Reports Server (NTRS)
Tsing, N.-K.; Fan, M. K. H.; Barlow, J.; Tits, A. L.; Tischler, M. B.
1993-01-01
An optimization-based methodology for linear control system design is outlined by considering the design of a controller for a UH-60 rotorcraft in hover. A wide range of design specifications is taken into account: internal stability, decoupling between longitudinal and lateral motions, handling qualities, and rejection of windgusts. These specifications are investigated while taking into account physical limitations in the swashplate displacements and rates of displacement. The methodology crucially relies on user-machine interaction for tradeoff exploration.
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.
Stochastic Linear Quadratic Optimal Control Problems
Chen, S.; Yong, J.
2001-07-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.
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.
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.
Solving the optimal control problem of the parabolic PDEs in exploitation of oil
NASA Astrophysics Data System (ADS)
Effati, S.; Janfada, M.; Esmaeili, M.
2008-04-01
In this paper, the optimal control problem is governed by weak coupled parabolic PDEs and involves pointwise state and control constraints. We use measure theory method for solving this problem. In order to use the weak solution of problem, first problem has been transformed into measure form. This problem is reduced to a linear programming problem. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures. We find piecewise-constant optimal control functions which are an approximate control for the original optimal control problem.
Adaptive control based on retrospective cost optimization
NASA Astrophysics Data System (ADS)
Santillo, Mario A.
This dissertation studies adaptive control of multi-input, multi-output, linear, time-invariant, discrete-time systems that are possibly unstable and nonminimum phase. We consider both gradient-based adaptive control as well as retrospective-cost-based adaptive control. Retrospective cost optimization is a measure of performance at the current time based on a past window of data and without assumptions about the command or disturbance signals. In particular, retrospective cost optimization acts as an inner loop to the adaptive control algorithm by modifying the performance variables based on the difference between the actual past control inputs and the recomputed past control inputs based on the current control law. We develop adaptive control algorithms that are effective for systems that are nonminimum phase. We consider discrete-time adaptive control since these control laws can be implemented directly in embedded code without requiring an intermediate discretization step. Furthermore, the adaptive controllers in this dissertation are developed under minimal modeling assumptions. In particular, the adaptive controllers require knowledge of the sign of the high-frequency gain and a sufficient number of Markov parameters to approximate the nonminimum-phase zeros (if any). No additional modeling information is necessary. The adaptive controllers presented in this dissertation are developed for full-state-feedback stabilization, static-output-feedback stabilization, as well as dynamic compensation for stabilization, command following, disturbance rejection, and model reference adaptive control. Lyapunov-based stability and convergence proofs are provided for special cases. We present numerical examples to illustrate the algorithms' effectiveness in handling systems that are unstable and/or nonminimum phase and to provide insight into the modeling information required for controller implementation.
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.
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.
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.
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%).
Gain optimization with non-linear controls
NASA Technical Reports Server (NTRS)
Slater, G. L.; Kandadai, R. D.
1984-01-01
An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.
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 in a noisy system
NASA Astrophysics Data System (ADS)
Asenjo, F.; Toledo, B. A.; Muñoz, V.; Rogan, J.; Valdivia, J. A.
2008-09-01
We describe a simple method to control a known unstable periodic orbit (UPO) in the presence of noise. The strategy is based on regarding the control method as an optimization problem, which allows us to calculate a control matrix A. We illustrate the idea with the Rossler system, the Lorenz system, and a hyperchaotic system that has two exponents with positive real parts. Initially, a UPO and the corresponding control matrix are found in the absence of noise in these systems. It is shown that the strategy is useful even if noise is added as control is applied. For low noise, it is enough to find a control matrix such that the maximum Lyapunov exponent λmax<0, and with a single non-null entry. If noise is increased, however, this is not the case, and the full control matrix A may be required to keep the UPO under control. Besides the Lyapunov spectrum, a characterization of the control strategies is given in terms of the average distance to the UPO and the control effort required to keep the orbit under control. Finally, particular attention is given to the problem of handling noise, which can affect considerably the estimation of the UPO itself and its exponents, and a cleaning strategy based on singular value decomposition was developed. This strategy gives a consistent manner to approach noisy systems, and may be easily adapted as a parametric control strategy, and to experimental situations, where noise is unavoidable.
Vision-controlled paint spray optimization
NASA Astrophysics Data System (ADS)
Ettinger, Gary; Christian, Donald J.
1992-04-01
This paper is a case history of spray paint optimization system based on machine vision technology in a factory automation application. The system is implemented as an industrial control for a reciprocating electrostatic sprayer used for priming and painting of armor plate for military ground vehicles. Incoming plates are highly variable in size, shape, and orientation, and are processes in very small production lots. A laser imager is used to digitize visual cross sections of each plate one line at a time. The raster lines are then assembled into a two dimensional image and processed. The spray pattern is optimized for precise paint coverage with minimum overspray. The paint optimizer system has yielded a measured 25 percent savings in bulk paint use, resulting in less booth and equipment maintenance, reduced paint fumes in the atmosphere, and reduced waste disposal, and now has several months of successful production history.
Modal methods in optimal control synthesis
NASA Technical Reports Server (NTRS)
Bryson, A. E., Jr.; Hall, W. E., Jr.
1980-01-01
Efficient algorithms for solving linear smoother-follower problems with quadratic criteria are presented. For time-invariant systems, the algorithm consists of one backward integration of a linear vector equation and one forward integration of another linear vector equation. Furthermore, the backward and forward Riccati matrices can be expressed in terms of the eigenvalues and eigenvectors of the Euler-Lagrange equations. Hence, the gains of the forward and backward Kalman-Bucy filters and of the optimal state-feedback regulator can be determined without integration of matrix Riccati equations. A computer program has been developed, based on this method of determining the gains, to synthesize the optimal time-invariant compensator in the presence of random disturbance inputs and random measurement errors. The program also computes the rms state and control variables of the optimal closed-loop system.
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.
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.
NASA Astrophysics Data System (ADS)
Sardesai, Chetan R.
The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the
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 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.
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.
An Integrated Theory of Complement Control.
ERIC Educational Resources Information Center
Sag, Ivan A.; Pollard, Carl
1991-01-01
Presents an integrated theory of the syntactic and semantic representation of complements where the unexpressed subjects of the embedded verb-phrase complement are subject to certain interpretation restrictions. It is argued that the grammar of English controlled complements can be derived from the interaction of semantically based principles of…
Optimal Control of Magnetization Dynamics in Ferromagnetic Materials using TDDFT
NASA Astrophysics Data System (ADS)
Elliott, Peter; Krieger, Kevin; Gross, E. K. U.
2015-03-01
Recently intense laser-field induced ultrafast demagnetization was observed in ab-initio simulations using Time-Dependent Density Functional Theory (TDDFT) for various ferromagnetic materials (Fe,Co,Ni). From a practical and technological viewpoint, it is useful if the induced dynamics (e.g. of the total magnetic moment) are controllable. In this talk we apply optimal control theory together with TDDFT calculations to tailor the intense laser pulses so as to achieve a particular outcome (e.g. maximize the total moment lost) while also including any required constraints (e.g pulse duration, pulse frequencies, maximum fluence, etc). Support from European Communities FP7, through the CRONOS project Grant No. 280879.
NASA Astrophysics Data System (ADS)
Bulgakov, V. K.; Strigunov, V. V.
2009-05-01
The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories.
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.
Quantum computing gates via optimal control
NASA Astrophysics Data System (ADS)
Atia, Yosi; Elias, Yuval; Mor, Tal; Weinstein, Yossi
2014-10-01
We demonstrate the use of optimal control to design two entropy-manipulating quantum gates which are more complex than the corresponding, commonly used, gates, such as CNOT and Toffoli (CCNOT): A two-qubit gate called polarization exchange (PE) and a three-qubit gate called polarization compression (COMP) were designed using GRAPE, an optimal control algorithm. Both gates were designed for a three-spin system. Our design provided efficient and robust nuclear magnetic resonance (NMR) radio frequency (RF) pulses for 13C2-trichloroethylene (TCE), our chosen three-spin system. We then experimentally applied these two quantum gates onto TCE at the NMR lab. Such design of these gates and others could be relevant for near-future applications of quantum computing devices.
Augmented Lagrangian method for optimal laser control
NASA Astrophysics Data System (ADS)
Shen, Hai; Dussault, Jean-Pierre; Bandrauk, Andre D.
1994-06-01
We use penalty methods derived from Augmented Lagrangians coupled with unitary exponential operator methods to solve the optimal control problem for molecular time-dependent Schodinger equations involving laser pulse excitations. A stable numerical algorithm is presented which propagates directly from initial states to given final states. Results are reported for an analytically solvable model for the complete inversion of a three-state system.
Anxiety and cognitive performance: attentional control theory.
Eysenck, Michael W; Derakshan, Nazanin; Santos, Rita; Calvo, Manuel G
2007-05-01
Attentional control theory is an approach to anxiety and cognition representing a major development of Eysenck and Calvo's (1992) processing efficiency theory. It is assumed that anxiety impairs efficient functioning of the goal-directed attentional system and increases the extent to which processing is influenced by the stimulus-driven attentional system. In addition to decreasing attentional control, anxiety increases attention to threat-related stimuli. Adverse effects of anxiety on processing efficiency depend on two central executive functions involving attentional control: inhibition and shifting. However, anxiety may not impair performance effectiveness (quality of performance) when it leads to the use of compensatory strategies (e.g., enhanced effort; increased use of processing resources). Directions for future research are discussed.
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.
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
Primer Vector Optimization: Survey of Theory, new Analysis and Applications
NASA Astrophysics Data System (ADS)
Guzman
This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and
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
Optimal control for a tuberculosis model with reinfection and post-exposure interventions.
Silva, Cristiana J; Torres, Delfim F M
2013-08-01
We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure interventions. They depend on the parameters of the model and reduce effectively the number of active infectious and persistent latent individuals. The time that the optimal controls are at the upper bound increase with the transmission coefficient. A general explicit expression for the basic reproduction number is obtained and its sensitivity with respect to the model parameters is discussed. Numerical results show the usefulness of the optimization strategies.
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.
Optimal multiplexed sensing: bounds, conditions and a graph theory link.
Ratner, Netanel; Schechner, Yoav Y; Goldberg, Felix
2007-12-10
Measuring an array of variables is central to many systems, including imagers (array of pixels), spectrometers (array of spectral bands) and lighting systems. Each of the measurements, however, is prone to noise and potential sensor saturation. It is recognized by a growing number of methods that such problems can be reduced by multiplexing the measured variables. In each measurement, multiple variables (radiation channels) are mixed (multiplexed) by a code. Then, after data acquisition, the variables are decoupled computationally in post processing. Potential benefits of the use of multiplexing include increased signal-to-noise ratio and accommodation of scene dynamic range. However, existing multiplexing schemes, including Hadamard-based codes, are inhibited by fundamental limits set by sensor saturation and Poisson distributed photon noise, which is scene dependent. There is thus a need to find optimal codes that best increase the signal to noise ratio, while accounting for these effects. Hence, this paper deals with the pursuit of such optimal measurements that avoid saturation and account for the signal dependency of noise. The paper derives lower bounds on the mean square error of demultiplexed variables. This is useful for assessing the optimality of numerically-searched multiplexing codes, thus expediting the numerical search. Furthermore, the paper states the necessary conditions for attaining the lower bounds by a general code.We show that graph theory can be harnessed for finding such ideal codes, by the use of strongly regular graphs.
Methods for combined control-structure optimization
NASA Technical Reports Server (NTRS)
Milman, M.; Scheid, R. E.; Salama, M.; Bruno, R.
1989-01-01
This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objective of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to asist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further consideration, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose, and a numerical example is presented.
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.
An integrated optimal control algorithm for discrete-time nonlinear stochastic system
NASA Astrophysics Data System (ADS)
Kek, Sie Long; Lay Teo, Kok; Mohd Ismail, A. A.
2010-12-01
Consider a discrete-time nonlinear system with random disturbances appearing in the real plant and the output channel where the randomly perturbed output is measurable. An iterative procedure based on the linear quadratic Gaussian optimal control model is developed for solving the optimal control of this stochastic system. The optimal state estimate provided by Kalman filtering theory and the optimal control law obtained from the linear quadratic regulator problem are then integrated into the dynamic integrated system optimisation and parameter estimation algorithm. The iterative solutions of the optimal control problem for the model obtained converge to the solution of the original optimal control problem of the discrete-time nonlinear system, despite model-reality differences, when the convergence is achieved. An illustrative example is solved using the method proposed. The results obtained show the effectiveness of the algorithm proposed.
Vehicular Slip Ratio Control Using Nonlinear Control Theory
NASA Astrophysics Data System (ADS)
Ikeda, Yuichi; Nakajima, Takashi; Chida, Yuichi
In this paper, we discuss integrated vehicle slip ratio control under both deceleration and acceleration without the need for controller switching, and also propose a design method for such an integrated slip ratio controller based on the slip ratio dynamics. When a vehicle switches from acceleration to deceleration and vice versa, the slip ratio varies discontinuously. Here, the slip ratio is approximated to a continuous function by using a sigmoid function. And a controller is then designed by using feedback linearization based on the approximated slip ratio. The stability of the designed control system is proven by Lyapunov stability theorem. Furthermore, we propose a robust control method based on a disturbance observer and sliding mode control theory. Finally, the effectiveness of the proposed control method is verified through numerical simulation.
Optimal finite horizon control in gene regulatory networks
NASA Astrophysics Data System (ADS)
Liu, Qiuli
2013-06-01
As a paradigm for modeling gene regulatory networks, probabilistic Boolean networks (PBNs) form a subclass of Markov genetic regulatory networks. To date, many different stochastic optimal control approaches have been developed to find therapeutic intervention strategies for PBNs. A PBN is essentially a collection of constituent Boolean networks via a probability structure. Most of the existing works assume that the probability structure for Boolean networks selection is known. Such an assumption cannot be satisfied in practice since the presence of noise prevents the probability structure from being accurately determined. In this paper, we treat a case in which we lack the governing probability structure for Boolean network selection. Specifically, in the framework of PBNs, the theory of finite horizon Markov decision process is employed to find optimal constituent Boolean networks with respect to the defined objective functions. In order to illustrate the validity of our proposed approach, an example is also displayed.
Local control theory applied to molecular photoassociation.
Marquetand, Philipp; Engel, Volker
2007-08-28
Local control theory (LCT) is employed to achieve molecular photoassociation with shaped laser pulses. Within LCT, the control fields are constructed from the response of the system to the perturbation which makes them accessible to a straightforward interpretation. This is shown regarding the ground-state collision of H+F and H+I atoms. Different objectives are defined, which aim at the formation of vibrational cold or hot associated molecules, respectively. Results are presented for s-wave scattering, where the rotational degree of freedom is ignored and also for full scale calculations including rotations, in order to describe more realistic conditions.
Optimal Control of Active Recoil Mechanisms
1977-02-01
forces from 25 to 2.5% for lower zones and cavitation was avoided for zone 8. Tachometer feedback was shown to be effective for low zones. The...concept of feedback control system coupled with optimization procedure to design recoil mechanisms was demonstrated to be an efficient and very effective ...122o •nl260 .01300 .01340 .01380 • ouzo #01460 •01500 •01540 •01580 •0162" .0166 i 309o,6 504P.6 9964.5 10075,9 39121.5 75397.3
Quantum gate and quantum state preparation through neighboring optimal control
NASA Astrophysics Data System (ADS)
Peng, Yuchen
Successful implementation of fault-tolerant quantum computation on a system of qubits places severe demands on the hardware used to control the many-qubit state. It is known that an accuracy threshold Pa exists for any quantum gate that is to be used for such a computation to be able to continue for an unlimited number of steps. Specifically, the error probability Pe for such a gate must fall below the accuracy threshold: Pe < Pa. Estimates of Pa vary widely, though Pa ˜ 10-4 has emerged as a challenging target for hardware designers. I present a theoretical framework based on neighboring optimal control that takes as input a good quantum gate and returns a new gate with better performance. I illustrate this approach by applying it to a universal set of quantum gates produced using non-adiabatic rapid passage. Performance improvements are substantial comparing to the original (unimproved) gates, both for ideal and non-ideal controls. Under suitable conditions detailed below, all gate error probabilities fall by 1 to 4 orders of magnitude below the target threshold of 10-4. After applying the neighboring optimal control theory to improve the performance of quantum gates in a universal set, I further apply the general control theory in a two-step procedure for fault-tolerant logical state preparation, and I illustrate this procedure by preparing a logical Bell state fault-tolerantly. The two-step preparation procedure is as follow: Step 1 provides a one-shot procedure using neighboring optimal control theory to prepare a physical qubit state which is a high-fidelity approximation to the Bell state |beta 01> = 1/√2(|01> + |10>). I show that for ideal (non-ideal) control, an approximate |beta01> state could be prepared with error probability epsilon ˜ 10-6 (10-5) with one-shot local operations. Step 2 then takes a block of p pairs of physical qubits, each prepared in |beta 01> state using Step 1, and fault-tolerantly prepares the logical Bell state for the C4
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.
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.
Redmond, J.; Parker, G.
1993-07-01
This paper examines the role of the control objective and the control time in determining fuel-optimal actuator placement for structural vibration suppression. A general theory is developed that can be easily extended to include alternative performance metrics such as energy and time-optimal control. The performance metric defines a convex admissible control set which leads to a max-min optimization problem expressing optimal location as a function of initial conditions and control time. A solution procedure based on a nested Genetic Algorithm is presented and applied to an example problem. Results indicate that the optimal locations vary widely as a function of control time and initial conditions.
An introduction to stochastic control theory, path integrals and reinforcement learning
NASA Astrophysics Data System (ADS)
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
Analytic theory of optimal plane change by low aerodynamic forces
NASA Astrophysics Data System (ADS)
Ma, Der-Ming; Wu, Chi-Hang; Vinh, Nguyen X.
The properites of the optimal and sub-optimal solutions to multiple-pass aeroassisted plane change were previously studied in terms of the trajectory variables. The solutions show the strong orbital nature. Then, it is proposed to obtain the variational equations of the orbital elements. We shall use these equations and the approximate control derived in Vinh and Ma (1990) to calculate the trajectories. In this respect, the approximate control law and the transversality condition are transformed in terms of the orbital elements. Following the above results, we can reduce the computational task by further simplification. Within omega and Omega being small and returning to the value of zero after each revolution, we neglect the equations for omega, and Omega. Also, since omega approximately equal to 0, that is alpha approximately equal to f, we can neglect the equation for the alpha and have only three state equations for the integration. Still the computation over several revolutions is long since it is performed using the eccentric anomaly along the osculating orbit as the independent variable. Here, we shall use the method of averaging as applied to the problem of orbit contraction to solve the problem of optimal plane change. This will lead to the integration of a reduced set of two nonlinear equations.
Optimal threshold estimation for binary classifiers using game theory.
Sanchez, Ignacio Enrique
2016-01-01
Many bioinformatics algorithms can be understood as binary classifiers. They are usually compared using the area under the receiver operating characteristic ( ROC) curve. On the other hand, choosing the best threshold for practical use is a complex task, due to uncertain and context-dependent skews in the abundance of positives in nature and in the yields/costs for correct/incorrect classification. We argue that considering a classifier as a player in a zero-sum game allows us to use the minimax principle from game theory to determine the optimal operating point. The proposed classifier threshold corresponds to the intersection between the ROC curve and the descending diagonal in ROC space and yields a minimax accuracy of 1-FPR. Our proposal can be readily implemented in practice, and reveals that the empirical condition for threshold estimation of "specificity equals sensitivity" maximizes robustness against uncertainties in the abundance of positives in nature and classification costs.
Optimal threshold estimation for binary classifiers using game theory
Sanchez, Ignacio Enrique
2017-01-01
Many bioinformatics algorithms can be understood as binary classifiers. They are usually compared using the area under the receiver operating characteristic ( ROC) curve. On the other hand, choosing the best threshold for practical use is a complex task, due to uncertain and context-dependent skews in the abundance of positives in nature and in the yields/costs for correct/incorrect classification. We argue that considering a classifier as a player in a zero-sum game allows us to use the minimax principle from game theory to determine the optimal operating point. The proposed classifier threshold corresponds to the intersection between the ROC curve and the descending diagonal in ROC space and yields a minimax accuracy of 1-FPR. Our proposal can be readily implemented in practice, and reveals that the empirical condition for threshold estimation of “specificity equals sensitivity” maximizes robustness against uncertainties in the abundance of positives in nature and classification costs. PMID:28003875
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.
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 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.
Optimization methods in control of electromagnetic fields
NASA Astrophysics Data System (ADS)
Angell, Thomas S.; Kleinman, Ralph E.
1991-05-01
This program is developing constructive methods for certain constrained optimization problems arising in the design and control of electromagnetic fields and in the identification of scattering objects. The problems addressed fall into three categories: (1) the design of antennas with optimal radiation characteristics measured in terms of directivity; (2) the control of the electromagnetic scattering characteristics of an object, in particular the minimization of its radar cross section, by the choice of material properties; and (3) the determination of the shape of scattering objects with various electromagnetic properties from scattered field data. The main thrust of the program is toward the development of constructive methods based on the use of complete families of solutions of the time-harmonic Maxwell equations in the infinite domain exterior to the radiating or scattering body. During the course of the work an increasing amount of attention has been devoted to the use of iterative methods for the solution of various direct and inverse problems. The continued investigation and development of these methods and their application in parameter identification has become a significant part of the program.
Manual control theory and applications. [physiological and neurological applications
NASA Technical Reports Server (NTRS)
Sadoff, M.; Repa, B.
1974-01-01
Control theory, including manual control theory, and a review of some previous physiological and neurological applications of control theory and associated engineering concepts are reported. The discussion includes a specially tailored battery of critical control tasks that are being developed to monitor astronaut performance in long term orbital flight. The application of these concepts and tasks to patients with various neurological disorders is considered.
NASA Astrophysics Data System (ADS)
Golinko, I. M.; Kovrigo, Yu. M.; Kubrak, A. I.
2014-03-01
An express method for optimally tuning analog PI and PID controllers is considered. An integral quality criterion with minimizing the control output is proposed for optimizing control systems. The suggested criterion differs from existing ones in that the control output applied to the technological process is taken into account in a correct manner, due to which it becomes possible to maximally reduce the expenditure of material and/or energy resources in performing control of industrial equipment sets. With control organized in such manner, smaller wear and longer service life of control devices are achieved. A unimodal nature of the proposed criterion for optimally tuning a controller is numerically demonstrated using the methods of optimization theory. A functional interrelation between the optimal controller parameters and dynamic properties of a controlled plant is numerically determined for a single-loop control system. The results obtained from simulation of transients in a control system carried out using the proposed and existing functional dependences are compared with each other. The proposed calculation formulas differ from the existing ones by a simple structure and highly accurate search for the optimal controller tuning parameters. The obtained calculation formulas are recommended for being used by specialists in automation for design and optimization of control systems.
Kobayashi, Koichi; Hiraishi, Kunihiko
2014-01-01
One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs.
Hiraishi, Kunihiko
2014-01-01
One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs. PMID:24587766
Optimal diet theory: behavior of a starved predatory snail.
Perry, D M
1987-06-01
The tenets of optimal foraging theory are used to contrast the behavior of the predatory snail Acantina spirata when feeding on the barnacles Balanus glandula and Chthamalus fissus under conditions of satiation and starvation. As predicted in optimal diet models, A. spirata is less selective (ratio of attack frequency on a prey species to number of individuals available) when the higher ranking prey has low abundance. When given a choice, starved snails attack both barnacle species equally, whereas satiated individuals preferentially attack B. glandula, the more profitable prey (ash-free dry weight of barnacles ingested per unit handling time). Under starvation conditions, equal attack frequency does not result in equal prey species consumption because Acanthina spirata is more successful at attacking C. fissus than B. glandula.The assumption of constant prey encounter rates in optimal diet models is not met when A. spirata goes from a state of satiation to starvation. The encounter rate on B. glandula is lowered due to a decrease in attack success. A loss of feeding skills in starved A. spirata is responsible for the greater difficulty snails have in gaining access through the opercular plates of B. glandula.Behavioral changes in A. spirata as snails pass from satiation to hunger translate into an energetic disadvantage during feeding for hungry snails for two reasons. First, higher prey handling times result in a decreased rate of biomass intake. Second, alteration in the relative attack frequency between barnacle species, combined with a decrease in attack success on the more profitable prey leads to more frequent ingestion of the less profitable prey.
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).
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 digital control of a Stirling cycle cooler
NASA Technical Reports Server (NTRS)
Feeley, J.; Feeley, P.; Langford, G.
1990-01-01
This short paper describes work in progress on the conceptual design of a control system for a cryogenic cooler intended for use aboard spacecraft. The cooler will produce 5 watts of cooling at 65 K and will be used to support experiments associated with the following: earth observation; atmospheric measurements; infrared, x-ray, and gamma-ray astronomy; and magnetic field characterization. The cooler has been designed and constructed for NASA/GSFC by Philips Laboratories and is described in detail. The cooler has a number of unique design features intended to enhance long life and maintenance free operation in space including use of the high efficiency Stirling thermodynamic refrigeration cycle, linear magnetic motors, clearance-seals, and magnetic bearings. The proposed control system design is based on optimal control theory and is targeted for custom integrated circuit implementation. The resulting control system will meet the following mission requirements: efficiency, reliability, optimal thermodynamic, electrical, and mechanical performance; freedom from operator intervention; light weight; and small size.
Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics
NASA Astrophysics Data System (ADS)
Pukdeboon, Chutiphon
2015-10-01
This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.
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.
Linear control theory for gene network modeling.
Shin, Yong-Jun; Bleris, Leonidas
2010-09-16
Systems biology is an interdisciplinary field that aims at understanding complex interactions in cells. Here we demonstrate that linear control theory can provide valuable insight and practical tools for the characterization of complex biological networks. We provide the foundation for such analyses through the study of several case studies including cascade and parallel forms, feedback and feedforward loops. We reproduce experimental results and provide rational analysis of the observed behavior. We demonstrate that methods such as the transfer function (frequency domain) and linear state-space (time domain) can be used to predict reliably the properties and transient behavior of complex network topologies and point to specific design strategies for synthetic networks.
varying airframe dynamics. Guidance techniques for tactical missiles are also reviewed and a number of steering laws, derived from optimal control ... theory , are evaluated. Quantitative comparisons are made between different guidance laws on the basis of intercept accuracy and control effort expended.
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.
Numerical methods for control optimization in linear systems
NASA Astrophysics Data System (ADS)
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
The quality control theory of aging.
Ladiges, Warren
2014-01-01
The quality control (QC) theory of aging is based on the concept that aging is the result of a reduction in QC of cellular systems designed to maintain lifelong homeostasis. Four QC systems associated with aging are 1) inadequate protein processing in a distressed endoplasmic reticulum (ER); 2) histone deacetylase (HDAC) processing of genomic histones and gene silencing; 3) suppressed AMPK nutrient sensing with inefficient energy utilization and excessive fat accumulation; and 4) beta-adrenergic receptor (BAR) signaling and environmental and emotional stress. Reprogramming these systems to maintain efficiency and prevent aging would be a rational strategy for increased lifespan and improved health. The QC theory can be tested with a pharmacological approach using three well-known and safe, FDA-approved drugs: 1) phenyl butyric acid, a chemical chaperone that enhances ER function and is also an HDAC inhibitor, 2) metformin, which activates AMPK and is used to treat type 2 diabetes, and 3) propranolol, a beta blocker which inhibits BAR signaling and is used to treat hypertension and anxiety. A critical aspect of the QC theory, then, is that aging is associated with multiple cellular systems that can be targeted with drug combinations more effectively than with single drugs. But more importantly, these drug combinations will effectively prevent, delay, or reverse chronic diseases of aging that impose such a tremendous health burden on our society.
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.
NASA Astrophysics Data System (ADS)
Gómez Pueyo, Adrián; Budagosky M., Jorge A.; Castro, Alberto
2016-12-01
We present an implementation of optimal control theory for the first-principles nonadiabatic Ehrenfest molecular dynamics model, which describes a condensed matter system by considering classical point-particle nuclei, and quantum electrons, handled in our case with time-dependent density-functional theory. The scheme is demonstrated by optimizing the Coulomb explosion of small sodium clusters: the algorithm is set to find the optimal femtosecond laser pulses that disintegrate the clusters, for a given total duration, fluence, and cutoff frequency. We describe the numerical details and difficulties of the method.
Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints
NASA Astrophysics Data System (ADS)
Kmet', Tibor; Kmet'ová, Mária
2009-09-01
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.
Web malware spread modelling and optimal control strategies.
Liu, Wanping; Zhong, Shouming
2017-02-10
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks. The spreading threshold of the model system is calculated, and the dynamics of the model is theoretically analyzed. Moreover, the optimal control theory is employed to study malware immunization strategies, aiming to keep the total economic loss of security investment and infection loss as low as possible. The existence and uniqueness of the results concerning the optimality system are confirmed. Finally, numerical simulations show that the spread of malware links can be controlled effectively with proper control strategy of specific parameter choice.
Web malware spread modelling and optimal control strategies
Liu, Wanping; Zhong, Shouming
2017-01-01
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks. The spreading threshold of the model system is calculated, and the dynamics of the model is theoretically analyzed. Moreover, the optimal control theory is employed to study malware immunization strategies, aiming to keep the total economic loss of security investment and infection loss as low as possible. The existence and uniqueness of the results concerning the optimality system are confirmed. Finally, numerical simulations show that the spread of malware links can be controlled effectively with proper control strategy of specific parameter choice. PMID:28186203
Web malware spread modelling and optimal control strategies
NASA Astrophysics Data System (ADS)
Liu, Wanping; Zhong, Shouming
2017-02-01
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks. The spreading threshold of the model system is calculated, and the dynamics of the model is theoretically analyzed. Moreover, the optimal control theory is employed to study malware immunization strategies, aiming to keep the total economic loss of security investment and infection loss as low as possible. The existence and uniqueness of the results concerning the optimality system are confirmed. Finally, numerical simulations show that the spread of malware links can be controlled effectively with proper control strategy of specific parameter choice.
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.
Optimal control of a dynamical system representing a gantry crane
Karihaloo, B.L.; Parbery, R.D.
1982-03-01
Problems arising in the optimal control of gantry crane installations are considered. Continuous controls to minimize a control squared objective function are obtained. The amplitude of in-plane oscillations of the suspended mass is assumed small. The optimal controls are sufficiently simple for practical realization.
Frequency domain quantum optimal control under multiple constraints
NASA Astrophysics Data System (ADS)
Shu, Chuan-Cun; Ho, Tak-San; Xing, Xi; Rabitz, Herschel
2016-03-01
Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research. Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives. This optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral-phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.
Differentiating a Finite Element Biodegradation Simulation Model for Optimal Control
NASA Astrophysics Data System (ADS)
Minsker, Barbara S.; Shoemaker, Christine A.
1996-01-01
An optimal control model for improving the design of in situ bioremediation of groundwater has been developed. The model uses a finite element biodegradation simulation model called Bio2D to find optimal pumping strategies. Analytical derivatives of the bioremediation finite element model are derived; these derivatives must be computed for the optimal control algorithm. The derivatives are complex and nonlinear; the bulk of the computational effort in solving the optimal control problem is required to calculate the derivatives. An overview of the optimal control and simulation model formulations is also given.
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
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.
Optimal and suboptimal control technique for aircraft spin recovery
NASA Technical Reports Server (NTRS)
Young, J. W.
1974-01-01
An analytic investigation has been made of procedures for effecting recovery from equilibrium spin conditions for three assumed aircraft configurations. Three approaches which utilize conventional aerodynamic controls are investigated. Included are a constant control recovery mode, optimal recoveries, and a suboptimal control logic patterned after optimal recovery results. The optimal and suboptimal techniques are shown to yield a significant improvement in recovery performance over that attained by using a constant control recovery procedure.
Global optimization strategies for high-performance controls
Hartman, T.B.
1995-12-31
The current trend of extending digital heating, ventilating, and air-conditioning (HVAC) and lighting controls to terminal devices has had an enormous impact on the role of global strategies for energy and comfort optimization. In some respects optimization algorithms are becoming simpler because more complete information about conditions throughout the building is now available to the control system. However, the task of analyzing this information often adds a new layer of complexity to the process of developing these algorithms. Also, the extension of direct digital control (DDC) to terminal devices offers new energy and comfort control optimization opportunities that require additional global optimization algorithms. This paper discusses the changing role of global optimization strategies as the integration of DDC systems is extended to terminal equipment. The discussion offers suggestions about how the development of more powerful global optimization strategies needs to be considered in the design of the mechanical equipment. Specifically, four areas of global optimization are discussed: optimization of variable-air-volume (VAV) airflow, optimization of lighting level via dimming ballasts, optimization of space temperature setpoint, and optimization of chiller and boiler operation. In each of these categories, a control philosophy employing global optimization is discussed, sample control algorithms are provided, and a discussion of the implication of these new control opportunities on the design of the mechanical components is included.
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
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.
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.
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…
Two level optimization of a redundant linear control system
NASA Technical Reports Server (NTRS)
Martin, C. F.; Harding, R. S.
1975-01-01
A linear system with two sets of controls, one primary and the other redundant, is considered. A two level optimization procedure is used to control the system and to maintain maximal availability of the primary control.
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.
Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints.
Kunisch, Karl; Wang, Lijuan
2012-11-01
Time optimal control governed by the internally controlled linear Fitzhugh-Nagumo equation with pointwise control constraint is considered. Making use of Ekeland's variational principle, we obtain Pontryagin's maximum principle for a time optimal control problem. Using the maximum principle, the bang-bang property of the optimal controls is established under appropriate assumptions.
Time optimal controls of the linear Fitzhugh–Nagumo equation with pointwise control constraints
Kunisch, Karl; Wang, Lijuan
2012-01-01
Time optimal control governed by the internally controlled linear Fitzhugh–Nagumo equation with pointwise control constraint is considered. Making use of Ekeland’s variational principle, we obtain Pontryagin’s maximum principle for a time optimal control problem. Using the maximum principle, the bang–bang property of the optimal controls is established under appropriate assumptions. PMID:23576818
Optimal tuberculosis prevention and control strategy from a mathematical model based on real data.
Choi, Sunhwa; Jung, Eunok
2014-07-01
A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
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
Aircraft nonlinear optimal control using fuzzy gain scheduling
NASA Astrophysics Data System (ADS)
Nusyirwan, I. F.; Kung, Z. Y.
2016-10-01
Fuzzy gain scheduling is a common solution for nonlinear flight control. The highly nonlinear region of flight dynamics is determined throughout the examination of eigenvalues and the irregular pattern of root locus plots that show the nonlinear characteristic. By using the optimal control for command tracking, the pitch rate stability augmented system is constructed and the longitudinal flight control system is established. The outputs of optimal control for 21 linear systems are fed into the fuzzy gain scheduler. This research explores the capability in using both optimal control and fuzzy gain scheduling to improve the efficiency in finding the optimal control gains and to achieve Level 1 flying qualities. The numerical simulation work is carried out to determine the effectiveness and performance of the entire flight control system. The simulation results show that the fuzzy gain scheduling technique is able to perform in real time to find near optimal control law in various flying conditions.
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 Control Strategies for Constrained Relative Orbits
2007-09-01
in the next chapter. 50 IV. The Optimal Trajectory The optimal trajectory will be the output of a nonlinear programming algo- rithm that searches for...surface and watch the iteration path of the nonlinear programming algorithm. Let ψ1 = π 4 The results of the optimization algorithm for each of the...T̃max 170 since kz is an integer kz = ⌈ T̃T T̃max ⌉ (134) where d e represents the ceiling function. The total ∆V expended performing these optimal
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.
RTM And VARTM Design, Optimization, And Control With SLIC
2003-07-02
UD-CCM l 2 July 2003 1 RTM AND VARTM DESIGN, OPTIMIZATION, AND CONTROL WITH SLIC Kuang-Ting Hsiao UD-CCM Report Documentation Page Form ApprovedOMB...COVERED - 4. TITLE AND SUBTITLE RTM And VARTM Design, Optimization, And Control With SLIC 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM...ONR Workshop - 5 Simulation-based Liquid Injection Control: Philosophy SLIC Artificial Intelligence Optimized Design For RTM / VARTM Sensors
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.
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
Searching for quantum optimal controls under severe constraints
Riviello, Gregory; Tibbetts, Katharine Moore; Brif, Constantin; Long, Ruixing; Wu, Re-Bing; Ho, Tak-San; Rabitz, Herschel
2015-04-06
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 prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and 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 facilitate successful optimization.
Searching for quantum optimal controls under severe constraints
Riviello, Gregory; Tibbetts, Katharine Moore; Brif, Constantin; ...
2015-04-06
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, butmore » certain control constraints can still prevent successful optimization of the objective. Using optimal control simulations, we show that the most severe field constraints are those that limit essential control resources, such as the number of control variables, the control duration, and the field strength. Proper management of these resources is an issue of great practical importance for optimization in the laboratory. For each resource, we show that constraints exceeding quantifiable limits can introduce artificial traps to the control landscape and 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 facilitate successful optimization.« less
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.
Minimum energy control and optimal-satisfactory control of Boolean control network
NASA Astrophysics Data System (ADS)
Li, Fangfei; Lu, Xiwen
2013-12-01
In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.
NASA Technical Reports Server (NTRS)
Woolley, R. D.; Werking, R. D.
1973-01-01
An original technique for determining the optimal magnetic torque strategy for control of the attitude of spin stabilized spacecraft is presented. By employing Lagrange multipliers and the Calculus of Variations, optimal control equations are derived which define minimum time and minimum energy attitude maneuvers. Computer program algorithms to numerically solve these optimal control equations are also described. The performance of this technique is compared with a commonly employed planning method.
Action Theory, Control and Motivation: A Symposium.
ERIC Educational Resources Information Center
Eckensberger, L. H.; Meacham, J. A., Eds.
1984-01-01
Describes the symposium on action theory presented at the 1983 meeting of the International Society for the Study of Behavioral Development in Munich. The symposium included reactions to action theory from a variety of theoretical perspectives. (Author/RH)
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.
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.
Adaptive and Optimal Control of Stochastic Dynamical Systems
2015-09-14
control and stochastic differential games . Stochastic linear-quadratic, continuous time, stochastic control problems are solved for systems with noise...control problems for systems with arbitrary correlated n 15. SUBJECT TERMS Adaptive control, optimal control, stochastic differential games 16. SECURITY...explicit results have been obtained for problems of stochastic control and stochastic differential games . Stochastic linear- quadratic, continuous time
React or wait: which optimal culling strategy to control infectious diseases in wildlife.
Bolzoni, Luca; Tessoni, Valentina; Groppi, Maria; De Leo, Giulio A
2014-10-01
We applied optimal control theory to an SI epidemic model to identify optimal culling strategies for diseases management in wildlife. We focused on different forms of the objective function, including linear control, quadratic control, and control with limited amount of resources. Moreover, we identified optimal solutions under different assumptions on disease-free host dynamics, namely: self-regulating logistic growth, Malthusian growth, and the case of negligible demography. We showed that the correct characterization of the disease-free host growth is crucial for defining optimal disease control strategies. By analytical investigations of the model with negligible demography, we demonstrated that the optimal strategy for the linear control can be either to cull at the maximum rate at the very beginning of the epidemic (reactive culling) when the culling cost is low, or never to cull, when culling cost is high. On the other hand, in the cases of quadratic control or limited resources, we demonstrated that the optimal strategy is always reactive. Numerical analyses for hosts with logistic growth showed that, in the case of linear control, the optimal strategy is always reactive when culling cost is low. In contrast, if the culling cost is high, the optimal strategy is to delay control, i.e. not to cull at the onset of the epidemic. Finally, we showed that for diseases with the same basic reproduction number delayed control can be optimal for acute infections, i.e. characterized by high disease-induced mortality and fast dynamics, while reactive control can be optimal for chronic ones.
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…
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.
NASA Technical Reports Server (NTRS)
Rakowska, Joanna
1992-01-01
The paper describes the conditions for continuation of the efficient curve for bi-objective control-structure optimization of a ten-bar truss with two collocated sensors and actuators. The curve has been obtained with an active set algorithm using a homotopy method. The curve is discontinuous. A general stability theory has been implemented to determine sufficient conditions for the persistence of minima, and bifurcation theory has been used to characterize the possible points of discontinuity of the path.
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 and robust control and estimation of transition, convection, and turbulence
NASA Astrophysics Data System (ADS)
Bewley, Thomas Robinson
The large increases in drag, cyclic structural loading, internal stresses, mixing, and heat transfer caused by turbulence in flows of engineering interest have motivated engineers to study turbulence and attempt to alter its effects. Recent advances in MEMS capabilities may soon make it possible to measure small-scale turbulent fluctuations of a flow and, subsequently, to apply coordinated small-scale forcing to the flow in order to achieve a desired large-scale effect. The present work attempts to develop techniques to derive the necessary control strategies for such control problems from first principles, leveraging our knowledge of the Navier-Stokes equation which governs these flows and our ability to simulate this equation accurately in simple configurations. By so doing, we bypass the ad hoc assumptions about the turbulence dynamics often used to determine such control strategies and develop several new tools for analysis of flow systems in the control setting. Approaching this difficult problem in steps of gradually increasing complexity, optimal and robust control theories are used in the present work to derive and demonstrate effective control and estimation strategies for three important model problems in fluid mechanics. The model problems considered are: (1)the application of linear optimal/robust control theory to the linear paths to transition in a plane channel, (2)the application of linear optimal/robust control theory to a low-order nonlinear chaotic convection problem, and (3)the application of optimal control theory in a DNS-based predictive control setting to the fully nonlinear problem of turbulence. In order to develop feedback algorithms for practical (disturbed) environments, it is recognized that a degree of robustness will be necessary in the control rules. In the final section of this work, a general framework for robust control for problems governed by the Navier-Stokes equation is established by mathematical analysis, laying the
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.
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.
Optimal defense theory explains deviations from latitudinal herbivory defense hypothesis.
Kooyers, Nicholas J; Blackman, Benjamin K; Holeski, Liza M
2017-04-01
The latitudinal herbivory defense hypothesis (LHDH) postulates that the prevalence of species interactions, including herbivory, is greater at lower latitudes, leading to selection for increased levels of plant defense. While latitudinal defense clines may be caused by spatial variation in herbivore pressure, optimal defense theory predicts that clines could also be caused by ecogeographic variation in the cost of defense. For instance, allocation of resources to defense may not increase plant fitness when growing seasons are short and plants must reproduce quickly. Here we use a common garden experiment to survey genetic variation for constitutive and induced phenylpropanoid glycoside (PPG) concentrations across 35 Mimulus guttatus populations over a ~13° latitudinal transect. Our sampling regime is unique among studies of the LHDH in that it allows us to disentangle the effects of growing season length from those of latitude, temperature, and elevation. For five of the seven PPGs surveyed, we find associations between latitude and plant defense that are robust to population structure. However, contrary to the LHDH, only two PPGs were found at higher levels in low latitude populations, and total PPG concentrations were higher at higher latitudes. PPG levels are strongly correlated with growing season length, with higher levels of PPGs in plants from areas with longer growing seasons. Further, flowering time is positively correlated with the concentration of nearly all PPGs, suggesting that there may be a strong trade-off between development time and defense production. Our results reveal that ecogeographic patterns in plant defense may reflect variation in the cost of producing defense compounds in addition to variation in herbivore pressure. Thus, the biogeographic pattern predicted by the LHDH may not be accurate because the underlying factors driving variation in defense, in this case, growing season length, are not always associated with latitude in the same
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.
Robustified time-optimal control of uncertain structural dynamic systems
NASA Technical Reports Server (NTRS)
Liu, Qiang; Wie, Bong
1991-01-01
A new approach for computing open-loop time-optimal control inputs for uncertain linear dynamical systems is developed. In particular, the single-axis, rest-to-rest maneuvering problem of flexible spacecraft in the presence of uncertainty in model parameters is considered. Robustified time-optimal control inputs are obtained by solving a parameter optimization problem subject to robustness constraints. A simple dynamical system with a rigid-body mode and one flexible mode is used to illustrate the concept.
Dynamical Systems and Control Theory Inspired by Molecular Biology
2014-10-02
AFRL-OSR-VA-TR-2014-0282 DYNAMICAL SYSTEMS AND CONTROL THEORY INSPIRED BY MOLECULAR BIOLOGY Eduardo Sontag RUTGERS THE STATE UNIVERSITY OF NEW JERSEY...Standard Form 298 (Re . 8-98) v Prescribed by ANSI Std. Z39.18 DYNAMICAL SYSTEMS AND CONTROL THEORY INSPIRED BY MOLECULAR BIOLOGY AFOSR FA9550-11-1-0247...is to develop new concepts, theory, and algorithms for control and signal processing using ideas inspired by molecular systems biology. Cell biology
Actively Controlled Structures Theory. Volume 1. Theory of Design Methods
1979-11-01
Introduction to Circuits , Instruments and Electronics, New York: Harcourt, Brace & World, 1968. -,.,>i A-14 ^ ,’ sm APPENDIX B CONTROLLABILITY AND...34Controllability of Linear Dynamical Systems," Contributions to Differential Equations, Vol. 1, No. 2, pp. 189-213, 1962. 11. Zadeh, L.A. and C.A. Desoer
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…
Pseudospectral Optimal Control: Hidden Properties and Flight Results
2011-11-30
on solving optimal control problems , we focus on developing PS methods over arbitrary grids for Problem B. Such research can provides a unified...more efficient algorithms for solving optimal control problems , for example, multiscale PS methods for dynamical systems with different timescales
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.
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.
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…
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
Nonlinear Robust Control Theory and Applications
1997-01-18
and the other to the state-space realization theory developed mainly in the s by Gilbert [2], Zadeh and Desoer [3], Kalman [4], Rosenbrock [5...3] L. Zadeh and C. Desoer , Linear System Theory - A State-Space Approach. McGraw- Hill, New York, 1963. [4] R. E. Kalman, "Mathematical descriptions
A multidisciplinary approach to optimization of controlled space structures
NASA Technical Reports Server (NTRS)
Woodard, Stanley E.; Padula, Sharon L.; Graves, Philip C.; James, Benjamin B.
1990-01-01
A fundamental problem facing controls-structures analysts is a means of determining the trade-offs between structural design parameters and control design parameters in meeting some particular performance criteria. Developing a general optimization-based design methodology integrating the disciplines of structural dynamics and controls is a logical approach. The objective of this study is to develop such a method. Classical design methodology involves three phases. The first is structural optimization, wherein structural member sizes are varied to minimize structural mass, subject to open-loop frequency constraints. The next phase integrates control and structure design with control gains as additional design variables. The final phase is analysis of the 'optimal' integrated design phase considering 'real' actuators and 'standard' member sizes. The control gains could be further optimized for fixed structure, and actuator saturation constraints could be imposed. However, such an approach does not take full advantage of opportunities to tailor the structure and control system design as one system.
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.
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.
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.
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
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 sequential linear optimization approach for controller design
NASA Technical Reports Server (NTRS)
Horta, L. G.; Juang, J.-N.; Junkins, J. L.
1985-01-01
A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.
Optimal Control In Predation Of Models And Mimics
NASA Astrophysics Data System (ADS)
Tsoularis, A.
2007-09-01
This paper examines optimal predation by a predator preying upon two types of prey, modes and mimics. Models are unpalatable prey and mimics are palatable prey resembling the models so as to derive some protection from predation. This biological phenomenon is known in Ecology as Batesian mimicry. An optimal control problem in continuous time is formulated with the sole objective to maximize the net energetic benefit to the predator from predation in the presence of evolving prey populations. The constrained optimal control is bang-bang with the scalar control taken as the probability of attacking prey. Conditions for the existence of singular controls are obtained.
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.
Design of Optimally Robust Control Systems.
1980-01-01
approach is that the optimization framework is an artificial device. While some design constraints can easily be incorporated into a single cost function...indicating that that point was indeed the solution. Also, an intellegent initial guess for k was important in order to avoid being hung up at the double
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.
Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains
NASA Astrophysics Data System (ADS)
Zhang, Xiong-Peng; Shao, Bin; Zou, Jian
2017-02-01
Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.
Optimization of Feedback Control of Flow over a Circular Cylinder
NASA Astrophysics Data System (ADS)
Son, Donggun; Kim, Euiyoung; Choi, Haecheon
2012-11-01
We perform a feedback gain optimization of the proportional-integral-differential (PID) control for flow over a circular cylinder at Re = 60 and 100. We measure the transverse velocity at a centerline location in the wake as a sensing variable and provide blowing and suction at the upper and lower slots on the cylinder surface as an actuation. The cost function to minimize is defined as the mean square of the sensing variable, and the PID control gains are optimized by iterative feedback tuning method which is a typical model free gain optimization method. In this method, the control gains are iteratively updated by the gradient of cost function until the control system satisfies a certain stopping criteria. The PID control with optimal control gains successfully reduces the velocity fluctuations at the sensing location and attenuates (or annihilates) vortex shedding in the wake, resulting in the reduction in the mean drag and lift fluctuations. Supported by the NRF Program (2011-0028032).
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.
Asymptotically optimal feedback control for a system of linear oscillators
NASA Astrophysics Data System (ADS)
Ovseevich, Alexander; Fedorov, Aleksey
2013-12-01
We consider problem of damping of an arbitrary number of linear oscillators under common bounded control. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large.
Control optimization, stabilization and computer algorithms for aircraft applications
NASA Technical Reports Server (NTRS)
1975-01-01
Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.
Optimization of the observations and control of aircraft
NASA Astrophysics Data System (ADS)
Malyshev, Veniamin V.; Krasil'Shchikov, Mikhail N.; Karlov, Valerii I.
Problems related to the optimization of the measured parameters, navigational equipment operation, aircraft control, and combined operation of control and navigation equipment are analyzed. The problems considered rely on probabilistic optimality criteria, with varying availability of data on the uncontrolled factors, such as measurement errors and perturbations. A new generalized approach is proposed which makes it possible to reduce the initially nonlinear control problems to equivalent linear (with respect to phase variables) problems by using the analytical properties of the Riccati problem.
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.
Optimal control problem for impulsive systems with integral boundary conditions
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Sharifov, Y. A.
2012-08-01
In the present work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
On unified modeling, theory, and method for solving multi-scale global optimization problems
NASA Astrophysics Data System (ADS)
Gao, David Yang
2016-10-01
A unified model is proposed for general optimization problems in multi-scale complex systems. Based on this model and necessary assumptions in physics, the canonical duality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are proposed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming.
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.
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.
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.
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
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…
Time-optimal control of the magnetically levitated photolithography platen
Redmond, J.; Tucker, S.
1995-01-01
This report summarizes two approaches to time-optimal control of a nonlinear magnetically levitated platen. The system of interest is a candidate technology for next-generation photolithography machines used in the manufacture of integrated circuits. The dynamics and the variable peak control force of the electro-magnetic actuators preclude the direct application of classical time-optimal control methodologies for determining optimal rest-to-rest maneuver strategies. Therefore, this study explores alternate approaches using a previously developed computer simulation. In the first approach, conservative estimates of the available control forces are used to generate suboptimal switching curves. In the second approach, exact solutions are determined iteratively and used as a training set for an artificial neural network. The trained network provides optimal actuator switching times that incorporate the full nonlinearities of the magnetic levitation actuators. Sample problems illustrate the effectiveness of these techniques as compared to traditional proportional-derivative control.
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.
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.
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.
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.
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.
Optimal Stationary Linear Control of the Wiener Process.
1980-02-29
OPTIMAL STATIONARY LINEAR CONTROL OF THE WIENER PROCESS. (U) FES 80 V E BENES. I KARATZAS AFOSR-76-3063 UNCLASSIFIED AFOSR -TR-8O-0338 NL...mElllllllllll mhmmmmmmmmm mmmmmmmr( EFOSR-TR- 2 0-0S8 0 3 OPTIMAL STATIONARY LINEAR CONTROL OF THE WIENER PROCESS by LEVEL CVACLAV E. BENES Bell Telephone...or " DIst. special D U L I. F UNCLASSIFIED _ _ _ , ,_I_ _ _ _ _ _. OPTIMAL STATIONARY LINEAR CONTROL OF TIlE WIENER PROCESS V’aclav E. Benes and
Optimal Control of the Starfire Beam Director
1992-12-01
amplifier has built-in proportional plus integral ( PI ) control circuitry for the purpose of rejecting the back EMF. Since measured closed-loop amplifier...throughout a satellite pass. PI control yields zero steady state error to a step input. At worse case the commanded position input has a small...designed in a classical sense in that it consists of PI control and a lead, where high gain and the lead are required to achieve the necessary bandwidth
Evaluation of muscle force predictions using optimization theory
NASA Astrophysics Data System (ADS)
Ziya Arslan, Yunus; Kaya, Motoshi; Herzog, Walter
2013-02-01
Prediction of muscle forces using optimization based models of muscle coordination is an active research area in biomechanics. Theoretical calculation of individual muscle forces depends on solving the redundancy problem. In a musculoskeletal model, redundancy arises since the number of muscles in the model exceeds the number of degrees-of-freedom present. One of the widely used methods to solve this problem is to formulate a physiologically sound cost function and optimize this function subject to mechanical equality and inequality constraint equations. In this study, force predictions obtained from different optimization-based models were compared with those obtained from experimentally measured individual muscle forces recorded during a variety of movement conditions. Advantages and limitations of the tested models were discussed.
Toward real-time en route air traffic control optimization
NASA Astrophysics Data System (ADS)
Jardin, Matthew Robert
The increase in air traffic along the existing jet route structure has led to inefficiencies and frequent congestion in en route airspace. Analysis of air-traffic data suggests that direct operating costs might be reduced by about 4.5%, or $500 million per year, if aircraft were permitted to fly optimal wind routes instead of the structured routes allowed today. To enable aircraft to fly along unstructured optimal routes safely, automation is required to aid air-traffic controllers. This requires the global solution for conflict-free optimal routes for many aircraft in real time. The constraint that all aircraft must maintain adequate separation from one another results in a greater-than-exponential increase in the complexity of the multi-aircraft optimization problem. The main challenges addressed in this dissertation are in the areas of optimal wind routing, computationally efficient aircraft conflict detection, and efficient conflict resolution. A core contribution is the derivation of an analytical neighboring optimal control solution for the efficient computation of optimal wind routes. The neighboring optimal control algorithm uses an order of magnitude less computational effort to achieve the same performance as existing algorithms, and is easily extended to compute near-optimal conflict free trajectories. A conflict detection algorithm as been developed which eliminates the need to compute inter-aircraft distances. Simulation results are presented to demonstrate an integrated horizontal route-optimization and conflict-resolution method for air-traffic control. Conflict-free solutions have been computed for roughly double the current-day traffic density for a single flight level (over 600 aircraft) in less than 1 minute on a 450-MHz UNIX work station. This corresponds to a computation rate of better than 25 optimal routes per second. Extrapolation of the two-dimensional results to the multi-flight-level domain suggests that the complete solution for optimal
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.
Illumination pattern optimization for fluorescence tomography: theory and simulation studies.
Dutta, Joyita; Ahn, Sangtae; Joshi, Anand A; Leahy, Richard M
2010-05-21
Fluorescence molecular tomography is a powerful tool for 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degrees of absorption and scattering of light through tissue, the fluorescence tomographic inverse problem is inherently ill-posed. In order to improve source localization and the conditioning of the light propagation model, multiple sets of data are acquired by illuminating the animal surface with different spatial patterns of near-infrared light. However, the choice of these patterns in most experimental setups is ad hoc and suboptimal. This paper presents a systematic approach for designing efficient illumination patterns for fluorescence tomography. Our objective here is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. We achieve this by improving the conditioning of the Fisher information matrix. We parameterize the spatial illumination patterns and formulate our problem as a constrained optimization problem that, for a fixed number of illumination patterns, yields the optimal set of patterns. For geometric insight, we used our method to generate a set of three optimal patterns for an optically homogeneous, regular geometrical shape and observed expected symmetries in the result. We also generated a set of six optimal patterns for an optically homogeneous cuboidal phantom set up in the transillumination mode. Finally, we computed optimal illumination patterns for an optically inhomogeneous realistically shaped mouse atlas for different given numbers of patterns. The regularized pseudoinverse matrix, generated using the singular value decomposition, was employed to reconstruct the point spread function for each set of patterns in the presence of a sample fluorescent point source deep inside the mouse atlas. We have evaluated the performance of our method by examining the singular value spectra as well as plots of average spatial
Deterministic methods for multi-control fuel loading optimization
NASA Astrophysics Data System (ADS)
Rahman, Fariz B. Abdul
We have developed a multi-control fuel loading optimization code for pressurized water reactors based on deterministic methods. The objective is to flatten the fuel burnup profile, which maximizes overall energy production. The optimal control problem is formulated using the method of Lagrange multipliers and the direct adjoining approach for treatment of the inequality power peaking constraint. The optimality conditions are derived for a multi-dimensional multi-group optimal control problem via calculus of variations. Due to the Hamiltonian having a linear control, our optimal control problem is solved using the gradient method to minimize the Hamiltonian and a Newton step formulation to obtain the optimal control. We are able to satisfy the power peaking constraint during depletion with the control at beginning of cycle (BOC) by building the proper burnup path forward in time and utilizing the adjoint burnup to propagate the information back to the BOC. Our test results show that we are able to achieve our objective and satisfy the power peaking constraint during depletion using either the fissile enrichment or burnable poison as the control. Our fuel loading designs show an increase of 7.8 equivalent full power days (EFPDs) in cycle length compared with 517.4 EFPDs for the AP600 first cycle.
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 quantum superpositions in a bosonic Josephson junction
NASA Astrophysics Data System (ADS)
Lapert, M.; Ferrini, G.; Sugny, D.
2012-02-01
We show how to optimally control the creation of quantum superpositions in a bosonic Josephson junction within the two-site Bose-Hubbard-model framework. Both geometric and purely numerical optimal-control approaches are used, the former providing a generalization of the proposal of Micheli [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.67.013607 67, 013607 (2003)]. While this method is shown not to lead to significant improvements in terms of time of formation and fidelity of the superposition, a numerical optimal-control approach appears more promising, as it allows creation of an almost perfect superposition, within a time short compared to other existing protocols. We analyze the robustness of the optimal solution against atom-number variations. Finally, we discuss the extent to which these optimal solutions could be implemented with state-of-the-art technology.
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.
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…
Application of fuzzy GA for optimal vibration control of smart cylindrical shells
NASA Astrophysics Data System (ADS)
Jin, Zhanli; Yang, Yaowen; Kiong Soh, Chee
2005-12-01
In this paper, a fuzzy-controlled genetic-based optimization technique for optimal vibration control of cylindrical shell structures incorporating piezoelectric sensor/actuators (S/As) is proposed. The geometric design variables of the piezoelectric patches, including the placement and sizing of the piezoelectric S/As, are processed using fuzzy set theory. The criterion based on the maximization of energy dissipation is adopted for the geometric optimization. A fuzzy-rule-based system (FRBS) representing expert knowledge and experience is incorporated in a modified genetic algorithm (GA) to control its search process. A fuzzy logic integrated GA is then developed and implemented. The results of three numerical examples, which include a simply supported plate, a simply supported cylindrical shell, and a clamped simply supported plate, provide some meaningful and heuristic conclusions for practical design. The results also show that the proposed fuzzy-controlled GA approach is more effective and efficient than the pure GA method.
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)
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…
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.
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.
The discrete complementary variational principle and optimal control systems
NASA Technical Reports Server (NTRS)
Chan, W. L.; Leininger, G. G.
1974-01-01
A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.
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...
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…
An introduction to optimal power flow: Theory, formulation, and examples
Frank, Stephen; Rebennack, Steffen
2016-05-21
The set of optimization problems in electric power systems engineering known collectively as Optimal Power Flow (OPF) is one of the most practically important and well-researched subfields of constrained nonlinear optimization. OPF has enjoyed a rich history of research, innovation, and publication since its debut five decades ago. Nevertheless, entry into OPF research is a daunting task for the uninitiated--both due to the sheer volume of literature and because OPF's ubiquity within the electric power systems community has led authors to assume a great deal of prior knowledge that readers unfamiliar with electric power systems may not possess. This article provides an introduction to OPF from an operations research perspective; it describes a complete and concise basis of knowledge for beginning OPF research. The discussion is tailored for the operations researcher who has experience with nonlinear optimization but little knowledge of electrical engineering. Topics covered include power systems modeling, the power flow equations, typical OPF formulations, and common OPF extensions.
Optimal reimbursement health insurance and the theory of Ramsey taxation.
Besley, T J
1988-12-01
This paper explores the trade-off between risk sharing and the incentives to consume increased medical care inherent in reimbursement insurance. The results for the theory of reimbursement insurance are compared with those on Ramsey taxation. It is shown that there is a close formal analogy and interpretations are given.
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
Inverse Optimal Pinning Control for Complex Networks of Chaotic Systems
NASA Astrophysics Data System (ADS)
Sanchez, Edgar N.; Rodriguez, David I.
In this paper, a control strategy based on the inverse optimal control approach is applied for pinning weighted complex networks with chaotic systems at their nodes; additionally, a cost functional is minimized. This control strategy does not require to have the same coupling strength for all node connections.
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.
Adjoint optimal control problems for the RANS system
NASA Astrophysics Data System (ADS)
Attavino, A.; Cerroni, D.; Da Vià, R.; Manservisi, S.; Menghini, F.
2017-01-01
Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.
Dual structural-control optimization of large space structures
NASA Technical Reports Server (NTRS)
Messac, A.; Turner, J.
1984-01-01
A new approach is proposed for solving dual structural-control optimization problems for high-order flexible space structures where reduced-order structural models are employed. For a given initial structural dessign, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the stuctural design variables is then determined and used to obtain successive structural redesigns using a contrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.
Optimal Control Surface Layout for an Aeroservoelastic Wingbox
NASA Technical Reports Server (NTRS)
Stanford, Bret K.
2017-01-01
This paper demonstrates a technique for locating the optimal control surface layout of an aeroservoelastic Common Research Model wingbox, in the context of maneuver load alleviation and active utter suppression. The combinatorial actuator layout design is solved using ideas borrowed from topology optimization, where the effectiveness of a given control surface is tied to a layout design variable, which varies from zero (the actuator is removed) to one (the actuator is retained). These layout design variables are optimized concurrently with a large number of structural wingbox sizing variables and control surface actuation variables, in order to minimize the sum of structural weight and actuator weight. Results are presented that demonstrate interdependencies between structural sizing patterns and optimal control surface layouts, for both static and dynamic aeroelastic physics.
EPA Optimal Corrosion Control Treatment Regional Training Workshops
EPA is hosting face-to-face regional training workshops throughout 2016-2017 on optimal corrosion control treatment (OCCT). These will be held at each of the Regions and is intended for primacy agency staff and technical assistance providers.
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.
Optimal feedback control of turbulent channel flow
NASA Technical Reports Server (NTRS)
Bewley, Thomas; Choi, Haecheon; Temam, Roger; Moin, Parviz
1993-01-01
Feedback control equations were developed and tested for computing wall normal control velocities to control turbulent flow in a channel with the objective of reducing drag. The technique used is the minimization of a 'cost functional' which is constructed to represent some balance of the drag integrated over the wall and the net control effort. A distribution of wall velocities is found which minimizes this cost functional some time shortly in the future based on current observations of the flow near the wall. Preliminary direct numerical simulations of the scheme applied to turbulent channel flow indicates it provides approximately 17 percent drag reduction. The mechanism apparent when the scheme is applied to a simplified flow situation is also discussed.
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.
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.
Shaped optimal control pulses for increased excitation bandwidth in EPR.
Spindler, Philipp E; Zhang, Yun; Endeward, Burkhard; Gershernzon, Naum; Skinner, Thomas E; Glaser, Steffen J; Prisner, Thomas F
2012-05-01
A 1 ns resolution pulse shaping unit has been developed for pulsed EPR spectroscopy to enable 14-bit amplitude and phase modulation. Shaped broadband excitation pulses designed using optimal control theory (OCT) have been tested with this device at X-band frequency (9 GHz). FT-EPR experiments on organic radicals in solution have been performed with the new pulses, designed for uniform excitation over a significantly increased bandwidth compared to a classical rectangular π/2 pulse of the same B(1) amplitude. The concept of a dead-time compensated prefocused pulse has been introduced to EPR with a self-refocusing of 200 ns after the end of the pulse. Echo-like refocused signals have been recorded and compared to the performance of a classical Hahn-echo sequence. The impulse response function of the microwave setup has been measured and incorporated into the algorithm for designing OCT pulses, resulting in further significant improvements in performance. Experimental limitations and potential new applications of OCT pulses in EPR spectroscopy will be discussed.
Optimal control and cost-effective analysis of malaria/visceral leishmaniasis co-infection
Agusto, Folashade B.; ELmojtaba, Ibrahim M.
2017-01-01
In this paper, a deterministic model involving the transmission dynamics of malaria/visceral leishmaniasis co-infection is presented and studied. Optimal control theory is then applied to investigate the optimal strategies for curtailing the spread of the diseases using the use of personal protection, indoor residual spraying and culling of infected reservoirs as the system control variables. Various combination strategies were examined so as to investigate the impact of the controls on the spread of the disease. And we investigated the most cost-effective strategy of all the control strategies using three approaches, the infection averted ratio (IAR), the average cost-effectiveness ratio (ACER) and incremental cost-effectiveness ratio (ICER). Our results show that the implementation of the strategy combining all the time dependent control variables is the most cost-effective control strategy. This result is further emphasized by using the results obtained from the cost objective functional, the ACER, and the ICER. PMID:28166308
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.
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.
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.
Optimization of a fluidic temperature control device
NASA Technical Reports Server (NTRS)
Zabsky, J. M.; Rask, D. R.; Starr, J. B.
1970-01-01
Refinements are described to an existing fluidic temperature control system developed under a prior study which modulated temperature at the inlet to the liquid-cooled garment by using existing liquid supply and return lines to transmit signals to a fluidic controller located in the spacecraft. This earlier system produced a limited range of garment inlet temperatures, requiring some bypassing of flow around the suit to make the astronaut comfortable at rest conditions. Refinements were based on a flow visualization study of the key element in the fluidic controller: the fluidic mixing valve. The valve's mixing-ratio range was achieved by making five key changes: (1) geometrical changes to the valve; (2) attenuation of noise generated in proportional amplifier cascades; (3) elimination of vortices at the exit of the fluidic mixing valve; (4) reduction of internal heat transfer; and (5) flow balancing through venting. As a result, the refined system is capable of modulating garment inlet temperature from 45 F to 70 F with a single manual control valve in series with the garment. This control valve signals without changing or bypassing flow through the garment.
NASA Astrophysics Data System (ADS)
Li, Ying; Cheng, Bo
2009-10-01
With the development of remote sensing satellites, the data quantity of remote sensing image is increasing tremendously, which brings a huge workload to the image geometric rectification through manual ground control point (GCP) selections. GCP database is one of the effective methods to cut down manual operation. The GCP loaded from database is generally redundant, which may result in a rectification slowdown. How to automatically optimize these ground control points is a problem that should be resolved urgently. According to the basic theory of geometric rectification and the principle of GCP selection, this paper deeply comprehends some existing methods about automatic optimization of GCP, and puts forward a new method of automatic optimization of GCP based on voronoi diagram to filter ground control points from the overfull ones without manual subjectivity for better accuracy. The paper is organized as follows: First, it clarifies the basic theory of remote sensing image multinomial geometric rectification and the arithmetic of how to get the GCP error. Second, it particularly introduces the voronoi diagram including its origin, development and characteristics, especially the creating process. Third, considering the deficiencies of existing methods about automatic optimization of GCP, the paper presents the idea of applying voronoi diagram to filter GCP in order to complete automatic optimization. During this process, it advances the conception of single GCP's importance value based on voronoi diagram. Then by integrating the GCP error and GCP's importance value, the paper gives the theory and the flow of automatic optimization of GCPs as well. It also presents an example of the application of this method. In the conclusion, it points out the advantages of automatic optimization of GCP based on the voronoi diagram.
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.
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.
Impulsive optimal control model for the trajectory of horizontal wells
NASA Astrophysics Data System (ADS)
Li, An; Feng, Enmin; Wang, Lei
2009-01-01
This paper presents an impulsive optimal control model for solving the optimal designing problem of the trajectory of horizontal wells. We take fully into account the effect of unknown disturbances in drilling. The optimal control problem can be converted into a nonlinear parametric optimization by integrating the state equation. We discuss here that the locally optimal solution depends in a continuous way on the parameters (disturbances) and utilize this property to propose a revised Hooke-Jeeves algorithm. The uniform design technique is incorporated into the revised Hooke-Jeeves algorithm to handle the multimodal objective function. The numerical simulation is in accordance with theoretical results. The numerical results illustrate the validity of the model and efficiency of the algorithm.
Optimal Control of the Obstacle for an Elliptic Variational Inequality
Adams, D. R.; Lenhart, S. M.; Yong, J.
1998-09-15
An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H{sup 1}{sub 0} ({omega}) so that the state is close to the desired profile while the H{sup 1}({omega}) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established.
Optimal Discounted Linear Control of the Wiener Process.
1979-09-01
1r~~ ~~ • 7 ~O—AO7 8 ~87 BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAM— ETC F/s IUt I OPTIMAL DISCOUNTED LINEAR CONTROL OF THE WIENER...4I • —~~~~~ A — --a -I’ p.posa-ra- 79~~ 124 9 OPTIMAL DISCOU NTED LINEAR CONTROL OF THE WIENER PROCESS~ by -J loannis Kara t:as Lefsche tz Center for...DISCOUNTED LINEAR CONTROL OF THE WIENER PROCESS~ loannis Karat zas ABSTRACT The following stochastic control problem is considered
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.
Numerical methods for solving terminal optimal control problems
NASA Astrophysics Data System (ADS)
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
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.
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
Kalman meets neuron: the emerging intersection of control theory with neuroscience.
Schiff, Steven J
2009-01-01
Since the 1950s, we have developed mature theories of modern control theory and computational neuroscience with almost no interaction between these disciplines. With the advent of computationally efficient nonlinear Kalman filtering techniques, along with improved neuroscience models that provide increasingly accurate reconstruction of dynamics in a variety of important normal and disease states in the brain, the prospects for a synergistic interaction between these fields are now strong. I show recent examples of the use of nonlinear control theory for the assimilation and control of single neuron dynamics, the modulation of oscillatory wave dynamics in brain cortex, a control framework for Parkinsonian dynamics and seizures, and the use of optimized parameter model networks to assimilate complex network data - the 'consensus set'.
Optimal Control through Biologically-Inspired Pursuit
2004-01-01
Transactions on Automatic Control 48, 988– 1001. Roumeliotis, S.I. and G.A. Bekey (2002). Distributed multi-robot localization. IEEE Transactions on Robotics and...1999). Distributed covering by ant- robots using evaporating traces. IEEE Transactions on Robotics and Automation 15(5), 918–933.
Decentralized Control Using Global Optimization (DCGO) (Preprint)
2007-03-01
simulation environment using BAE System’s proprietary M2CS (multi-vehicle mission control system) planner running in version 1.3 of the Boeing OEP...copies of M2CS are allowed to create plans for a SEAD mission. The coordination between the planners is handled using either an ideal communication
Decentralized Control Using Global Optimization (DCGO) (Postprint)
2007-03-01
protocol was used in a simulation environment using BAE System’s proprietary M2CS (multi-vehicle mission control system) planner running in version 1.3...system delays. vehicles utilizing identical copies of M2CS are allowed to create plans for a SEAD mission. The coordination between the planners is handled
Turbine engine power optimization control system
Moore, M.S.
1984-09-04
Pushbutton controls are provided for the power management of a turbine powered aircraft; and these pushbuttons may be mounted on the aircraft pilot's control handwheel. The turbine engine has a maximum rated permissible rotational speed which initially increases with increasing air temperature and with increasing altitude or reduced pressure; and has an absolute maximum limitation, with this maximum permissible rotational speed decreasing at increasing temperatures starting at about 10 or 15 degrees below zero, centigrade; and these limitations are reduced when supplemental equipment such as de-icing equipment is turned on. In accordance with the present invention, a series of ''maps'', or rotational speed control characteristics reflecting the factors mentioned above, are provided, and the pushbutton controls select among these characteristics, with the ''take-off'' power button permitting the highest maximum speeds, etc. In addition, automatic timing to reduce the maximum power levels, such as ''Take-Off'' power or ''Performance Climb'' power, is provided, to avoid over-stressing the turbine engines. The system may include additional arrangements for limiting the maximum allowable rotational speed of the turbine engine to a speed below that indicated by any of the ''maps'', when certain pushbuttons such as the ''Approach'' pushbutton is actuated.
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.
Vijaya Kumar, B K; Mahalanobis, A; Takessian, A
2000-01-01
Correlation methods are becoming increasingly attractive tools for image recognition and location. This renewed interest in correlation methods is spurred by the availability of high-speed image processors and the emergence of correlation filter designs that can optimize relevant figures of merit. In this paper, a new correlation filter design method is presented that allows one to optimally tradeoff among potentially conflicting correlation output performance criteria while achieving desired correlation peak value behavior in response to in-plane rotation of input images. Such controlled in-plane rotation response is useful in image analysis and pattern recognition applications where the sensor follows a pre-arranged trajectory while imaging an object. Since this new correlation filter design is based on circular harmonic function (CHF) theory, we refer to the resulting filters as optimal tradeoff circular harmonic function (OTCHF) filters. Underlying theory, OTCHF filter design method, and illustrative numerical results are presented.
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
Optimal charge control strategies for stationary photovoltaic battery systems
NASA Astrophysics Data System (ADS)
Li, Jiahao; Danzer, Michael A.
2014-07-01
Battery systems coupled to photovoltaic (PV) modules for example fulfill one major function: they locally decouple PV generation and consumption of electrical power leading to two major effects. First, they reduce the grid load, especially at peak times and therewith reduce the necessity of a network expansion. And second, they increase the self-consumption in households and therewith help to reduce energy expenses. For the management of PV batteries charge control strategies need to be developed to reach the goals of both the distribution system operators and the local power producer. In this work optimal control strategies regarding various optimization goals are developed on the basis of the predicted household loads and PV generation profiles using the method of dynamic programming. The resulting charge curves are compared and essential differences discussed. Finally, a multi-objective optimization shows that charge control strategies can be derived that take all optimization goals into account.
Dippong, Joseph; Kalkhoff, Will
2015-03-01
Affect control theory (ACT) and status characteristics theory (SCT) offer separate and distinct explanations for how individuals interpret and process status- and power-relevant information about interaction partners. Existing research within affect control theory offers evidence that status and power are related to the affective impressions that individuals form of others along the dimensions of evaluation and potency, respectively. Alternately, status characteristics theory suggests that status and power influence interaction through the mediating cognitive construct of performance expectations. Although both theories have amassed an impressive amount of empirical support, research has yet to articulate theoretical and empirical connections between affective impressions and performance expectations. The purpose of our study is to address this gap. Elaborating a link between ACT and SCT in terms of their central concepts can serve as a stepping stone to improving the explanatory capacity of both theories, while providing a potential bridge by which they can be employed jointly.
Total energy control system autopilot design with constrained parameter optimization
NASA Technical Reports Server (NTRS)
Ly, Uy-Loi; Voth, Christopher
1990-01-01
A description is given of the application of a multivariable control design method (SANDY) based on constrained parameter optimization to the design of a multiloop aircraft flight control system. Specifically, the design method is applied to the direct synthesis of a multiloop AFCS inner-loop feedback control system based on total energy control system (TECS) principles. The design procedure offers a structured approach for the determination of a set of stabilizing controller design gains that meet design specifications in closed-loop stability, command tracking performance, disturbance rejection, and limits on control activities. The approach can be extended to a broader class of multiloop flight control systems. Direct tradeoffs between many real design goals are rendered systematic by proper formulation of the design objectives and constraints. Satisfactory designs are usually obtained in few iterations. Performance characteristics of the optimized TECS design have been improved, particularly in the areas of closed-loop damping and control activity in the presence of turbulence.
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.
LQ (optimal) control of hyperbolic PDAEs
NASA Astrophysics Data System (ADS)
Alizadeh Moghadam, Amir; Aksikas, Ilyasse; Dubljevic, Stevan; Fraser Forbes, J.
2014-10-01
The linear quadratic control synthesis for a set of coupled first-order hyperbolic partial differential and algebraic equations is presented by using the infinite-dimensional Hilbert state-space representation of the system and the well-known operator Riccati equation (ORE) method. Solving the algebraic equations and substituting them into the partial differential equations (PDEs) results in a model consisting of a set of pure hyperbolic PDEs. The resulting PDE system involves a hyperbolic operator in which the velocity matrix is spatially varying, non-symmetric, and its eigenvalues are not necessarily negative through of the domain. The C0-semigroup generation property of such an operator is proven and it is shown that the generated C0-semigroup is exponentially stable and, consequently, the ORE has a unique and non-negative solution. Conversion of the ORE into a matrix Riccati differential equation allows the use of a numerical scheme to solve the control problem.
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.
Optimal chaos control through reinforcement learning.
Gadaleta, Sabino; Dangelmayr, Gerhard
1999-09-01
A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.
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.
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.
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
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…
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.
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.
Evidence for the flexible sensorimotor strategies predicted by optimal feedback control.
Liu, Dan; Todorov, Emanuel
2007-08-29
Everyday movements pursue diverse and often conflicting mixtures of task goals, requiring sensorimotor strategies customized for the task at hand. Such customization is mostly ignored by traditional theories emphasizing movement geometry and servo control. In contrast, the relationship between the task and the strategy most suitable for accomplishing it lies at the core of our optimal feedback control theory of coordination. Here, we show that the predicted sensitivity to task goals affords natural explanations to a number of novel psychophysical findings. Our point of departure is the little-known fact that corrections for target perturbations introduced late in a reaching movement are incomplete. We show that this is not simply attributable to lack of time, in contradiction with alternative models and, somewhat paradoxically, in agreement with our model. Analysis of optimal feedback gains reveals that the effect is partly attributable to a previously unknown trade-off between stability and accuracy. This yields a testable prediction: if stability requirements are decreased, then accuracy should increase. We confirm the prediction experimentally in three-dimensional obstacle avoidance and interception tasks in which subjects hit a robotic target with programmable impedance. In additional agreement with the theory, we find that subjects do not rely on rigid control strategies but instead exploit every opportunity for increased performance. The modeling methodology needed to capture this extra flexibility is more general than the linear-quadratic methods we used previously. The results suggest that the remarkable flexibility of motor behavior arises from sensorimotor control laws optimized for composite cost functions.
Optimal control design of turbo spin‐echo sequences with applications to parallel‐transmit systems
Hoogduin, Hans; Hajnal, Joseph V.; van den Berg, Cornelis A. T.; Luijten, Peter R.; Malik, Shaihan J.
2016-01-01
Purpose The design of turbo spin‐echo sequences is modeled as a dynamic optimization problem which includes the case of inhomogeneous transmit radiofrequency fields. This problem is efficiently solved by optimal control techniques making it possible to design patient‐specific sequences online. Theory and Methods The extended phase graph formalism is employed to model the signal evolution. The design problem is cast as an optimal control problem and an efficient numerical procedure for its solution is given. The numerical and experimental tests address standard multiecho sequences and pTx configurations. Results Standard, analytically derived flip angle trains are recovered by the numerical optimal control approach. New sequences are designed where constraints on radiofrequency total and peak power are included. In the case of parallel transmit application, the method is able to calculate the optimal echo train for two‐dimensional and three‐dimensional turbo spin echo sequences in the order of 10 s with a single central processing unit (CPU) implementation. The image contrast is maintained through the whole field of view despite inhomogeneities of the radiofrequency fields. Conclusion The optimal control design sheds new light on the sequence design process and makes it possible to design sequences in an online, patient‐specific fashion. Magn Reson Med 77:361–373, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine PMID:26800383
Optimal Pid Controller Design Using Adaptive Vurpso Algorithm
NASA Astrophysics Data System (ADS)
Zirkohi, Majid Moradi
2015-04-01
The purpose of this paper is to improve theVelocity Update Relaxation Particle Swarm Optimization algorithm (VURPSO). The improved algorithm is called Adaptive VURPSO (AVURPSO) algorithm. Then, an optimal design of a Proportional-Integral-Derivative (PID) controller is obtained using the AVURPSO algorithm. An adaptive momentum factor is used to regulate a trade-off between the global and the local exploration abilities in the proposed algorithm. This operation helps the system to reach the optimal solution quickly and saves the computation time. Comparisons on the optimal PID controller design confirm the superiority of AVURPSO algorithm to the optimization algorithms mentioned in this paper namely the VURPSO algorithm, the Ant Colony algorithm, and the conventional approach. Comparisons on the speed of convergence confirm that the proposed algorithm has a faster convergence in a less computation time to yield a global optimum value. The proposed AVURPSO can be used in the diverse areas of optimization problems such as industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning. The proposed AVURPSO algorithm is efficiently used to design an optimal PID controller.
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.
Aston-Jones, Gary; Cohen, Jonathan D
2005-01-01
Historically, the locus coeruleus-norepinephrine (LC-NE) system has been implicated in arousal, but recent findings suggest that this system plays a more complex and specific role in the control of behavior than investigators previously thought. We review neurophysiological and modeling studies in monkey that support a new theory of LC-NE function. LC neurons exhibit two modes of activity, phasic and tonic. Phasic LC activation is driven by the outcome of task-related decision processes and is proposed to facilitate ensuing behaviors and to help optimize task performance (exploitation). When utility in the task wanes, LC neurons exhibit a tonic activity mode, associated with disengagement from the current task and a search for alternative behaviors (exploration). Monkey LC receives prominent, direct inputs from the anterior cingulate (ACC) and orbitofrontal cortices (OFC), both of which are thought to monitor task-related utility. We propose that these frontal areas produce the above patterns of LC activity to optimize utility on both short and long timescales.
Theory, Methods, and Applications of Nonlinear Control
2012-08-29
help capture hybrid settings where the system switches between different modes of operation by moving between different regions of the state space... Lyapunov -Krasovskii functionals. The UAV work can be applied when there are rate constraints on the controls (which are constant bounds on the rate of... Lyapunov Functions, Communications and Control Engineering Series, Springer-Verlag London Ltd., London, UK, 2009. [MMZ11] Malisoff, M., F. Mazenc, and
Fetsch, Christopher R; Deangelis, Gregory C; Angelaki, Dora E
2010-05-01
The perception of self-motion is crucial for navigation, spatial orientation and motor control. In particular, estimation of one's direction of translation, or heading, relies heavily on multisensory integration in most natural situations. Visual and nonvisual (e.g., vestibular) information can be used to judge heading, but each modality alone is often insufficient for accurate performance. It is not surprising, then, that visual and vestibular signals converge frequently in the nervous system, and that these signals interact in powerful ways at the level of behavior and perception. Early behavioral studies of visual-vestibular interactions consisted mainly of descriptive accounts of perceptual illusions and qualitative estimation tasks, often with conflicting results. In contrast, cue integration research in other modalities has benefited from the application of rigorous psychophysical techniques, guided by normative models that rest on the foundation of ideal-observer analysis and Bayesian decision theory. Here we review recent experiments that have attempted to harness these so-called optimal cue integration models for the study of self-motion perception. Some of these studies used nonhuman primate subjects, enabling direct comparisons between behavioral performance and simultaneously recorded neuronal activity. The results indicate that humans and monkeys can integrate visual and vestibular heading cues in a manner consistent with optimal integration theory, and that single neurons in the dorsal medial superior temporal area show striking correlates of the behavioral effects. This line of research and other applications of normative cue combination models should continue to shed light on mechanisms of self-motion perception and the neuronal basis of multisensory integration.
Optimal Control of Mixing in Stokes Fluid Flows
NASA Astrophysics Data System (ADS)
Mathew, George; Mezic, Igor; Grivopoulos, Symeon; Vaidya, Umesh; Petzold, Linda
2006-11-01
Motivated by the problem of microfluidic mixing, the problem of optimal control of advective mixing in Stokes fluid flows is considered. The velocity field is assumed to be induced by a finite set of spatially distributed force fields that can be modulated arbitrarily with time and a passive material is advected by the flow. To quantify the degree of mixedness of a density field, we use a Sobolev space norm of negative index. We pose a finite-time optimal control problem where we aim to achieve the best mixing for a fixed value of the action (time integral of the kinetic energy of the fluid body) per unit mass. We derive the first order necessary conditions for optimality that can be expressed as a two point boundary value problem and we discuss some elementary properties that the optimal controls need to satisfy. A conjugate gradient descent method is used to solve the optimal control problem and we present numerical results for two problems involving arrays of vortices. A comparison of the mixing performance shows that optimal aperiodic inputs can do better than periodic inputs.
A control theory approach to clock steering techniques.
Farina, Marcello; Galleani, Lorenzo; Tavella, Patrizia; Bittanti, Sergio
2010-10-01
Several clock and time scale steering methods have been developed according to different viewpoints by various time laboratories. By resorting to control theory ideas, we propose a common theoretical framework encompassing these methods. A comparison of the most common steering methodologies, namely, the classical steering approach, the GPS bang-bang method, and the linear quadratic Gaussian technique, is carried out. We believe that the use of control theory methods can potentially lead to a better understanding of clock steering algorithms.
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
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.
An adaptive precision gradient method for optimal control.
NASA Technical Reports Server (NTRS)
Klessig, R.; Polak, E.
1973-01-01
This paper presents a gradient algorithm for unconstrained optimal control problems. The algorithm is stated in terms of numerical integration formulas, the precision of which is controlled adaptively by a test that ensures convergence. Empirical results show that this algorithm is considerably faster than its fixed precision counterpart.-
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...
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.
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 ...
Optimal birth control of age-dependent competitive species
NASA Astrophysics Data System (ADS)
He, Ze-Rong
2005-05-01
We study optimal birth policies for two age-dependent populations in a competing system, which is controlled by fertilities. New results on problems with free final time and integral phase constraints are presented, and the approximate controllability of system is discussed.
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.
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.
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.
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.
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.