New results on robust exponential stability of integral delay systems
NASA Astrophysics Data System (ADS)
Melchor-Aguilar, Daniel
2016-06-01
The robust exponential stability of integral delay systems with exponential kernels is investigated. Sufficient delay-dependent robust conditions expressed in terms of linear matrix inequalities and matrix norms are derived by using the Lyapunov-Krasovskii functional approach. The results are combined with a new result on quadratic stabilisability of the state-feedback synthesis problem in order to derive a new linear matrix inequality methodology of designing a robust non-fragile controller for the finite spectrum assignment of input delay systems that guarantees simultaneously a numerically safe implementation and also the robustness to uncertainty in the system matrices and to perturbation in the feedback gain.
Exponentially Stabilizing Robot Control Laws
NASA Technical Reports Server (NTRS)
Wen, John T.; Bayard, David S.
1990-01-01
New class of exponentially stabilizing laws for joint-level control of robotic manipulators introduced. In case of set-point control, approach offers simplicity of proportion/derivative control architecture. In case of tracking control, approach provides several important alternatives to completed-torque method, as far as computational requirements and convergence. New control laws modified in simple fashion to obtain asymptotically stable adaptive control, when robot model and/or payload mass properties unknown.
Robust Variable Selection with Exponential Squared Loss.
Wang, Xueqin; Jiang, Yunlu; Huang, Mian; Zhang, Heping
2013-04-01
Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this paper, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are [Formula: see text] and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower non-causal selection rate. Furthermore, we re-analyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.
Robust exponential acceleration in time-dependent billiards.
Gelfreich, Vassili; Rom-Kedar, Vered; Shah, Kushal; Turaev, Dmitry
2011-02-18
A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.
NASA Astrophysics Data System (ADS)
Mao, Yanbing; Zhang, Hongbin
2014-05-01
This paper deals with stability and robust H∞ control of discrete-time switched non-linear systems with time-varying delays. The T-S fuzzy models are utilised to represent each sub-non-linear system. Thus, with two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce a discrete-time switched fuzzy systems, which inherently contain the features of the switched hybrid systems and T-S fuzzy systems. Piecewise fuzzy weighting-dependent Lyapunov-Krasovskii functionals (PFLKFs) and average dwell-time approach are utilised in this paper for the exponentially stability analysis and controller design, and with free fuzzy weighting matrix scheme, switching control laws are obtained such that H∞ performance is satisfied. The conditions of stability and the control laws are given in the form of linear matrix inequalities (LMIs) that are numerically feasible. The state decay estimate is explicitly given. A numerical example and the control of delayed single link robot arm with uncertain part are given to demonstrate the efficiency of the proposed method.
Circuit design and exponential stabilization of memristive neural networks.
Wen, Shiping; Huang, Tingwen; Zeng, Zhigang; Chen, Yiran; Li, Peng
2015-03-01
This paper addresses the problem of circuit design and global exponential stabilization of memristive neural networks with time-varying delays and general activation functions. Based on the Lyapunov-Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs). Two numerical examples are elaborated to illustrate the characteristics of the results. It is noteworthy that the traditional assumptions on the boundness of the derivative of the time-varying delays are removed.
Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks.
Wang, Huamin; Duan, Shukai; Huang, Tingwen; Wang, Lidan; Li, Chuandong
2017-03-01
In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.
On exponential stability of gravity driven viscoelastic flows
NASA Astrophysics Data System (ADS)
Jiang, Fei; Wu, Guochun; Zhong, Xin
2016-05-01
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω ⊂R3 of class C3. First, we establish a critical number κC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ >κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ bar is a Rayleigh-Taylor (RT) type and ρbar‧ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C. H.
1993-01-01
This report presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design.
Robust Stabilizing Compensators for Flexible Structures with Collocated Controls
NASA Technical Reports Server (NTRS)
Balakrishman, A. V.
1996-01-01
For flexible structures with collocated rate and attitude sensors/actuators, we characterize compensator transfer functions which guarantee modal stability even when stiffness/inertia parameters are uncertain. While the compensators are finite-dimensional, the structure models are allowed to be infinite-dimensional (continuum models), with attendant complexity of the notion of stability; thus exponential stability is not possible and the best we can obtain is strong stability. Robustness is interpreted essentially as maintaining stability in the worst case. The conditions require that the compensator transfer functions be positive real and use is made of the Kalman-Yakubovic lemma to characterize them further. The concept of positive realness is shown to be equivalent to dissipativity in infinite dimensions. In particular we show that for a subclass of compensators it is possible to make the system strongly stable as well as dissipative in an appropriate energy norm.
Non-exponential Stabilization of Linear Time-invariant Systems by Time-varying Controllers
NASA Astrophysics Data System (ADS)
Inoue, Masaki; Wada, Teruyo; Ikeda, Masao
This paper proposes non-exponential stabilization of linear time-invariant systems by linear time-varying controllers. We consider state feedback and dynamic output feedback to make the states of the closed-loop systems decay non-exponentially. We first introduce a non-exponential stability concept that the state of a time-varying system converges to the origin with a bound provided by a desired function. Then, we give non-exponential stabilizability conditions and time-varying controllers to achieve the desired behavior of the closed-loop systems. By the proposed methods, we can realize various non-exponential behaviors, which may improve control performance.
Robust stabilization of the Space Station
NASA Technical Reports Server (NTRS)
Wie, Bong
1991-01-01
A robust H-infinity control design methodology and its application to a Space Station Freedom (SSF) attitude and momentum control problem are presented. This approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the SSF control problem yields remarkable results in stability robustness with respect to moments of inertia variation of about 73 percent in one of the structured uncertainty directions. The performance and stability of this robust H-infinity controller for the SSF are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.
Generalized exponential input-to-state stability of nonlinear systems with time delay
NASA Astrophysics Data System (ADS)
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
NASA Astrophysics Data System (ADS)
Xiao, Shuiming; Chen, Huabin
2017-03-01
In this paper, the existence and uniqueness, the exponential stability, and the almost sure exponential stability of mild solution for impulsive stochastic partial functional differential equations with finite delay are considered. Some sufficient conditions are established for our concerned problems, and some existing results are generalized and improved. Finally, an illustrative example is provided to show the feasibility and effectiveness of the obtained results.
Semigroup approximation and robust stabilization of distributed parameter systems
NASA Technical Reports Server (NTRS)
Kurdila, A. J.; Fabiano, R.; Strganac, T.; Hsu, S.
1994-01-01
Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.
Robust fuzzy logic stabilization with disturbance elimination.
Danapalasingam, Kumeresan A
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design.
Robust Fuzzy Logic Stabilization with Disturbance Elimination
Danapalasingam, Kumeresan A.
2014-01-01
A robust fuzzy logic controller is proposed for stabilization and disturbance rejection in nonlinear control systems of a particular type. The dynamic feedback controller is designed as a combination of a control law that compensates for nonlinear terms in a control system and a dynamic fuzzy logic controller that addresses unknown model uncertainties and an unmeasured disturbance. Since it is challenging to derive a highly accurate mathematical model, the proposed controller requires only nominal functions of a control system. In this paper, a mathematical derivation is carried out to prove that the controller is able to achieve asymptotic stability by processing state measurements. Robustness here refers to the ability of the controller to asymptotically steer the state vector towards the origin in the presence of model uncertainties and a disturbance input. Simulation results of the robust fuzzy logic controller application in a magnetic levitation system demonstrate the feasibility of the control design. PMID:25177713
Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid
2017-01-01
In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.
Robust Stabilization Control for an Electric Bicycle
NASA Astrophysics Data System (ADS)
Kawamura, Takuro; Murakami, Toshiyuki
Recently, bicycles have gained immense popularity because they have high mobility and are an environment-friendly means of transport. However, many people tend to avoid riding a bicycle because it is unstable. In order to solve this problem, stabilization control for a bicycle has been researched. The aim of this study is improvement of the robustness in stabilization control. To achieve this goal, control systems that use a camber angle disturbance observer (CADO) are proposed. Two kinds of CADOs are proposed in this paper, and the performances of these two observers are compared. The proposed control systems provide higher robustness than does the conventional method. The validity of the proposed methods is confirmed by the experimental results.
Song, Xueli; Xin, Xing; Huang, Wenpo
2012-05-01
The paper discusses exponential stability of distributed delayed and impulsive cellular neural networks with partially Lipschitz continuous activation functions. By relative nonlinear measure method, some novel criteria are obtained for the uniqueness and exponential stability of the equilibrium point. Our method abandons usual assumptions on global Lipschitz continuity, boundedness and monotonicity of activation functions. Our results are generalization and improvement of some existing ones. Finally, two examples and their simulations are presented to illustrate the correctness of our analysis.
Numerical robust stability estimation in milling process
NASA Astrophysics Data System (ADS)
Zhang, Xiaoming; Zhu, Limin; Ding, Han; Xiong, Youlun
2012-09-01
The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment. In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.
Lu, Hongtao; Amari, Shun-ichi
2006-09-01
In this paper, we study the global exponential stability of a multitime scale competitive neural network model with nonsmooth functions, which models a literally inhibited neural network with unsupervised Hebbian learning. The network has two types of state variables, one corresponds to the fast neural activity and another to the slow unsupervised modification of connection weights. Based on the nonsmooth analysis techniques, we prove the existence and uniqueness of equilibrium for the system and establish some new theoretical conditions ensuring global exponential stability of the unique equilibrium of the neural network. Numerical simulations are conducted to illustrate the effectiveness of the derived conditions in characterizing stability regions of the neural network.
Cao, Jinde; Wang, Jun
2004-04-01
This paper investigates the absolute exponential stability of a general class of delayed neural networks, which require the activation functions to be partially Lipschitz continuous and monotone nondecreasing only, but not necessarily differentiable or bounded. Three new sufficient conditions are derived to ascertain whether or not the equilibrium points of the delayed neural networks with additively diagonally stable interconnection matrices are absolutely exponentially stable by using delay Halanay-type inequality and Lyapunov function. The stability criteria are also suitable for delayed optimization neural networks and delayed cellular neural networks whose activation functions are often nondifferentiable or unbounded. The results herein answer a question: if a neural network without any delay is absolutely exponentially stable, then under what additional conditions, the neural networks with delay is also absolutely exponentially stable.
On global exponential stability of positive neural networks with time-varying delay.
Hien, Le Van
2017-03-01
This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positive neural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable condition is derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. The effectiveness of the obtained results is illustrated by a numerical example.
Global exponential stability for switched memristive neural networks with time-varying delays.
Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia
2016-08-01
This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples.
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
On exponential stability of linear Levin-Nohel integro-differential equations
NASA Astrophysics Data System (ADS)
Tien Dung, Nguyen
2015-02-01
The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].
NASA Astrophysics Data System (ADS)
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
Robust stability of second-order systems
NASA Technical Reports Server (NTRS)
Chuang, C.-H.
1995-01-01
It has been shown recently how virtual passive controllers can be designed for second-order dynamic systems to achieve robust stability. The virtual controllers were visualized as systems made up of spring, mass and damping elements. In this paper, a new approach emphasizing on the notion of positive realness to the same second-order dynamic systems is used. Necessary and sufficient conditions for positive realness are presented for scalar spring-mass-dashpot systems. For multi-input multi-output systems, we show how a mass-spring-dashpot system can be made positive real by properly choosing its output variables. In particular, sufficient conditions are shown for the system without output velocity. Furthermore, if velocity cannot be measured then the system parameters must be precise to keep the system positive real. In practice, system parameters are not always constant and cannot be measured precisely. Therefore, in order to be useful positive real systems must be robust to some degrees. This can be achieved with the design presented in this paper.
An approximation theorem for entire functions of exponential type and stability of zero sequences
Khabibullin, B N
2004-02-28
Let L be an entire function of exponential type in C with indicator function h{sub L}; let {lambda}={l_brace}{lambda}{sub n}{r_brace}, n=1,2,..., be a subsequence of zeros of the entire function of exponential type L{ne}0; let {gamma}={l_brace}{gamma}{sub n}{r_brace} be a complex number sequence and assume that {sigma}{sub n}|1/{lambda}{sub n} - 1/{gamma}{sub n}|<{infinity}. A simple construction of a sequence of entire functions of exponential type {l_brace}L{sub n}{r_brace} transforming {lambda} into a subsequence {gamma} of zeros of an entire function of exponential type G{ne}0 such that h{sub G}=h{sub L} is put forward (an approximation theorem). This result is applied to stability problems of zero sequences and non-uniqueness sequences for spaces of entire functions of exponential type with constraints on the indicators and to the problem of the stability of the completeness property of exponential systems in the space of germs of analytic functions on a compact convex set.
Probabilistic robust stabilization of fractional order systems with interval uncertainty.
Alagoz, Baris Baykant; Yeroglu, Celaleddin; Senol, Bilal; Ates, Abdullah
2015-07-01
This study investigates effects of fractional order perturbation on the robust stability of linear time invariant systems with interval uncertainty. For this propose, a probabilistic stability analysis method based on characteristic root region accommodation in the first Riemann sheet is developed for interval systems. Stability probability distribution is calculated with respect to value of fractional order. Thus, we can figure out the fractional order interval, which makes the system robust stable. Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials. This probabilistic approach is also used to develop a robust stabilization algorithm based on parametric perturbation strategy. We present numerical examples demonstrating utilization of stability probability distribution in robust stabilization problems of interval uncertain systems.
Hamed, Kaveh Akbari; Gregg, Robert D.
2016-01-01
This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059
Liu, Xiwei; Chen, Tianping
2016-03-01
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent real-valued system. The network model is described by a continuous-time equation. There are two main differences of this paper with previous works: 1) time delays can be asynchronous, i.e., delays between different nodes are different, which make our model more general and 2) we prove the exponential convergence directly, while the existence and uniqueness of the equilibrium point is just a direct consequence of the exponential convergence. Using three generalized norms, we present some sufficient conditions for the uniqueness and global exponential stability of the equilibrium point for delayed complex-valued neural networks. These conditions in our results are less restrictive because of our consideration of the excitatory and inhibitory effects between neurons; so previous works of other researchers can be extended. Finally, some numerical simulations are given to demonstrate the correctness of our obtained results.
Manivannan, R; Samidurai, R; Cao, Jinde; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-03-01
This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov-Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly (Q,S,R)-γ-dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network.
Computation of robustly stabilizing PID controllers for interval systems.
Matušů, Radek; Prokop, Roman
2016-01-01
The paper is focused on the computation of all possible robustly stabilizing Proportional-Integral-Derivative (PID) controllers for plants with interval uncertainty. The main idea of the proposed method is based on Tan's (et al.) technique for calculation of (nominally) stabilizing PI and PID controllers or robustly stabilizing PI controllers by means of plotting the stability boundary locus in either P-I plane or P-I-D space. Refinement of the existing method by consideration of 16 segment plants instead of 16 Kharitonov plants provides an elegant and efficient tool for finding all robustly stabilizing PID controllers for an interval system. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example in which the uncertain mathematical model of an experimental oblique wing aircraft is robustly stabilized.
Yang, Shiju; Li, Chuandong; Huang, Tingwen
2016-03-01
The problem of exponential stabilization and synchronization for fuzzy model of memristive neural networks (MNNs) is investigated by using periodically intermittent control in this paper. Based on the knowledge of memristor and recurrent neural network, the model of MNNs is formulated. Some novel and useful stabilization criteria and synchronization conditions are then derived by using the Lyapunov functional and differential inequality techniques. It is worth noting that the methods used in this paper are also applied to fuzzy model for complex networks and general neural networks. Numerical simulations are also provided to verify the effectiveness of theoretical results.
Xu, Changjin; Li, Peiluan; Pang, Yicheng
2016-12-01
In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).
Stagnation-point flow and heat transfer over an exponentially shrinking sheet: A stability analysis
NASA Astrophysics Data System (ADS)
Ismail, Nurul Syuhada; Arifin, Norihan Md.; Bachok, Norfifah; Mahiddin, Norhasimah
2016-06-01
Numerical solutions for the stagnation-point flow and heat transfer over an exponentially shrinking sheet have been investigated. The governing boundary layer equations are transformed into an ordinary differential equation using a non-similar transformation. By using the bvp4c solver in MATLAB, the results of the equations can be solved numerically. Numerical results indicate that in certain parameter, the non-unique solutions for the velocity and the temperature do exist. A linear stability analysis shows that only one solution is linearly stable otherwise is unstable. Then, the stability analysis is performed to identify which solution is stable between the two non-unique solutions.
Robust stabilization, robust performance, and disturbance attenuation for uncertain linear systems
NASA Technical Reports Server (NTRS)
Wang, Yeih J.; Shieh, Leang S.; Sunkel, John W.
1992-01-01
This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both the robust stability with optimal performance and the disturbance attenuation with H-infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance-attenuation robust-stabilizing controllers.
Wavelet Filtering to Reduce Conservatism in Aeroservoelastic Robust Stability Margins
NASA Technical Reports Server (NTRS)
Brenner, Marty; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification was used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins was reduced with parametric and nonparametric time-frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data was used to reduce the effects of external desirableness and unmodeled dynamics. Parametric estimates of modal stability were also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. F-18 high Alpha Research Vehicle aeroservoelastic flight test data demonstrated improved robust stability prediction by extension of the stability boundary beyond the flight regime.
On-Line Robust Modal Stability Prediction using Wavelet Processing
NASA Technical Reports Server (NTRS)
Brenner, Martin J.; Lind, Rick
1998-01-01
Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points.
Generic super-exponential stability of elliptic equilibrium positions for symplectic vector fields
NASA Astrophysics Data System (ADS)
Niederman, Laurent
2013-11-01
In this article, we consider linearly stable elliptic fixed points (equilibrium) for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. We will focus on the neighborhood of elliptic fixed points but the case of linearly stable isotropic reducible invariant tori in a Hamiltonian system should be similar. More specifically, Morbidelli and Giorgilli have proved a result of stability over superexponentially long times if one considers an analytic Lagrangian torus, invariant for an analytic Hamiltonian system, with a diophantine translation vector which admits a sign-definite torsion. Then, the solutions of the system move very little over times which are super-exponentially long with respect to the inverse of the distance to the invariant torus. The proof proceeds in two steps: first one constructs a high-order Birkhoff normal form, then one applies the Nekhoroshev theory. Bounemoura has shown that the second step of this construction remains valid if the Birkhoff normal form linked to the invariant torus or the elliptic fixed point belongs to a generic set among the formal series. This is not sufficient to prove this kind of super-exponential stability results in a general setting. We should also establish that the most strongly non resonant elliptic fixed point or invariant torus in a Hamiltonian system admits Birkhoff normal forms fitted for the application of the Nekhoroshev theory. Actually, the set introduced by Bounemoura is already very large but not big enough to ensure that a typical Birkhoff normal form falls into this class. We show here that this property is satisfied generically in the sense of the measure (prevalence) through infinite-dimensional probe spaces (that is, an infinite number of parameters chosen at random) with methods similar to those developed in a paper of Gorodetski, Kaloshin and Hunt in another setting.
Exponential stabilization for sampled-data neural-network-based control systems.
Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian
2014-12-01
This paper investigates the problem of sampled-data stabilization for neural-network-based control systems with an optimal guaranteed cost. Using time-dependent Lyapunov functional approach, some novel conditions are proposed to guarantee the closed-loop systems exponentially stable, which fully use the available information about the actual sampling pattern. Based on the derived conditions, the design methods of the desired sampled-data three-layer fully connected feedforward neural-network-based controller are established to obtain the largest sampling interval and the smallest upper bound of the cost function. A practical example is provided to demonstrate the effectiveness and feasibility of the proposed techniques.
Zhou, Liqun; Zhang, Yanyan
2016-01-01
In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.
NASA Astrophysics Data System (ADS)
Grobbelaar-Van Dalsen, Marié
2015-08-01
This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.
Yielding Elastic Tethers Stabilize Robust Cell Adhesion
Whitfield, Matt J.; Luo, Jonathon P.; Thomas, Wendy E.
2014-01-01
Many bacteria and eukaryotic cells express adhesive proteins at the end of tethers that elongate reversibly at constant or near constant force, which we refer to as yielding elasticity. Here we address the function of yielding elastic adhesive tethers with Escherichia coli bacteria as a model for cell adhesion, using a combination of experiments and simulations. The adhesive bond kinetics and tether elasticity was modeled in the simulations with realistic biophysical models that were fit to new and previously published single molecule force spectroscopy data. The simulations were validated by comparison to experiments measuring the adhesive behavior of E. coli in flowing fluid. Analysis of the simulations demonstrated that yielding elasticity is required for the bacteria to remain bound in high and variable flow conditions, because it allows the force to be distributed evenly between multiple bonds. In contrast, strain-hardening and linear elastic tethers concentrate force on the most vulnerable bonds, which leads to failure of the entire adhesive contact. Load distribution is especially important to noncovalent receptor-ligand bonds, because they become exponentially shorter lived at higher force above a critical force, even if they form catch bonds. The advantage of yielding is likely to extend to any blood cells or pathogens adhering in flow, or to any situation where bonds are stretched unequally due to surface roughness, unequal native bond lengths, or conditions that act to unzip the bonds. PMID:25473833
Zhang, Guodong; Shen, Yi
2015-11-01
This paper is concerned with the global exponential stability on a class of delayed neural networks with state-dependent switching. Under the novel conditions, some sufficient criteria ensuring exponential stability of the proposed system are obtained. In particular, the obtained conditions complement and improve earlier publications on conventional neural networks with continuous or discontinuous right-hand side. Numerical simulations are also presented to illustrate the effectiveness of the obtained results.
Robust stability of positive switched systems with dwell time
NASA Astrophysics Data System (ADS)
Liu, Jinjin; Zhang, Kanjian; Wei, Haikun
2016-08-01
This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results.
Robust Stabilization, Robust Performance, and Disturbance Attenuation for Uncertain Linear Systems
1992-01-01
the following Riccati equation: [ - ] B Tp+!I+ 1 CTC+Q=O. (7) Then, a disturbance-attenuation robust- stabilizing control law is given by u(t) = K z(t...disturbance-attenuation robust- stabilizing control law with the attenuation constant 6 is given by u(t) = K x(t), where K = -- BT P with 7> 1/2... stabilizing control law with the attenuation constant 6 is given by u(t) = K z(t), where K = -7 BT P with 7> - 1/2. Furthermore, the state-feedback
Robust Stabilization of a Class of passive Nonlinear Systems
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Absolute exponential stability of recurrent neural networks with generalized activation function.
Xu, Jun; Cao, Yong-Yan; Sun, Youxian; Tang, Jinshan
2008-06-01
In this paper, the recurrent neural networks (RNNs) with a generalized activation function class is proposed. In this proposed model, every component of the neuron's activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space. All of the convex hulls are composed of generalized activation function classes. The novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes. The absolute exponential stability (AEST) of the RNN with a generalized activation function class is studied through three steps. The first step is to demonstrate the global exponential stability (GES) of the equilibrium point of original RNN with a generalized activation function being equivalent to that of RNN under all vertex functions of convex hull. The second step transforms the RNN under every vertex activation function into neural networks under an array of saturated linear activation functions. Because the GES of the equilibrium point of three systems are equivalent, the next stability analysis focuses on the GES of the equilibrium point of RNN system under an array of saturated linear activation functions. The last step is to study both the existence of equilibrium point and the GES of the RNN under saturated linear activation functions using the theory of M-matrix. In the end, a two-neuron RNN with a generalized activation function is constructed to show the effectiveness of our results.
Song, Qiankun; Yan, Huan; Zhao, Zhenjiang; Liu, Yurong
2016-09-01
This paper investigates the stability problem for a class of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. By employing the idea of vector Lyapunov function, M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of equilibrium point. When the impulsive effects are not considered, several sufficient conditions are also given to guarantee the existence, uniqueness and global exponential stability of equilibrium point. Two examples are given to illustrate the effectiveness and lower level of conservatism of the proposed criteria in comparison with some existing results.
Wehbe, Ali; Youssef, Wael
2010-10-15
In this paper, we study the energy decay rate for the elastic Bresse system in one-dimensional bounded domain. The physical system consists of three wave equations. The two wave equations about the rotation angle and the longitudinal displacement are damped by two locally distributed feedbacks at the neighborhood of the boundary. Then indirect damping is applied to the equation for the transverse displacement of the beam through the coupling terms. We will establish the exponential stability for this system in the case of the same speed of propagation in the equation for the vertical displacement and the equation for the rotation angle of the system. When the wave speeds are different, nonexponential decay rate is proved and a polynomial-type decay rate is obtained. The frequency domain method and the multiplier technique are applied.
Robust stability analysis of uncertain switched linear systems with unstable subsystems
NASA Astrophysics Data System (ADS)
Yu, Qiang; Wu, Baowei
2015-05-01
The problem of robust stability for switched linear systems with all the subsystems being unstable is investigated. Unlike the most existing results in which each switching mode in the system is asymptotically stable, the subsystems may be unstable in this paper. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, sufficient conditions of exponential stability for both deterministic and uncertain switched linear systems are presented by using the invariant subspace theory and average dwell time method. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law. Several examples are included to show the effectiveness of the theoretical findings.
Xi, Qiang
2016-01-01
In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.
Robust Stabilization of Uncertain Systems Based on Energy Dissipation Concepts
NASA Technical Reports Server (NTRS)
Gupta, Sandeep
1996-01-01
Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis.
Robustness for slope stability modelling under deep uncertainty
NASA Astrophysics Data System (ADS)
Almeida, Susana; Holcombe, Liz; Pianosi, Francesca; Wagener, Thorsten
2015-04-01
Landslides can have large negative societal and economic impacts, such as loss of life and damage to infrastructure. However, the ability of slope stability assessment to guide management is limited by high levels of uncertainty in model predictions. Many of these uncertainties cannot be easily quantified, such as those linked to climate change and other future socio-economic conditions, restricting the usefulness of traditional decision analysis tools. Deep uncertainty can be managed more effectively by developing robust, but not necessarily optimal, policies that are expected to perform adequately under a wide range of future conditions. Robust strategies are particularly valuable when the consequences of taking a wrong decision are high as is often the case of when managing natural hazard risks such as landslides. In our work a physically based numerical model of hydrologically induced slope instability (the Combined Hydrology and Stability Model - CHASM) is applied together with robust decision making to evaluate the most important uncertainties (storm events, groundwater conditions, surface cover, slope geometry, material strata and geotechnical properties) affecting slope stability. Specifically, impacts of climate change on long-term slope stability are incorporated, accounting for the deep uncertainty in future climate projections. Our findings highlight the potential of robust decision making to aid decision support for landslide hazard reduction and risk management under conditions of deep uncertainty.
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ε-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
NASA Astrophysics Data System (ADS)
Sun, Yeong-Jeu; Wu, Yu-Biaw; Wang, Ching-Cheng
2013-06-01
In this study, the concept of global exponential ɛ-stabilization is introduced and the robust stabilization for a class of nonlinear systems with single input is investigated. Based on Lyapunov-like Theorem with differential and integral inequalities, a feedback control is proposed to realize the global stabilization of such nonlinear systems with any pre-specified exponential convergence rate. The guaranteed exponential convergence rate can be also correctly estimated. This result can be straightforwardly applicable to some famous chaotic systems. Besides, it will be proven that a single and linear control, with lower dimensions than that of the states, can realize the global exponential stability of some famous chaotic systems. Finally, comparisons of our main results with recently published results as well as numerical examples with circuit realization are provided to show the effectiveness and superiority of the obtained results.
Decentralized adaptive control of robot manipulators with robust stabilization design
NASA Technical Reports Server (NTRS)
Yuan, Bau-San; Book, Wayne J.
1988-01-01
Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.
Gong, Weiqiang; Liang, Jinling; Cao, Jinde
2015-10-01
In this paper, based on the matrix measure method and the Halanay inequality, global exponential stability problem is investigated for the complex-valued recurrent neural networks with time-varying delays. Without constructing any Lyapunov functions, several sufficient criteria are obtained to ascertain the global exponential stability of the addressed complex-valued neural networks under different activation functions. Here, the activation functions are no longer assumed to be derivative which is always demanded in relating references. In addition, the obtained results are easy to be verified and implemented in practice. Finally, two examples are given to illustrate the effectiveness of the obtained results.
Zhang, Guodong; Shen, Yi
2015-07-01
This paper is concerned with the global exponential stabilization of memristor-based chaotic neural networks with both time-varying delays and general activation functions. Here, we adopt nonsmooth analysis and control theory to handle memristor-based chaotic neural networks with discontinuous right-hand side. In particular, several new sufficient conditions ensuring exponential stabilization of memristor-based chaotic neural networks are obtained via periodically intermittent control. In addition, the proposed results here are easy to verify and they also extend the earlier publications. Finally, numerical simulations illustrate the effectiveness of the obtained results.
NASA Astrophysics Data System (ADS)
Lu, Junjie; She, Zhikun
2016-11-01
In this paper, we investigate sufficient and necessary conditions of uniform local exponential stability (ULES) for the discrete-time nonlinear switched system (DTNSS). We start with the definition of T-step common Lyapunov functions (CLFs), which is a relaxation of traditional CLFs. Then, for a time-varying DTNSS, by constructing such a T-step CLF, a necessary and sufficient condition for its ULES is provided. Afterwards, we strengthen it based on a T-step Lipschitz continuous CLF. Especially, when the system is time-invariant, by the smooth approximation theorem, the Lipschitz continuity condition of T-step CLFs can further be replaced by continuous differentiability; and when the system is time-invariant and homogeneous, due to the extension of Weierstrass approximation theorem, T-step continuously differentiable CLFs can even be strengthened to be T-step polynomial CLFs. Furthermore, three illustrative examples are additionally used to explain our main contribution. In the end, an equivalence between time-varying DTNSSs and their corresponding linearisations is discussed.
Robust stabilization of rotor-active magnetic bearing systems
NASA Astrophysics Data System (ADS)
Li, Guoxin
Active magnetic bearings (AMBs) are emerging as a beneficial technology for high-speed and high-performance suspensions in rotating machinery applications. A fundamental feedback control problem is robust stabilization in the presence of uncertain destabilizing mechanisms in aeroelastic, hydroelastic dynamics, and AMB feedback. As rotating machines are evolving in achieving high speed, high energy density, and high performance, the rotor and the support structure become increasingly flexible, and highly coupled. This makes rotor-AMB system more challenging to stabilize. The primary objective of this research is to develop a systematic control synthesis procedure for achieving highly robust stabilization of rotor-AMB systems. Of special interest is the stabilization of multivariable systems such as the AMB supported flexible rotors and gyroscopic rotors, where the classical control design may encounter difficulties. To this end, we first developed a systematic modeling procedure. This modeling procedure exploited the best advantages of technology developed in rotordynamics and the unique system identification tool provided by the AMBs. A systematic uncertainty model for rotor-AMB systems was developed, eliminating the iterative process of selecting uncertainty structures. The consequences of overestimation or underestimation of uncertainties were made transparent to control engineers. To achieve high robustness, we explored the fundamental performance/robustness limitations due to rotor-AMB system unstable poles. We examined the mixed sensitivity performance that is closely related to the unstructured uncertainty. To enhance transparency of the synthesis, we analyzed multivariable controllers from classical control perspectives. Based on these results, a systematic robust control synthesis procedure was established. For a strong gyroscopic rotor over a wide speed range, we applied the advanced gain-scheduled synthesis, and compared two synthesis frameworks in
Impact of pilots' biodynamic feedthrough on rotorcraft by robust stability
NASA Astrophysics Data System (ADS)
Quaranta, Giuseppe; Masarati, Pierangelo; Venrooij, Joost
2013-09-01
The coupling of rotorcraft dynamics with the dynamics of one of the main systems devoted to its control, the pilot, may lead to several peculiar phenomena, known as Rotorcraft-Pilot Couplings (RPCs), all characterized by an abnormal behavior that may jeopardize flight safety. Among these phenomena, there is a special class of couplings which is dominated by the biodynamic behavior of the pilot's limbs that close the loop between the vibrations and the control inceptors in the cockpit. Leveraging robust stability analysis, the inherently uncertain pilot biodynamics can be treated as the uncertain portion of a feedback system, making analytical, numerical or graphical determination of proneness to RPC possible by comparing robust stability margins of helicopter models with experimental Biodynamic Feedthrough (BDFT) data. The application of the proposed approach to collective bounce is exemplified using simple analytical helicopter and pilot models. The approach is also applied to detailed helicopter models and experimental BDFT measurement data.
Li, Bing; Li, Yongkun; Zhang, Xuemei
2016-01-01
In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).
Impossibility of unconditional stability and robustness of diffusive acceleration schemes
Azmy, Y.Y.
1998-01-01
The authors construct a problem for which exists no preconditioner with a cell-centered diffusion coupling stencil that is unconditionally stable and robust. In particular they consider an asymptotic limit of the Periodic Horizontal Interface (PHI) configuration wherein the cell height in both layers approaches zero like {sigma}{sup 2} while the total cross section varies like a in one layer and like 1/{sigma} in the other layer. In such case they show that the conditions for stability and robustness of the flat eigenmodes of the iteration residual imply instability of the modes flat in the y-dimension and rapidly varying in the x-dimension. This paper is important for radiation transport studies.
Zhang, Ancai; Qiu, Jianlong; She, Jinhua
2014-02-01
This paper concerns the existence and exponential stability of periodic solution for the high-order discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. First, we present the criteria for the existence of periodic solution based on the continuation theorem of coincidence degree theory and the Young's inequality, and then we give the criteria for the global exponential stability of periodic solution by using a non-Lyapunov method. After that, we give a numerical example that demonstrates the effectiveness of the theoretical results. The criteria presented in this paper are easy to verify. In addition, the proposed analysis method is easy to extend to other high-order neural networks.
NASA Astrophysics Data System (ADS)
Arthi, G.; Park, Ju H.; Jung, H. Y.
2016-03-01
In this paper, we establish the results on existence and uniqueness of mild solution of impulsive neutral stochastic integrodifferential equations driven by a fractional Brownian motion. Further, by using an impulsive integral inequality, some novel sufficient conditions are derived to ensure the exponential stability of mild solution in the mean square moment. The results are obtained by utilizing the fractional power of operators and the semigroup theory. Finally, an example is presented to demonstrate the effectiveness of the proposed result.
Implementation of Robust Stability Augmentation Systems for a Blimp
NASA Astrophysics Data System (ADS)
Mo, Yong-Hwan; Kawashima, Mitsutoyo; Goto, Norihiro
This paper applies robust control techniques to a blimp. The project “Mine Detection System Using Blimps” is in progress. The aim of the project is the development of a practical technique for the autonomous detection of landmines and their positions. In order for a blimp to perform observation and detection, precise flight path control is needed. The error resulting from modeling a real system cannot be avoided, however accurate the model is. In order to aim for realistic control, robust control can compensate model uncertainty. In the two-motion models presented (experimental model and analytical model), it was found that since the yawing motion mode is unstable, lateral-directional movement becomes unstable. This paper proposes a robust stability augmentation system for the yawing motion of the blimp developed for the project. The numerical simulation presents a comparison between a Kharitonov theory controller and a H∞ theory controller. The experimental results show that control of the blimp using a H∞ controller is more suitable for the project objective. An emphasis is placed on implementation of the controller.
NASA Astrophysics Data System (ADS)
Zhong, Kai; Zhu, Song; Yang, Qiqi
2016-11-01
In recent years, the stability problems of memristor-based neural networks have been studied extensively. This paper not only takes the unavoidable noise into consideration but also investigates the global exponential stability of stochastic memristor-based neural networks with time-varying delays. The obtained criteria are essentially new and complement previously known ones, which can be easily validated with the parameters of system itself. In addition, the study of the nonlinear dynamics for the addressed neural networks may be helpful in qualitative analysis for general stochastic systems. Finally, two numerical examples are provided to substantiate our results.
Robust enzyme design: bioinformatic tools for improved protein stability.
Suplatov, Dmitry; Voevodin, Vladimir; Švedas, Vytas
2015-03-01
The ability of proteins and enzymes to maintain a functionally active conformation under adverse environmental conditions is an important feature of biocatalysts, vaccines, and biopharmaceutical proteins. From an evolutionary perspective, robust stability of proteins improves their biological fitness and allows for further optimization. Viewed from an industrial perspective, enzyme stability is crucial for the practical application of enzymes under the required reaction conditions. In this review, we analyze bioinformatic-driven strategies that are used to predict structural changes that can be applied to wild type proteins in order to produce more stable variants. The most commonly employed techniques can be classified into stochastic approaches, empirical or systematic rational design strategies, and design of chimeric proteins. We conclude that bioinformatic analysis can be efficiently used to study large protein superfamilies systematically as well as to predict particular structural changes which increase enzyme stability. Evolution has created a diversity of protein properties that are encoded in genomic sequences and structural data. Bioinformatics has the power to uncover this evolutionary code and provide a reproducible selection of hotspots - key residues to be mutated in order to produce more stable and functionally diverse proteins and enzymes. Further development of systematic bioinformatic procedures is needed to organize and analyze sequences and structures of proteins within large superfamilies and to link them to function, as well as to provide knowledge-based predictions for experimental evaluation.
NASA Astrophysics Data System (ADS)
Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan
2016-11-01
Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.
NASA Astrophysics Data System (ADS)
Zhang, Jianlin
2017-04-01
In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H 1 for the compressible viscous radiative and reactive gas in multi-dimension with large initial data. Precisely, if the initial data are spherically symmetric or cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential stability of a solution toward the stationary solution as time goes to infinity. We obtain the uniform positive lower and upper bounds of the density by using different methods.
The 32nd CDC: Robust stabilizer synthesis for interval plants using Nevanlina-pick theory
NASA Technical Reports Server (NTRS)
Bhattacharya, Saikat; Keel, L. H.; Bhattacharyya, S. P.
1989-01-01
The synthesis of robustly stabilizing compensators for interval plants, i.e., plants whose parameters vary within prescribed ranges is discussed. Well-known H(sup infinity) methods are used to establish robust stabilizability conditions for a family of plants and also to synthesize controllers that would stabilize the whole family. Though conservative, these methods give a very simple way to come up with a family of robust stabilizers for an interval plant.
The Parameterization of All Robust Stabilizing Simple Repetitive Controllers
NASA Astrophysics Data System (ADS)
Yamada, Kou; Sakanushi, Tatsuya; Ando, Yoshinori; Hagiwara, Takaaki; Murakami, Iwanori; Takenaga, Hiroshi; Tanaka, Hiroshi; Matsuura, Shun
The modified repetitive control system is a type of servomechanism for the periodic reference input. That is, the modified repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or an uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles. When transfer functions from the periodic reference input to the output and from the disturbance to the output have infinite numbers of poles, it is difficult to specify the input-output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that the input-output characteristic and the disturbance attenuation characteristic are easily specified. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, transfer functions from the periodic reference input to the output and from the disturbance to the output are desirable to have finite numbers of poles. From this viewpoint, Yamada et al. proposed the concept of simple repetitive control systems such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. However, the method by Yamada et al. cannot be applied for the plant with uncertainty. The purpose of this paper is to propose the parameterization of all robust stabilizing simple repetitive controllers for the plant with uncertainty.
A design method for robust stabilizing simple repetitive control systems
NASA Astrophysics Data System (ADS)
Yamada, Kou; Takenaga, Hiroshi; Tanaka, Hiroshi
2007-12-01
The modified repetitive control system is a type of servomechanism for the periodic reference input. That is, the modified repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plants does not includes time-delay, the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles. When the transfer function from the periodic reference input to the output and that from the disturbance to the output have an infinite number of poles, it is difficult to specify the input-output characteristic and the disturbance attenuation characteristic. From the practical point of view, it is desirable that the input-output characteristic and the disturbance attenuation characteristic are easily specified. In order to specify the input-output characteristic and the disturbance attenuation characteristic easily, the transfer function from the periodic reference input to the output and that from the disturbance to the output are desirable to have a finite number of poles. Yamada et al. proposed the concept of simple repetitive control systems such that the controller works as a modified repetitive controller and the transfer function from the periodic reference input to the output and that from the disturbance to the output have a finite number of poles. In addition, Yamada et al. clarified the parametrization of all stabilizing simple repetitive controllers. However the method by Yamada et al. cannot be applied for the plant with uncertainty. The purpose of this paper is to propose the parametrization of all robust stabilizing simple repetitive controllers for the plant with uncertainty.
Liang, X B; Si, J
2001-01-01
This paper investigates the existence, uniqueness, and global exponential stability (GES) of the equilibrium point for a large class of neural networks with globally Lipschitz continuous activations including the widely used sigmoidal activations and the piecewise linear activations. The provided sufficient condition for GES is mild and some conditions easily examined in practice are also presented. The GES of neural networks in the case of locally Lipschitz continuous activations is also obtained under an appropriate condition. The analysis results given in the paper extend substantially the existing relevant stability results in the literature, and therefore expand significantly the application range of neural networks in solving optimization problems. As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed box set, which includes the box constrained quadratic programming and the linear complementarity problem as the special cases. It can be inferred that the linear VIP has a unique solution for the class of Lyapunov diagonally stable matrices, and that the synthesized RNN is globally exponentially convergent to the unique solution. Some illustrative simulation examples are also given.
NASA Technical Reports Server (NTRS)
Blackwell, C. C.
1987-01-01
A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.
Analysis and synthesis of HVDC controls for robust stability of power systems
Venkataraman, S.; Khammash, M.H.; Vittal, V.
1995-11-01
High Voltage DC (HVDC) links have controllable characteristics with potential for affecting system stability. This paper follows the robustness methodology procedure to analyze the stability robustness of HVDC controls in power systems over a range of operating conditions. A novel method to design power system controllers using the robustness methodology is also proposed. Numerical results for a sample test-system are obtained and compared with those obtained by conventional techniques.
Li, Hongfei; Jiang, Haijun; Hu, Cheng
2016-03-01
In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results.
Apalara, Tijani A.; Messaoudi, Salim A.
2015-06-15
In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.
Robust stability and performance of time-delay control systems.
Keviczky, L; Bányász, Cs
2007-04-01
Most of the optimal and adaptive regulators assume an a priori known time delay. The time-delay mismatch can cause unwanted instability. Influence of this uncertainty is investigated in connection with the required performance and robustness.
Probability-based stability robustness assessment of controlled structures
Field, R.V. Jr.; Voulgaris, P.G.; Bergman, L.A.
1996-01-01
Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst-case analyses. These traditional methods include the use of the structured singular value, as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. In this paper an attempt to view controller robustness as a probability measure is presented. The probability of failure due to parametric uncertainty is estimated using first-order reliability methods (FORM). It is demonstrated that this method can provide quite accurate results on the probability of failure of actively controlled structures. Moreover, a comparison of this method to a suitability modified structured singular value robustness analysis in a probabilistic framework is performed. It is shown that FORM is the superior analysis technique when applied to a controlled three degree-of-freedom structure. In addition, the robustness qualities of various active control design schemes such as LQR, H{sub 2}, H {sub oo}, and {mu}-synthesis is discussed in order to provide some design guidelines.
Li, Zhihong; Liu, Lei; Zhu, Quanxin
2016-12-01
This paper studies the mean-square exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. By using the vector Lyapunov function and property of M-matrix, two generalized Halanay inequalities are established. By means of the generalized Halanay inequalities, sufficient conditions are also obtained, which can ensure the exponential input-to-state stability of delayed Cohen-Grossberg neural networks with Markovian switching. Two numerical examples are given to illustrate the efficiency of the derived results.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Robust stabilization of marginally stable positive-real systems
NASA Technical Reports Server (NTRS)
Joshi, Suresh M.; Gupta, Sandeep
1994-01-01
This paper investigates the stability of the negative feedback interconnection to two positive-real systems which have poles in the closed left-half of the complex plane. A new definition of marginally strict positive real systems is introduced, and sufficient conditions are obtained for the stability of the feedback interconnection of such systems, using the Lyapunov method. The conditions obtained have direct applications to dynamic dissipative controllers for flexible spacecraft and are the least restrictive ones published to date.
Wang, Dongshu; Huang, Lihong
2014-03-01
In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results.
NASA Technical Reports Server (NTRS)
Ryan, R.
1993-01-01
Robustness is a buzz word common to all newly proposed space systems design as well as many new commercial products. The image that one conjures up when the word appears is a 'Paul Bunyon' (lumberjack design), strong and hearty; healthy with margins in all aspects of the design. In actuality, robustness is much broader in scope than margins, including such factors as simplicity, redundancy, desensitization to parameter variations, control of parameter variations (environments flucation), and operational approaches. These must be traded with concepts, materials, and fabrication approaches against the criteria of performance, cost, and reliability. This includes manufacturing, assembly, processing, checkout, and operations. The design engineer or project chief is faced with finding ways and means to inculcate robustness into an operational design. First, however, be sure he understands the definition and goals of robustness. This paper will deal with these issues as well as the need for the requirement for robustness.
An improved robust stability result for uncertain neural networks with multiple time delays.
Arik, Sabri
2014-06-01
This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.
BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel
2009-03-05
In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.
Stability and robustness of metal-supported SOFCs
NASA Astrophysics Data System (ADS)
Tucker, Michael C.; Lau, Grace Y.; Jacobson, Craig P.; DeJonghe, Lutgard C.; Visco, Steven J.
Tubular metal-supported SOFCs with YSZ electrolyte and electrodes comprising porous YSZ backbone and infiltrated Ni and LSM catalysts are operated at 700 °C. Tolerance to five complete anode redox cycles and five very rapid thermal cycles is demonstrated. The power output of a cell with as-infiltrated Ni anode degrades rapidly over 15 h operation. This degradation can be attributed primarily to coarsening of the fine infiltrated Ni particles. A cell in which the infiltrated Ni anode is precoarsened at 800 °C before operation at 700 °C shows dramatically improved stability. Stable operation over 350 h is demonstrated.
Intuitive robust stability metric for PID control of self-regulating processes.
Arbogast, Jeffrey E; Beauregard, Brett M; Cooper, Douglas J
2008-10-01
Published methods establish how plant-model mismatch in the process gain and dead time impacts closed-loop stability. However, these methods assume no plant-model mismatch in the process time constant. The work presented here proposes the robust stability factor metric, RSF, to examine the effect of plant-model mismatch in the process gain, dead time, and time constant. The RSF is presented in two forms: an equation form and a visual form displayed on robustness plots derived from the Bode and Nyquist stability criteria. This understanding of robust stability is reinforced through visual examples of how closed-loop performance changes with various levels of plant-model mismatch. One example shows how plant-model mismatch in the time constant can impact closed-loop stability as much as plant-model mismatch in the gain and/or dead time. Theoretical discussion shows that the impact is greater for small dead time to time constant ratios. As the closed-loop time constant used in Internal Model Control (IMC) tuning decreases, the impact becomes significant for a larger range of dead time to time constant ratios. To complete the presentation, the RSF is used to compare the robust stability of IMC-PI tuning to other PI, PID, and PID with Filter tuning correlations.
Liu, Yanbin; Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods.
Liu, Mengying; Sun, Peihua
2014-01-01
A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods. PMID:24795535
McCartin, B.J.
1996-12-31
Herein, we discuss a generalization of the semiclassical cubic spline known in the literature as the exponential spline. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain {open_quotes}tension{close_quotes} parameters. We first outline the theoretical underpinnings of the exponential spline. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. We next discuss the numerical computation of the exponential spline. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines. We conclude with a consideration of the broad spectrum of possible uses of exponential splines in the applications. Our primary emphasis is on computational fluid dynamics although the imaginative reader will recognize the wider generality of the techniques developed.
Robust control design with real parameter uncertainty using absolute stability theory. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
How, Jonathan P.; Hall, Steven R.
1993-01-01
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
Robust Video Stabilization Using Particle Keypoint Update and l1-Optimized Camera Path
Jeon, Semi; Yoon, Inhye; Jang, Jinbeum; Yang, Seungji; Kim, Jisung; Paik, Joonki
2017-01-01
Acquisition of stabilized video is an important issue for various type of digital cameras. This paper presents an adaptive camera path estimation method using robust feature detection to remove shaky artifacts in a video. The proposed algorithm consists of three steps: (i) robust feature detection using particle keypoints between adjacent frames; (ii) camera path estimation and smoothing; and (iii) rendering to reconstruct a stabilized video. As a result, the proposed algorithm can estimate the optimal homography by redefining important feature points in the flat region using particle keypoints. In addition, stabilized frames with less holes can be generated from the optimal, adaptive camera path that minimizes a temporal total variation (TV). The proposed video stabilization method is suitable for enhancing the visual quality for various portable cameras and can be applied to robot vision, driving assistant systems, and visual surveillance systems. PMID:28208622
Robust Video Stabilization Using Particle Keypoint Update and l₁-Optimized Camera Path.
Jeon, Semi; Yoon, Inhye; Jang, Jinbeum; Yang, Seungji; Kim, Jisung; Paik, Joonki
2017-02-10
Acquisition of stabilized video is an important issue for various type of digital cameras. This paper presents an adaptive camera path estimation method using robust feature detection to remove shaky artifacts in a video. The proposed algorithm consists of three steps: (i) robust feature detection using particle keypoints between adjacent frames; (ii) camera path estimation and smoothing; and (iii) rendering to reconstruct a stabilized video. As a result, the proposed algorithm can estimate the optimal homography by redefining important feature points in the flat region using particle keypoints. In addition, stabilized frames with less holes can be generated from the optimal, adaptive camera path that minimizes a temporal total variation (TV). The proposed video stabilization method is suitable for enhancing the visual quality for various portable cameras and can be applied to robot vision, driving assistant systems, and visual surveillance systems.
Robust stabilization using LMI techniques of neutral time-delay systems subject to input saturation
NASA Astrophysics Data System (ADS)
El Fezazi, Nabil; El Haoussi, Fatima; Houssaine Tissir, El; Alvarez, Teresa; Tadeo, Fernando
2017-01-01
The robust stabilization of uncertain saturated neutral systems with state delay is solved in this paper: based on a free weighting matrix approach, sufficient conditions are obtained via an LMI formulation. From these conditions, state feedback gains that ensure stability for the largest set of admissible initial conditions can be calculated solving optimization problems with LMI constraints. Some applications of this methodology to feedback control are then presented and compared with previous results in the literature.
Robust Stability and Performance for Linear Systems with Structured and Unstructured Uncertainties
1990-06-01
Pick Problem in Circuit and System Theory ," Circuir Theory and Appl., vol. 9, pp. 177-187, 1981. [59] E.I. Jury, "Inners and Stability of Dynamic Systems...unstructured uncertainty has been receiving attention much longer and has produced many interesting results, notably the H. theory and the LQG/LTR theory ...stability 6 robustness. It wilL be shown that the aforementioned synthesis task is closely related to singular perturbation theory . The next result
Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays
Delgado, Emma; Barreiro, Antonio; Falcón, Pablo; Díaz-Cacho, Miguel
2016-01-01
We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency. PMID:27128914
Robust H∞ stabilization of a hard disk drive system with a single-stage actuator
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Kiin Woon, Raymond Song
2015-04-01
This paper considers a robust H∞ control problem for a hard disk drive system with a single stage actuator. The hard disk drive system is modeled as a linear time-invariant uncertain system where its uncertain parameters and high-order dynamics are considered as uncertainties satisfying integral quadratic constraints. The robust H∞ control problem is transformed into a nonlinear optimization problem with a pair of parameterized algebraic Riccati equations as nonconvex constraints. The nonlinear optimization problem is then solved using a differential evolution algorithm to find stabilizing solutions to the Riccati equations. These solutions are used for synthesizing an output feedback robust H∞ controller to stabilize the hard disk drive system with a specified disturbance attenuation level.
Control design for robust stability in linear regulators: Application to aerospace flight control
NASA Technical Reports Server (NTRS)
Yedavalli, R. K.
1986-01-01
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Karra, Udayarka; Huang, Guoxian; Umaz, Ridvan; Tenaglier, Christopher; Wang, Lei; Li, Baikun
2013-09-01
A novel and robust distributed benthic microbial fuel cell (DBMFC) was developed to address the energy supply issues for oceanographic sensor network applications, especially under scouring and bioturbation by aquatic life. Multi-anode/cathode configuration was employed in the DBMFC system for enhanced robustness and stability in the harsh ocean environment. The results showed that the DBMFC system achieved peak power and current densities of 190mW/m(2) and 125mA/m(2) respectively. Stability characterization tests indicated the DBMFC with multiple anodes achieved higher power generation over the systems with single anode. A computational model that integrated physical, electrochemical and biological factors of MFCs was developed to validate the overall performance of the DBMFC system. The model simulation well corresponded with the experimental results, and confirmed the hypothesis that using a multi anode/cathode MFC configuration results in reliable and robust power generation.
Robust Stability Analysis of the Space Launch System Control Design: A Singular Value Approach
NASA Technical Reports Server (NTRS)
Pei, Jing; Newsome, Jerry R.
2015-01-01
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
Computational analysis of a stability robustness margin for structured real-parameter perturbations
NASA Technical Reports Server (NTRS)
Wedell, Evan; Chuang, C.-H.; Wie, Bong
1989-01-01
An efficient computational method is presented for stability robustness analysis with structured real-parameter perturbations. A generic model of a class of uncertain dynamical systems is used as an example. The parameter uncertainty is characterized by a real scalar, epsilon. Multilinearity of the closed-loop characteristic polynomial is exploited to permit application of the mapping theorem to calculate the stability robustness margin. It is found that sensitive geometry of the stability boundary in the epsilon, omega-plane renders problematic the calculation of the minimum epsilon as a function of omega. This difficulty is avoided by calculating the minimum distance to the image of the uncertainty domain over omega as a function of epsilon. It is also shown that a certain class of uncertain dynamical systems has the required multilinearity property and are thus amenable to the proposed technique.
Nevsky, A; Alighanbari, S; Chen, Q-F; Ernsting, I; Vasilyev, S; Schiller, S; Barwood, G; Gill, P; Poli, N; Tino, G M
2013-11-15
We have demonstrated a compact, robust device for simultaneous absolute frequency stabilization of three diode lasers whose carrier frequencies can be chosen freely relative to the reference. A rigid ULE multicavity block is employed, and, for each laser, the sideband locking technique is applied. A small lock error, computer control of frequency offset, wide range of frequency offset, simple construction, and robust operation are the useful features of the system. One concrete application is as a stabilization unit for the cooling and trapping lasers of a neutral-atom lattice clock. The device significantly supports and improves the clock's operation. The laser with the most stringent requirements imposed by this application is stabilized to a line width of 70 Hz, and a residual frequency drift less than 0.5 Hz/s. The carrier optical frequency can be tuned over 350 MHz while in lock.
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results. PMID:27190502
Jiang, Haijun; Zhang, Long; Teng, Zhidong
2005-11-01
In this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature.
Xu, Lijun; Jiang, Qi; Gu, Guodong
2016-01-01
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.
Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay
NASA Astrophysics Data System (ADS)
Kalidass, Mathiyalagan; Su, Hongye; Rathinasamy, Sakthivel
2014-02-01
This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.
NASA Astrophysics Data System (ADS)
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Flight control application of new stability robustness bounds for linear uncertain systems
NASA Technical Reports Server (NTRS)
Yedavalli, Rama K.
1993-01-01
This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.
A new delay-independent condition for global robust stability of neural networks with time delays.
Samli, Ruya
2015-06-01
This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results.
Real-Time Stability Margin Measurements for X-38 Robustness Analysis
NASA Technical Reports Server (NTRS)
Bosworth, John T.; Stachowiak, Susan J.
2005-01-01
A method has been developed for real-time stability margin measurement calculations. The method relies on a tailored-forced excitation targeted to a specific frequency range. Computation of the frequency response is matched to the specific frequencies contained in the excitation. A recursive Fourier transformation is used to make the method compatible with real-time calculation. The method was incorporated into the X-38 nonlinear simulation and applied to an X-38 robustness test. X-38 stability margins were calculated for different variations in aerodynamic and mass properties over the vehicle flight trajectory. The new method showed results comparable to more traditional stability analysis techniques, and at the same time, this new method provided coverage that is more complete and increased efficiency.
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks.
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-09-02
The gene regulatory network (GRN) is the central decision-making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large-scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation.
Stability of discrete-time networked control systems and its extension for robust H ∞ control
NASA Astrophysics Data System (ADS)
Wang, Peng; Han, Chongzhao; Ding, Baocang
2013-02-01
The stability of discrete-time Networked Control Systems (NCSs) is studied in this article. By introducing some scalars into matrix cross-term bounding technique, we present a new approach for the state feedback controller, with less conservatism, based on the Bilinear Matrix Inequalities (BMIs) and the descriptor model transformation. We further extend the method to robust H ∞ control considering both disturbances and parametric uncertainties. For the BMI problem which is difficult to be solved directly, a modified optimisation algorithm is proposed. The practicability, less conservatism and effectiveness of the results are demonstrated by two examples.
An exponential polynomial observer for synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
Robust Global Control Strategies for Improvement of Angular Stability using FACTS and HVDC Devices
NASA Astrophysics Data System (ADS)
Agnihotri, P.; Kulkarni, A. M.; Gole, A. M.
2013-05-01
System-wide feedback signals made available by Wide-Area Measurement Systems technology can be used in FACTS/HVDC based controllers for the improvement of angular stability. These global signals can facilitate the efficient use of controller effort to stabilize critical swing modes. This paper introduces a restricted global strategy which involves the use of specific global feedback signals which are available at the HVDC/FACTS locations. The strategy is expected to be robust to changes in the power grid as well as communication uncertainties. This paper presents a heuristic introduction to this strategy using a circuit analogy of a simplified model of a power system. Preliminary results on a small system are also presented.
NASA Astrophysics Data System (ADS)
De la Sen, M.
2008-08-01
This paper discusses linear fractional representations (LFR) of parameter-dependent nonlinear systems with real-rational nonlinearities and point-delayed dynamics. Sufficient conditions for robust global asymptotic stability independent of the delays and the existence of a robust stabilizing gain-scheduled dynamic controller are investigated via linear matrix inequalities. Such inequalities are obtained from the values of the time-derivatives of appropriate Lyapunov functions at all the vertices of the polytope which contains the parametrized uncertainties. The synthesized stabilizing controller consists of an interpolation being performed with the stabilizing controllers at the set of vertices of a certain polytope where the nonlinear-rational parametrization belongs to. Some extensions are also given concerning robust global asymptotic stability dependent of the delays. Numerical examples corroborate the usefulness of the proposed formalism and its applicability to practical related problems.
NASA Astrophysics Data System (ADS)
Feng, Baowei
2017-02-01
This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback u_{tt}+α Δ ^2 u-int limits ^t_{-∞}g(t-s)Δ ^2 u(s)ds+μ _1u_t+μ _2u_t(t-τ (t))+f(u)=h(x), defined in a bounded domain of {R}^n (n≥1) with some suitable initial data and boundary conditions. For arbitrary real numbers μ _1 and μ _2, we proved the global well-posedness of the problem. Results on stability of energy are also proved under some restrictions on μ _1, μ _2 and h(x)=0.
A Robust Method of Vehicle Stability Accurate Measurement Using GPS and INS
NASA Astrophysics Data System (ADS)
Miao, Zhibin; Zhang, Hongtian; Zhang, Jinzhu
2015-12-01
With the development of the vehicle industry, controlling stability has become more and more important. Techniques of evaluating vehicle stability are in high demand. Integration of Global Positioning System (GPS) and Inertial Navigation System (INS) is a very practical method to get high-precision measurement data. Usually, the Kalman filter is used to fuse the data from GPS and INS. In this paper, a robust method is used to measure vehicle sideslip angle and yaw rate, which are two important parameters for vehicle stability. First, a four-wheel vehicle dynamic model is introduced, based on sideslip angle and yaw rate. Second, a double level Kalman filter is established to fuse the data from Global Positioning System and Inertial Navigation System. Then, this method is simulated on a sample vehicle, using Carsim software to test the sideslip angle and yaw rate. Finally, a real experiment is made to verify the advantage of this approach. The experimental results showed the merits of this method of measurement and estimation, and the approach can meet the design requirements of the vehicle stability controller.
Nominal and robust stability regions of optimization-based PID controllers.
Ou, Linlin; Zhang, Weidong; Gu, Danying
2006-07-01
In recent decades, several optimization-based methods have been developed for the proportional-integral-derivative (PID) controller design, and the common feature of these methods is that the controller has only one adjustable parameter. To keep the closed-loop systems stable is an essential requirement for the optimization-based PID controllers. In almost all these methods, however, no exact stability region for the single adjustable parameter was sketched. In this paper, using the proposed analytical procedure based on the dual-locus diagram technique, explicit stability regions of the optimization-based PID controllers are derived for stable, integrating, and unstable processes with time delay in the nominal and perturbed cases, respectively. It is revealed that the proposed analytical procedure is effective for the determination of the nominal and robust stability regions and it offers simplicity and ease of mathematical calculations over other available stability analysis methods. The results in this paper provide some insight into the tuning of the optimization-based PID controllers.
Robustness and cognition in stabilization problem of dynamical systems based on asymptotic methods
NASA Astrophysics Data System (ADS)
Dubovik, S. A.; Kabanov, A. A.
2017-01-01
The problem of synthesis of stabilizing systems based on principles of cognitive (logical-dynamic) control for mobile objects used under uncertain conditions is considered. This direction in control theory is based on the principles of guaranteeing robust synthesis focused on worst-case scenarios of the controlled process. The guaranteeing approach is able to provide functioning of the system with the required quality and reliability only at sufficiently low disturbances and in the absence of large deviations from some regular features of the controlled process. The main tool for the analysis of large deviations and prediction of critical states here is the action functional. After the forecast is built, the choice of anti-crisis control is the supervisory control problem that optimizes the control system in a normal mode and prevents escape of the controlled process in critical states. An essential aspect of the approach presented here is the presence of a two-level (logical-dynamic) control: the input data are used not only for generating of synthesized feedback (local robust synthesis) in advance (off-line), but also to make decisions about the current (on-line) quality of stabilization in the global sense. An example of using the presented approach for the problem of development of the ship tilting prediction system is considered.
A network-centric robust resource allocation strategy for unmanned systems: stability analysis
NASA Astrophysics Data System (ADS)
Bouyoucef, K.; Khorasani, K.
2007-04-01
It is widely understood that communication is a critical technological factor in designing autonomous unmanned networks consisting of a large number of heterogeneous nodes that may be configured in ad-hoc fashions and incorporating intricate architectures. In fact, one of the challenges in this field is to recognize the entire network as a heterogenous collection of physical and information systems with complicated interconnections and interactions. Using high data rates that are essential for real-time interactive command and control systems, these networks require utilization of optimal integration of local feedback loops into a scheduling and resource allocation systems. This integration becomes particularly problematic in presence of latencies and delays. Given that dynamics of a network of unmanned systems could easily become unstable depending on interconnections among nodes, in this paper stability of the resulting time-delayed controlled network based on configuration changes is studied. We also formally investigate sufficient conditions for our proposed robust resource allocation strategies to be able to cope with these interconnections and time-delays in an optimal fashion. Our time-delayed dependent network consists of three nodes that can be configured into different architectures. To model our traffic and network we use a fluid flow model that is of low order and simpler than a detailed Markovian queueing probabilistic model. Using sliding mode-based variable structure control (SM-VSC) techniques that enjoy robustness capabilities, we design on the basis of an inaccurate/uncertain model our proposed robust nonlinear feedback-based control approaches. The results presented are analyzed analytically to guarantee stability of known/unknown time-delayed dependent network of unmanned systems for different configurations.
NASA Astrophysics Data System (ADS)
Shi, Yunde; Longman, Richard W.
2012-06-01
Repetitive control (RC) can be used to design active vibration isolation mounts that aim to cancel the influence of spacecraft vibrations on fine pointing equipment. It can cancel the influence of slight imbalance in momentum wheels, reaction wheels, and CMGs. Because RC aims for zero error, it requires reasonably accurate knowledge of the system dynamics all the way to Nyquist frequency. As a result, special methods are needed to establish robustness to model error. A series of publications have demonstrated a method of averaging a cost function over models to increase the robustness. A previous paper improves on this by adjusting the learning rate as a function of frequency to further improve robustness, but there is still a hard limit on phase error. This paper considers yet one more approach, and all three can be used simultaneously. Here we compromise on the zero tracking error requirement for frequencies that require extra robustness. This allows one to extend this hard limit making RC tolerate larger model errors. A quadratic cost is used that penalizes not just the rate of change of the input function, but also the size of the input function. We first establish how to do this for the sister field of iterative learning control, and then the frequency response characteristics are produced for design of repetitive control. The method can improve tracking error for a frequency interval above the frequency at which one would otherwise have to cut off the learning because of model error. Model uncertainty can be used directly in the design process to produce stable RC laws for any level of uncertainty. The design approach differs from typical earlier work that used a sharp frequency cutoff, and instead uses a minimal amount of attenuation needed to produce stability.
NASA Astrophysics Data System (ADS)
Danik, Yulia
2016-08-01
This paper is dedicated to the robustness analysis of a stabilizing controller for quasi-linear state dependent coefficients discrete systems. The interval parametric uncertainties in the linear part of the system are investigated. The nonlinear stabilizing regulator proposed for such systems is calculated at the average values of the uncertainty parameters and is used for all realizations of the system. The basic idea is that the existence of only weak nonlinearity in the system allows us to study its robustness based on the robustness of the corresponding unperturbed discrete linear system. The robustness conditions are formulated in the form of linear matrix inequalities. Numerical experiments demonstrating the robustness of the closed-loop system are presented.
Anderson, Ericka L.; Li, Weizhong; Klitgord, Niels; Highlander, Sarah K.; Dayrit, Mark; Seguritan, Victor; Yooseph, Shibu; Biggs, William; Venter, J. Craig; Nelson, Karen E.; Jones, Marcus B.
2016-01-01
As reports on possible associations between microbes and the host increase in number, more meaningful interpretations of this information require an ability to compare data sets across studies. This is dependent upon standardization of workflows to ensure comparability both within and between studies. Here we propose the standard use of an alternate collection and stabilization method that would facilitate such comparisons. The DNA Genotek OMNIgene∙Gut Stool Microbiome Kit was compared to the currently accepted community standard of freezing to store human stool samples prior to whole genome sequencing (WGS) for microbiome studies. This stabilization and collection device allows for ambient temperature storage, automation, and ease of shipping/transfer of samples. The device permitted the same data reproducibility as with frozen samples, and yielded higher recovery of nucleic acids. Collection and stabilization of stool microbiome samples with the DNA Genotek collection device, combined with our extraction and WGS, provides a robust, reproducible workflow that enables standardized global collection, storage, and analysis of stool for microbiome studies. PMID:27558918
Li, Ning; Cao, Jinde; Hayat, Tasawar
2014-08-01
This paper is concerned with a class of nonlinear uncertain switched networks with discrete time-varying delays . Based on the strictly complete property of the matrices system and the delay-decomposing approach, exploiting a new Lyapunov-Krasovskii functional decomposing the delays in integral terms, the switching rule depending on the state of the network is designed. Moreover, by piecewise delay method, discussing the Lyapunov functional in every different subintervals, some new delay-dependent robust stability criteria are derived in terms of linear matrix inequalities, which lead to much less conservative results than those in the existing references and improve previous results. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.
NASA Technical Reports Server (NTRS)
Garg, Sanjay
1989-01-01
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
Buffered Qualitative Stability explains the robustness and evolvability of transcriptional networks
Albergante, Luca; Blow, J Julian; Newman, Timothy J
2014-01-01
The gene regulatory network (GRN) is the central decision‐making module of the cell. We have developed a theory called Buffered Qualitative Stability (BQS) based on the hypothesis that GRNs are organised so that they remain robust in the face of unpredictable environmental and evolutionary changes. BQS makes strong and diverse predictions about the network features that allow stable responses under arbitrary perturbations, including the random addition of new connections. We show that the GRNs of E. coli, M. tuberculosis, P. aeruginosa, yeast, mouse, and human all verify the predictions of BQS. BQS explains many of the small- and large‐scale properties of GRNs, provides conditions for evolvable robustness, and highlights general features of transcriptional response. BQS is severely compromised in a human cancer cell line, suggesting that loss of BQS might underlie the phenotypic plasticity of cancer cells, and highlighting a possible sequence of GRN alterations concomitant with cancer initiation. DOI: http://dx.doi.org/10.7554/eLife.02863.001 PMID:25182846
Practical robust stabilization of PMAC servo drive based on continuous variable structure control
Grcar, B.; Cafuta, P.; Znidaric, M.
1996-12-01
In the paper the two stage control design of a high performance PMAC servo drive is described. In the first stage the nominal PMAC motor model is discussed as an analytical nonlinear system, transformed into the controllable canonical Brunovsky`s forms on the basis of input-output linearization. The influence of the load torque is considered implicitly by introducing the disturbance observer. Due to the sensitivity of the nominal model based control to parameter perturbations the linear tracking control is extended in the second stage by a continuous variable structure stabilizing control derived from Lyapunov`s function of the augmented feedback system. The design of the variable structure control requires no knowledge of the upper bounds of the perturbation function; instead, it considers the variable bounds of the available control signal. Undesired chattering of states and controlled variables are excluded. The introduced two stage control design assures practical robust stabilization for the class of bounded nonlinear perturbations satisfying the matching conditions without affecting the relative degree of the feedback system. Experimental results of the proposed PMAC servo drive control are presented.
NASA Astrophysics Data System (ADS)
Ratschbacher, Lothar; Gallego, Jose; Ghosh, Sutapa; Alavi, Seyed; Alt, Wolfgang; Martinez-Dorantes, Miguel; Meschede, Dieter
2016-04-01
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal
NASA Astrophysics Data System (ADS)
Gayvoronskiy, S. A.; Ezangina, T.; Khozhaev, I.; Gunbo, Lan
2017-01-01
The authors of this article developed the technique of combined parametric synthesis of a linear controller on the basis of the coefficient method and the method of mathematical programming capable of ensuring the maximization of the degree of robust stability of a control system. The article also presents the numerical illustration of the PI controller synthesis of the position stabilization system of an underwater object.
ERIC Educational Resources Information Center
Ishigami, Yoko; Klein, Raymond M.
2015-01-01
The current study examined the robustness, stability, reliability, and isolability of the attention network scores (alerting, orienting, and executive control) when young children experienced repeated administrations of the child version of the Attention Network Test (ANT; Rueda et al., 2004). Ten test sessions of the ANT were administered to 12…
Faydasicok, Ozlem; Arik, Sabri
2013-08-01
The main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.
NASA Astrophysics Data System (ADS)
Al-Azzawi, Waleed; Al-Akaidi, Marwan
2015-04-01
In this paper, the robust stability analysis of solar wireless networked control systems (SWNCSs) with stochastic time delays and packet dropout is investigated. The robust model predictive controller (RMPC) technique for the SWNCS is discussed using the linear matrix inequality (LMI) technique. Based on the SWNCS model, the RMPC (a full state feedback controller) can be constructed by using the Lyapunov functional method. Both sensor-to-controller and controller-to-actuator time delays of the SWNCS are considered as stochastic variables controlled by a Markov chain. A discrete-time Markovian jump linear system (MJLS) with norm bounded time delay is presented to model the SWNCSs. Conditions for H∞-norm is used to evaluate stability and stabilization of the fundamental systems derived via LMIs formulation. Finally, an illustrative numerical example is given to demonstrate the effectiveness of the proposed techniques.
Theory, computation, and application of exponential splines
NASA Technical Reports Server (NTRS)
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Jaballi, Ahmed; Sakly, Anis; Hajjaji, Ahmed El
2016-07-01
This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results.
Jin, Q B; Liu, Q; Huang, B
2016-03-01
This paper considers the problem of determining all the robust PID (proportional-integral-derivative) controllers in terms of the gain and phase margins (GPM) for open-loop unstable first order plus time delay (UFOPTD) processes. It is the first time that the feasible ranges of the GPM specifications provided by a PID controller are given for UFOPTD processes. A gain and phase margin tester is used to modify the original model, and the ranges of the margin specifications are derived such that the modified model can be stabilized by a stabilizing PID controller based on Hermite-Biehlers Theorem. Furthermore, we obtain all the controllers satisfying a given margin specification. Simulation studies show how to use the results to design a robust PID controller.
NASA Astrophysics Data System (ADS)
Ripamonti, Francesco; Resta, Ferruccio; Vivani, Andrea
2015-04-01
The aim of this paper is to present two control logics and an attitude estimator for UAV stabilization and remote piloting, that are as robust as possible to physical parameters variation and to other external disturbances. Moreover, they need to be implemented on low-cost micro-controllers, in order to be attractive for commercial drones. As an example, possible applications of the two switching control logics could be area surveillance and facial recognition by means of a camera mounted on the drone: the high computational speed logic is used to reach the target, when the high-stability one is activated, in order to complete the recognition tasks.
Kim, Dongcheol; Rhee, Sehun
2002-01-01
CO(2) welding is a complex process. Weld quality is dependent on arc stability and minimizing the effects of disturbances or changes in the operating condition commonly occurring during the welding process. In order to minimize these effects, a controller can be used. In this study, a fuzzy controller was used in order to stabilize the arc during CO(2) welding. The input variable of the controller was the Mita index. This index estimates quantitatively the arc stability that is influenced by many welding process parameters. Because the welding process is complex, a mathematical model of the Mita index was difficult to derive. Therefore, the parameter settings of the fuzzy controller were determined by performing actual control experiments without using a mathematical model of the controlled process. The solution, the Taguchi method was used to determine the optimal control parameter settings of the fuzzy controller to make the control performance robust and insensitive to the changes in the operating conditions.
Ko, Hsien-Ju; Yu, Wen-Shyong
2004-08-01
In this paper, an approach for robust stability analysis of a digital closed-loop system for digital controller implementations subject to finite word length (FWL) effects is proposed. Uncertainties caused by the roundoff and computational errors subject to FWL effects are expressed in function of mantissa bit number when the mode of floating-point arithmetic is used in the process. Then, based on the Small Gain Theorem and the Bellman-Grownwall Lemma, a sufficient stability criterion for the digital closed-loop system is derived. The eigenvalue sensitivity of the closed-loop system is developed in terms of mixed matrix-2/Frobenius norms. Then, by minimizing this eigenvalue sensitivity and using orthogonal Hermitian transform as well, an optimal similarity transformation can be obtained. By substituting this optimal transformation into the stability criterion, a minimum mantissa bit number used for implementing the stabilizing digital controllers can be determined. The main contributions are that this approach provides an analytical closed-form solution for obtaining the optimal transformation and, in addition to the stability criterion, leads to the implementation of the stabilizing controllers with a lower mantissa bit number when using this optimal one. Finally, detailed numerical design processes and simulation results are used to illustrate the effectiveness of the proposed scheme.
Robust reliable control design for networked control system with sampling communication
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Santra, Srimanta; Mathiyalagan, K.; Su, Hongye
2015-12-01
In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov-Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.
Embaby, Amira M; Saeed, Hesham; Hussein, Ahmed
2016-12-01
Present study underlines an unusual non-cumbersome-powerful strategy for purification of SHG10 keratinolytic alkaline protease from Bacillus licheniformis SHG10 DSM 28096 with robust stability properties. The enzyme was impressively purified to homogeneity with specific activity, purification fold, and yield of 613.82 U mg(-1) , 58.91 and 99%, respectively, via a sequential two-step purification strategy: precipitation with 65% (NH4 )2 SO4 and flow through fractions of DEAE-cellulose DE 53 column. SDS-PAGE conferred a monomeric enzyme with a molecular mass of 30.4 kDa. The enzyme demonstrated optimal activity at pH (10.0-11.0) and at 65 °C. It exhibited full stability at pH (6.0-11.0) over 38 h at 4 °C and at 65 °C for 15 min. Remarkable enhanced enzyme activity (130.15 and 126.37%) was retained in presence of commercial laundry detergents Oxi and Ariel after 1 h, respectively. Organic solvent stability of the enzyme was verified in butanol, ether, acetonitrile, isopropanol, and chloroform. Imposingly, full storage stability (100%) of the enzyme along 1 year in -20 °C was confirmed. Km -Vmax was 0.00174 mM-534.2 mM Sub · min(-1) · mg protein(-1) and 1.266 mg-28.89 mg Sub · h(-1) · mg protein(-1) on N-Suc-Ala-Ala-Pro-Phe-pNA and keratin azure, respectively. Robust stability properties of SHG10 keratinolytic alkaline protease along with rapid-efficient purification underpin its potential commercialization for industrial exploitation.
Stabilization and robustness of non-linear unity-feedback system - Factorization approach
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Kabuli, M. G.
1988-01-01
The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.
An Exceptional Exponential Function
ERIC Educational Resources Information Center
Curgus, Branko
2006-01-01
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…
ERIC Educational Resources Information Center
Huynh, Huynh; Rawls, Anita
2011-01-01
There are at least two procedures to assess item difficulty stability in the Rasch model: robust z procedure and "0.3 Logit Difference" procedure. The robust z procedure is a variation of the z statistic that reduces dependency on outliers. The "0.3 Logit Difference" procedure is based on experiences in Rasch linking for tests…
Robust stability analysis of a class of neural networks with discrete time delays.
Faydasicok, Ozlem; Arik, Sabri
2012-05-01
This paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.
NASA Astrophysics Data System (ADS)
Schaefer, Bradley E.; Dyson, Samuel E.
1996-08-01
A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.
NASA Astrophysics Data System (ADS)
Balint, Stefan; Balint, Agneta M.
2017-01-01
Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].
Robust torque control of an elastic robotic arm based on invertibility and feedback stabilization
NASA Technical Reports Server (NTRS)
Singh, S. N.; Schy, A. A.
1985-01-01
An approach to the control of elastic robotic systems for space applications using inversion, servocompensation, and feedback stabilization is presented. For simplicity, a robot arm (PUMA-type) with three rotational joints is considered. The third link is assumed to be elastic. Using an inversion algorithm, a nonlinear decoupling control law, u sub d, is derived such that in the closed loop system, independent control of joint angles by the three joint torquers is accomplished. For the stabilization of elastic oscillations, a linear feedback torquer control law, u sub s, is obtained applying linear quadratic optimization to the linearized arm model augmented with a servocompensator about the terminal state. Simulation results show that, in spite of uncertainties in the payload and vehicle angular velocity, good joint angle control and damping of elastic oscillations are obtained with the torquer control law u = u sub d + u sub s.
ERIC Educational Resources Information Center
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Stability and Robustness Analysis Tools for Marine Robot Localization and Mapping Applications
2009-06-01
propeller, and shaft, and sometimes rivets and welds). DIDSON provides a range and bearing measurement associated with each pixel of each image... Springer - Verlag, 1990, pp. 167-193. [22] M. Csorba, Simultaneous Localisation and Map Building, PhD Thesis, University of Oxford, 1997. [23] G... Springer -Verlag, 2003, pp. 361-371. [39] E. Malis, “Stability Analysis of Invariant Visual Servoing and Robutness to Parametric Uncertainties,” A
Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach.
Khan, Qudrat; Akmeliawati, Rini; Bhatti, Aamer Iqbal; Khan, Mahmood Ashraf
2017-01-01
This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.
Nanoporous membrane robustness / stability in small form factor microfluidic filtration system.
Johnson, Dean G; Pan, Sabrina; Hayden, Andrew; McGrath, James L
2016-08-01
The development of wearable hemodialysis (HD) devices that replace center-based HD holds the promise to improve both outcomes and quality-of-life for patients with end-stage-renal disease (ERD). A prerequisite for these devices is the development of highly efficient membranes that can achieve high toxin clearance in small footprints. The ultrathin nanoporous membrane material developed by our group is orders of magnitude more permeable than conventional HD membranes. We report on our progress making a prototype wearable dialysis unit. First, we present data from benchtop studies confirming that clinical levels of urea clearance can be obtained in a small animal model with low blood flow rates. Second, we report on efforts to improve the mechanical robustness of high membrane area dialysis devices.
NASA Astrophysics Data System (ADS)
Balasubramaniam, P.; Sathy, R.
2011-02-01
In this paper, the robust asymptotic stability problem is considered for a class of fuzzy Markovian jumping genetic regulatory networks with uncertain parameters and switching probabilities by delay decomposition approach. The purpose of the addressed stability analysis problem is to establish an easy-to-verify condition under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing the delay interval into multiple subinterval, and choosing proper functionals with different weighting matrices corresponding to different subintervals in the LKFs. Employing these new LKFs for the time-varying delays, a new delay-dependent stability criterion is established with Markovian jumping parameters by T-S fuzzy model. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are exploited to illustrate the effectiveness of the proposed design procedures.
Reichert, Malinda D; Lin, Chia-Cheng; Vela, Javier
2014-07-08
Anisotropic II–VI semiconductor nanostructures are important photoactive materials for various energy conversion and optical applications. However, aside from the many available surface chemistry studies and from their ubiquitous photodegradation under continuous illumination, the general chemical reactivity and thermal stability (phase and shape transformations) of these materials are poorly understood. Using CdSe and CdS nanorods as model systems, we have investigated the behavior of II–VI semiconductor nanorods against various conditions of extreme chemical and physical stress (acids, bases, oxidants, reductants, and heat). CdSe nanorods react rapidly with acids, becoming oxidized to Se or SeO2. In contrast, CdSe nanorods remain mostly unreactive when treated with bases or strong oxidants, although bases do partially etch the tips of the nanorods (along their axis). Roasting (heating in air) of CdSe nanorods results in rock-salt CdO, but neither CdSe nor CdO is easily reduced by hydrogen (H2). Another reductant, n-BuLi, reduces CdSe nanorods to metallic Cd. Variable temperature X-ray diffraction experiments show that axial annealing and selective axial melting of the nanorods precede particle coalescence. Furthermore, thermal analysis shows that the axial melting of II–VI nanorods is a ligand-dependent process. In agreement with chemical reactivity and thermal stability observations, silica-coating experiments show that the sharpest (most curved) II–VI surfaces are most active against heterogeneous nucleation of a silica shell. These results provide valuable insights into the fate and possible ways to enhance the stability and improve the use of II–VI semiconductor nanostructures in the fields of optics, magnetism, and energy conversion.
Robust nonlinear controller design to improve the stability of a large scale photovoltaic system
NASA Astrophysics Data System (ADS)
Islam, Gazi Md. Saeedul
Recently interest in photovoltaic (PV) power generation systems is increasing rapidly and the installation of large PV systems or large groups of PV systems that are interconnected with the utility grid is accelerating despite their high cost and low efficiency due to environmental issues and depletions of fossil fuels. Most of the photovoltaic (PV) applications are grid connected. Existing power systems may face the stability problems because of the high penetration of PV systems to the grid. Therefore, more stringent grid codes are being imposed by the energy regulatory bodies for grid integration of PV plants. Recent grid codes dictate that PV plants need to stay connected with the power grid during the network faults because of their increased power penetration level. This requires the system to have large disturbance rejection capability to protect the system and provide dynamic grid support. This thesis presents a new control method to enhance the steady-state and transient stabilities of a grid connected large scale photovoltaic (PV) system. A new control coordination scheme is also presented to reduce the power mismatch during the fault condition in order to limit the fault currents, which is one of the salient features of this study. The performance of the overall system is analyzed using laboratory standard power system simulation software PSCAD/EMTDC.
Collaborative Research: Robust Climate Projections and Stochastic Stability of Dynamical Systems
Ghil, Michael; McWilliams, James; Neelin, J. David; Zaliapin, Ilya; Chekroun, Mickael; Kondrashov, Dmitri; Simonnet, Eric
2011-10-13
The project was completed along the lines of the original proposal, with additional elements arising as new results were obtained. The originally proposed three thrusts were expanded to include an additional, fourth one. (i) The e ffects of stochastic perturbations on climate models have been examined at the fundamental level by using the theory of deterministic and random dynamical systems, in both nite and in nite dimensions. (ii) The theoretical results have been implemented first on a delay-diff erential equation (DDE) model of the El-Nino/Southern-Oscillation (ENSO) phenomenon. (iii) More detailed, physical aspects of model robustness have been considered, as proposed, within the stripped-down ICTP-AGCM (formerly SPEEDY) climate model. This aspect of the research has been complemented by both observational and intermediate-model aspects of mid-latitude and tropical climate. (iv) An additional thrust of the research relied on new and unexpected results of (i) and involved reduced-modeling strategies and associated prediction aspects have been tested within the team's empirical model reduction (EMR) framework. Finally, more detailed, physical aspects have been considered within the stripped-down SPEEDY climate model. The results of each of these four complementary e fforts are presented in the next four sections, organized by topic and by the team members concentrating on the topic under discussion.
NASA Astrophysics Data System (ADS)
Requejo, Rubén J.; Camacho, Juan; Cuesta, José A.; Arenas, Alex
2012-08-01
The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.
Minakshi, Manickam; Barmi, Maryam J; Jones, Robert T
2017-03-14
Hybrid capacitors can replace or complement batteries, while storing energy through ion adsorption and fast surface redox reactions. There is a growing demand in developing nanostructured materials as electrodes for hybrid systems that can enhance the specific capacitance by ion desolvation in the nanopores. Here, we demonstrate that rescaling the pore diameter with the aid of biopolymer at an optimal level during the synthesis of metal molybdate leads to high capacitance 124 F g(-1) giving robust capacitance retention of 80% over 2000 cycles for a constructed device (activated carbon vs. metal molybdate). The presence of biopolymer (l-glutamic acid) in the metal molybdate acts as a complexing agent of the metal ion while enhancing the mass transport and hence it's improved electrochemical performance. However, XPS and other elemental analyses illustrated no evidence for N doping but traces of other surface functional groups (i.e. C and O) could be present on the molybdate surface. The biopolymer synthetic approach has the advantage of yielding nanostructured material with a relatively narrow pore size distribution controlled by l-glutamic acid. This study will provide a generic route to rescale other metal molybdate, phosphate or oxide counterparts and be an added value to the database.
Zhong, Xungao; Zhong, Xunyu; Peng, Xiafu
2013-10-08
In this paper, a global-state-space visual servoing scheme is proposed for uncalibrated model-independent robotic manipulation. The scheme is based on robust Kalman filtering (KF), in conjunction with Elman neural network (ENN) learning techniques. The global map relationship between the vision space and the robotic workspace is learned using an ENN. This learned mapping is shown to be an approximate estimate of the Jacobian in global space. In the testing phase, the desired Jacobian is arrived at using a robust KF to improve the ENN learning result so as to achieve robotic precise convergence of the desired pose. Meanwhile, the ENN weights are updated (re-trained) using a new input-output data pair vector (obtained from the KF cycle) to ensure robot global stability manipulation. Thus, our method, without requiring either camera or model parameters, avoids the corrupted performances caused by camera calibration and modeling errors. To demonstrate the proposed scheme's performance, various simulation and experimental results have been presented using a six-degree-of-freedom robotic manipulator with eye-in-hand configurations.
Exponentially fitted symplectic integrator
NASA Astrophysics Data System (ADS)
Simos, T. E.; Vigo-Aguiar, Jesus
2003-01-01
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the “classical” symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.
Robust design of polyrhythmic neural circuits
NASA Astrophysics Data System (ADS)
Schwabedal, Justus T. C.; Neiman, Alexander B.; Shilnikov, Andrey L.
2014-08-01
Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.
NASA Astrophysics Data System (ADS)
Frye, Michael Takaichi
This dissertation examines the problem of global decentralized control by output feedback for large-scale uncertain nonlinear systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. Several innovative techniques will be developed to create decentralized output feedback controllers rendering the closed-loop systems globally asymptotically stable. This is accomplished by extending an output feedback domination design that requires only limited information about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. A time-varying output feedback controller is also constructed for use with large-scale systems that have unknown parameters. Furthermore, a mixed large-scale system consisting of both lower and upper triangular systems is shown to be stabilizable by employing a combined high and low gain domination technique. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. In addition, a new design technique was developed using homogeneous system theory, which allows for the design of nonsmooth controllers and observers to stabilize a class of feedforward system with uncontrollable and unobservable linearization. An example of a large-scale system is a group of autonomous airships performing the function of a temporary mobile cell phone network. An airship mobile cell phone network is a novel solution to the problem of maintaining communication during the advent of extensive damage to the communication infrastructure; be it from a flood, earthquake, hurricane, or terrorist attack. A first principle force-based dynamic model for the Tri-Turbofan Airship was developed and will be discussed in detail. The mathematical model was based on actual flight test data that has been collected at the Gait Analysis and Innovative Technologies Laboratory. This model was developed to research autonomous airship
Exponential Localization of Photons
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo
1998-06-01
It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K; Ong, Ta-Chung; Keeler, Eric G; Kim, Hyunho; McKay, Ian S; Griffin, Robert G; Wang, Evelyn N
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg(2+) ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, (27)Al/(29)Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2(nd) law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications.
Li, Xiansen; Narayanan, Shankar; Michaelis, Vladimir K.; Ong, Ta-Chung; Keeler, Eric G.; Kim, Hyunho; McKay, Ian S.; Griffin, Robert G.; Wang, Evelyn N.
2014-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg,Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the labscale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N2 sorption, 27Al/29Si MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick’s 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. PMID:25395877
Leng, Yan; Wang, Zhifei; Tsai, Li-Kai; Leeds, Peter; Fessler, Emily Bame; Wang, Junyu; Chuang, De-Maw
2013-01-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and dramatically elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment dramatically prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels, and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers, and a potential new therapeutic target for CNS disorders. PMID:24468826
Li, XS; Narayanan, S; Michaelis, VK; Ong, TC; Keeler, EG; Kim, H; Mckay, IS; Griffin, RG; Wang, EN
2015-01-01
Modular and compact adsorption heat pumps (AHPs) promise an energy-efficient alternative to conventional vapor compression based heating, ventilation and air conditioning systems. A key element in the advancement of AHPs is the development of adsorbents with high uptake capacity, fast intracrystalline diffusivity and durable hydrothermal stability. Herein, the ion exchange of NaY zeolites with ingoing Mg2+ ions is systematically studied to maximize the ion exchange degree (IED) for improved sorption performance. It is found that beyond an ion exchange threshold of 64.1%, deeper ion exchange does not benefit water uptake capacity or characteristic adsorption energy, but does enhance the vapor diffusivity. In addition to using water as an adsorbate, the uptake properties of Mg, Na-Y zeolites were investigated using 20 wt.% MeOH aqueous solution as a novel anti-freeze adsorbate, revealing that the MeOH additive has an insignificant influence on the overall sorption performance. We also demonstrated that the lab-scale synthetic scalability is robust, and that the tailored zeolites scarcely suffer from hydrothermal stability even after successive 108-fold adsorption/desorption cycles. The samples were analyzed using N-2 sorption, Al-27/Si-29 MAS NMR spectroscopy, ICP-AES, dynamic vapor sorption, SEM, Fick's 2nd law and D-R equation regressions. Among these, close examination of sorption isotherms for H2O and N-2 adsorbates allows us to decouple and extract some insightful information underlying the complex water uptake phenomena. This work shows the promising performance of our modified zeolites that can be integrated into various AHP designs for buildings, electronics, and transportation applications. (C) 2014 Elsevier Inc. All rights reserved.
Leng, Y; Wang, Z; Tsai, L-K; Leeds, P; Fessler, E B; Wang, J; Chuang, D-M
2015-02-01
Fibroblast growth factor-21 (FGF-21) is a new member of the FGF super-family and an important endogenous regulator of glucose and lipid metabolism. It has been proposed as a therapeutic target for diabetes and obesity. Its function in the central nervous system (CNS) remains unknown. Previous studies from our laboratory demonstrated that aging primary neurons are more vulnerable to glutamate-induced excitotoxicity, and that co-treatment with the mood stabilizers lithium and valproic acid (VPA) induces synergistic neuroprotective effects. This study sought to identify molecule(s) involved in these synergistic effects. We found that FGF-21 mRNA was selectively and markedly elevated by co-treatment with lithium and VPA in primary rat brain neurons. FGF-21 protein levels were also robustly increased in neuronal lysates and culture medium following lithium-VPA co-treatment. Combining glycogen synthase kinase-3 (GSK-3) inhibitors with VPA or histone deacetylase (HDAC) inhibitors with lithium synergistically increased FGF-21 mRNA levels, supporting that synergistic effects of lithium and VPA are mediated via GSK-3 and HDAC inhibition, respectively. Exogenous FGF-21 protein completely protected aging neurons from glutamate challenge. This neuroprotection was associated with enhanced Akt-1 activation and GSK-3 inhibition. Lithium-VPA co-treatment markedly prolonged lithium-induced Akt-1 activation and augmented GSK-3 inhibition. Akt-1 knockdown markedly decreased FGF-21 mRNA levels and reduced the neuroprotection induced by FGF-21 or lithium-VPA co-treatment. In addition, FGF-21 knockdown reduced lithium-VPA co-treatment-induced Akt-1 activation and neuroprotection against excitotoxicity. Together, our novel results suggest that FGF-21 is a key mediator of the effects of these mood stabilizers and a potential new therapeutic target for CNS disorders.
Bapatu, Hanimi Reddy; Maram, Ravi Kumar; Murthy, R Satyanarayana
2015-10-01
A novel, reversed-phase high-performance liquid chromatographic method was developed and validated for the determination of related substances in Plerixafor (PLX) drug substance. PLX is an immunostimulant used to mobilize hematopoietic stem cells in cancer patients. The method is efficient for estimation of all degradation and process-related impurities. The method was developed using the Phenomenex Luna L11 column using the gradient program with mobile phase A and mobile phase B, where mobile phase A consists of pH 2.0 1-heptanesulfonic acid sodium salt buffer and acetonitrile in the ratio of 80:20 (v/v) and mobile phase B consists of pH 2.0 1-heptanesulfonic acid sodium salt buffer and acetonitrile in the ratio of 20:80 (v/v). PLX and its impurities were monitored at 210 nm. The present work is describing the role of ion-pair reagent in the separation of polar compounds. PLX was subjected to various stress conditions of oxidative, acid, base, hydrolytic, thermal, humidity and photolytic degradations. The degradation products were well separated from each other and with the main peak, demonstrating the stability-indicating power of the method. The performance of the method was validated according to the present ICH guidelines for specificity, limit of detection, limit of quantification, linearity, accuracy, precision, ruggedness and robustness.
Okaru, Alex O.; Abuga, Kennedy O.; Kamau, Franco N.; Ndwigah, Stanley N.; Lachenmeier, Dirk W.
2017-01-01
A simple, isocratic and robust RP-HPLC method for the analysis of azithromycin was developed, validated and applied for the analysis of bulk samples, tablets and suspensions. The optimum chromatographic conditions for separation were established as a mobile phase comprised of acetonitrile-0.1 M KH2PO4 pH 6.5–0.1 M tetrabutyl ammonium hydroxide pH 6.5-water (25:15:1:59 v/v/v/v) delivered at a flow rate of 1.0 mL/min. The stationary phase consisted of reverse-phase XTerra® (250 mm × 4.6 mm i.d., 5 µm particle size) maintained at a temperature of 43 °C with a UV detection at 215 nm. The method was found to be linear in the range 50%–150% (r2 = 0.997). The limits of detection and quantification were found to be 0.02% (20 µg) and 0.078% (78 µg), respectively, with a 100.7% recovery of azithromycin. Degradation products of azithromycin in acidic and oxidative environments at 37 °C were resolved from the active pharmaceutical ingredient and thus the method is fit for the purpose of drug stability confirmation. PMID:28245574
Exponentiated power Lindley distribution.
Ashour, Samir K; Eltehiwy, Mahmoud A
2015-11-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data.
Exponentiated power Lindley distribution
Ashour, Samir K.; Eltehiwy, Mahmoud A.
2014-01-01
A new generalization of the Lindley distribution is recently proposed by Ghitany et al. [1], called as the power Lindley distribution. Another generalization of the Lindley distribution was introduced by Nadarajah et al. [2], named as the generalized Lindley distribution. This paper proposes a more generalization of the Lindley distribution which generalizes the two. We refer to this new generalization as the exponentiated power Lindley distribution. The new distribution is important since it contains as special sub-models some widely well-known distributions in addition to the above two models, such as the Lindley distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Least square estimation is used to evaluate the parameters. Three algorithms are proposed for generating random data from the proposed distribution. An application of the model to a real data set is analyzed using the new distribution, which shows that the exponentiated power Lindley distribution can be used quite effectively in analyzing real lifetime data. PMID:26644927
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Wright, Charles; Henry, Jon; Burov, Stas; Lin, Yihan; Crosson, Sean; Dinner, Aaron; Scherer, Norbert
2013-03-01
The interplay between growth and division of cells is has been studied in the context of exponential growth of bacterial cells (in suitable conditions) for decades. However, bulk culture studies obscure phenomena that manifest in single cells over many generations. We introduce a unique technology combining microfluidics, single-cell imaging, and quantitative analysis. This enables us to track the growth of single Caulobacter crescentus stalked cells over hundreds of generations. The statistics that we extract indicate a size thresholding mechanism for cell division and a non-trivial scaling collapse of division time distributions at different temperatures. In this talk I shall discuss these observations and a stochastic model of growth and division that captures all our observations with no free parameters.
NASA Astrophysics Data System (ADS)
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
NASA Technical Reports Server (NTRS)
Soo, Han Lee
1991-01-01
Researchers developed a robust control law for slow motions for the accurate trajectory control of a flexible robot. The control law does not need larger velocity gains than position gains, which some researchers need to ensure the stability of a rigid robot. Initial experimentation for the Small Articulated Manipulator (SAM) shows that control laws that use smaller velocity gains are more robust to signal noise than the control laws that use larger velocity gains. Researchers analyzed the stability of the composite control law, the robust control for the slow motion, and the strain rate feedback for the fast control. The stability analysis was done by using a quadratic Liapunov function. Researchers found that the flexible motion of links could be controlled by relating the input force to the flexible signals which are sensed at the near tip of each link. The signals are contaminated by the time delayed input force. However, the effect of the time delayed input force can be reduced by giving a certain configuration to the SAM.
OPINION: Safe exponential manufacturing
NASA Astrophysics Data System (ADS)
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
Vaseem, Mohammad; McKerricher, Garret; Shamim, Atif
2016-01-13
Currently, silver-nanoparticle-based inkjet ink is commercially available. This type of ink has several serious problems such as a complex synthesis protocol, high cost, high sintering temperatures (∼200 °C), particle aggregation, nozzle clogging, poor shelf life, and jetting instability. For the emerging field of printed electronics, these shortcomings in conductive inks are barriers for their widespread use in practical applications. Formulating particle-free silver inks has potential to solve these issues and requires careful design of the silver complexation. The ink complex must meet various requirements, such as in situ reduction, optimum viscosity, storage and jetting stability, smooth uniform sintered films, excellent adhesion, and high conductivity. This study presents a robust formulation of silver-organo-complex (SOC) ink, where complexing molecules act as reducing agents. The 17 wt % silver loaded ink was printed and sintered on a wide range of substrates with uniform surface morphology and excellent adhesion. The jetting stability was monitored for 5 months to confirm that the ink was robust and highly stable with consistent jetting performance. Radio frequency inductors, which are highly sensitive to metal quality, were demonstrated as a proof of concept on flexible PEN substrate. This is a major step toward producing high-quality electronic components with a robust inkjet printing process.
On the Matrix Exponential Function
ERIC Educational Resources Information Center
Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai
2006-01-01
A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.
Rajchakit, G; Saravanakumar, R; Ahn, Choon Ki; Karimi, Hamid Reza
2017-02-01
This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.
Wang, Yonggang E-mail: yangwg@hpstar.ac.cn; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Zhao, Yusheng E-mail: yangwg@hpstar.ac.cn; Yang, Wenge E-mail: yangwg@hpstar.ac.cn
2016-01-14
The structure stability under high pressure and thermal expansion behavior of Na{sub 3}OBr and Na{sub 4}OI{sub 2}, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na{sub 3}OBr and Na{sub 4}OI{sub 2}, respectively. The cubic Na{sub 3}OBr structure and tetragonal Na{sub 4}OI{sub 2} with intergrowth K{sub 2}NiF{sub 4} structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na{sub 4}OI{sub 2} exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20–80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
NASA Astrophysics Data System (ADS)
Wang, Yonggang; Wen, Ting; Park, Changyong; Kenney-Benson, Curtis; Pravica, Michael; Yang, Wenge; Zhao, Yusheng
2016-01-01
The structure stability under high pressure and thermal expansion behavior of Na3OBr and Na4OI2, two prototypes of alkali-metal-rich antiperovskites, were investigated by in situ synchrotron X-ray diffraction techniques under high pressure and low temperature. Both are soft materials with bulk modulus of 58.6 GPa and 52.0 GPa for Na3OBr and Na4OI2, respectively. The cubic Na3OBr structure and tetragonal Na4OI2 with intergrowth K2NiF4 structure are stable under high pressure up to 23 GPa. Although being a characteristic layered structure, Na4OI2 exhibits nearly isotropic compressibility. Negative thermal expansion was observed at low temperature range (20-80 K) in both transition-metal-free antiperovskites for the first time. The robust high pressure structure stability was examined and confirmed by first-principles calculations among various possible polymorphisms qualitatively. The results provide in-depth understanding of the negative thermal expansion and robust crystal structure stability of these antiperovskite systems and their potential applications.
NASA Astrophysics Data System (ADS)
Faure, Guilhem; Koonin, Eugene V.
2015-05-01
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
Faure, Guilhem; Koonin, Eugene V
2015-04-30
Robustness to destabilizing effects of mutations is thought of as a key factor of protein evolution. The connections between two measures of robustness, the relative core size and the computationally estimated effect of mutations on protein stability (ΔΔG), protein abundance and the selection pressure on protein-coding genes (dN/dS) were analyzed for the organisms with a large number of available protein structures including four eukaryotes, two bacteria and one archaeon. The distribution of the effects of mutations in the core on protein stability is universal and indistinguishable in eukaryotes and bacteria, centered at slightly destabilizing amino acid replacements, and with a heavy tail of more strongly destabilizing replacements. The distribution of mutational effects in the hyperthermophilic archaeon Thermococcus gammatolerans is significantly shifted toward strongly destabilizing replacements which is indicative of stronger constraints that are imposed on proteins in hyperthermophiles. The median effect of mutations is strongly, positively correlated with the relative core size, in evidence of the congruence between the two measures of protein robustness. However, both measures show only limited correlations to the expression level and selection pressure on protein-coding genes. Thus, the degree of robustness reflected in the universal distribution of mutational effects appears to be a fundamental, ancient feature of globular protein folds whereas the observed variations are largely neutral and uncoupled from short term protein evolution. A weak anticorrelation between protein core size and selection pressure is observed only for surface residues in prokaryotes but a stronger anticorrelation is observed for all residues in eukaryotic proteins. This substantial difference between proteins of prokaryotes and eukaryotes is likely to stem from the demonstrable higher compactness of prokaryotic proteins.
Dynamic controller design for exponential synchronization of Chen chaotic system
NASA Astrophysics Data System (ADS)
Park, Ju H.; Lee, S. M.; Kwon, O. M.
2007-07-01
The Letter considers synchronization of Chen chaotic system. The problems of determining the exponential stability and estimating the exponential convergence rate for the synchronization are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. For this end, a dynamic controller is proposed for the first time and a criterion for existence of the controller is given in terms of LMIs. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.
Exponential approximations in optimal design
NASA Technical Reports Server (NTRS)
Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.
1990-01-01
One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.
Is radioactive decay really exponential?
NASA Astrophysics Data System (ADS)
Aston, P. J.
2012-03-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3000 years are in error, which is generally attributed to past variation in atmospheric levels of 14C. We note that predicted atmospheric variation (assuming exponential decay) does not agree with results from modelling, and that theoretical quantum mechanics does not predict exact exponential decay. We give mathematical arguments that non-exponential decay should be expected for slowly decaying isotopes and explore the consequences of non-exponential decay. We propose an experimental test of this prediction of non-exponential decay for 14C. If confirmed, a foundation stone of current dating methods will have been removed, requiring a radical reappraisal both of radioisotope dating methods and of currently predicted dates obtained using these methods.
Rauk, Adam P; Guo, Kevin; Hu, Yanling; Cahya, Suntara; Weiss, William F
2014-08-01
Defining a suitable product presentation with an acceptable stability profile over its intended shelf-life is one of the principal challenges in bioproduct development. Accelerated stability studies are routinely used as a tool to better understand long-term stability. Data analysis often employs an overall mass action kinetics description for the degradation and the Arrhenius relationship to capture the temperature dependence of the observed rate constant. To improve predictive accuracy and precision, the current work proposes a least-squares estimation approach with a single nonlinear covariate and uses a polynomial to describe the change in a product attribute with respect to time. The approach, which will be referred to as Arrhenius time-scaled (ATS) least squares, enables accurate, precise predictions to be achieved for degradation profiles commonly encountered during bioproduct development. A Monte Carlo study is conducted to compare the proposed approach with the common method of least-squares estimation on the logarithmic form of the Arrhenius equation and nonlinear estimation of a first-order model. The ATS least squares method accommodates a range of degradation profiles, provides a simple and intuitive approach for data presentation, and can be implemented with ease.
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Universality in Stochastic Exponential Growth
NASA Astrophysics Data System (ADS)
Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.
2014-07-01
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
NASA Astrophysics Data System (ADS)
Ankarali, M. Mert; Saranli, Uluç
2010-09-01
In this paper, we analyze the self-stability properties of planar running with a dissipative spring-mass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map for uncontrolled locomotion with this system under a fixed touchdown leg angle policy and an open-loop ramp torque profile exhibits only marginal self-stability that does not always persist for the exact system. We then propose a per-stride feedback strategy for the hip torque that explicitly compensates for damping losses, reducing the return map to a single dimension and substantially improving the robust stability of fixed points. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the behavior of the exact plant model. We illustrate the relevance and utility of our model both through the qualitative correspondence of its predictions to biological data as well as its use in the design of a task-level running controller.
Real-Time Exponential Curve Fits Using Discrete Calculus
NASA Technical Reports Server (NTRS)
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Barth, Aline Bergesch; de Oliveira, Gabriela Bolfe; Malesuik, Marcelo Donadel; Paim, Clésio Soldatelli; Volpato, Nadia Maria
2011-08-01
A stability-indicating liquid chromatography method for the determination of the antifungal agent butenafine hydrochloride (BTF) in a cream was developed and validated using the Plackett-Burman experimental design for robustness evaluation. Also, the drug photodegradation kinetics was determined. The analytical column was operated with acetonitrile, methanol and a solution of triethylamine 0.3% adjusted to pH 4.0 (6:3:1) at a flow rate of 1 mL/min and detection at 283 nm. BTF extraction from the cream was done with n-butyl alcohol and methanol in ultrasonic bath. The performed degradation conditions were: acid and basic media with HCl 1M and NaOH 1M, respectively, oxidation with H(2)O(2) 10%, and the exposure to UV-C light. No interference in the BTF elution was verified. Linearity was assessed (r(2) = 0.9999) and ANOVA showed non-significative linearity deviation (p > 0.05). Adequate results were obtained for repeatability, intra-day precision, and accuracy. Critical factors were selected to examine the method robustness with the two-level Plackett-Burman experimental design and no significant factors were detected (p > 0.05). The BTF photodegradation kinetics was determined for the standard and for the cream, both in methanolic solution, under UV light at 254 nm. The degradation process can be described by first-order kinetics in both cases.
Ishigami, Yoko; Klein, Raymond M.
2011-01-01
Ishigami and Klein (2010) showed that scores of the three attention networks (alerting, orienting, and executive control) measured with the two versions of the Attention Network Test (ANT; Fan et al., 2002; Callejas et al., 2005) were robust over 10 sessions of repeated testing even though practice effects were consistently observed especially in the executive network when young adults were tested. The current study replicated their method to examine robustness, stability, reliability, and isolability of the networks scores when older adults were tested with these ANTs. Ten test sessions, each containing two versions of the ANT, were administered to 10 older adults. Participants were asked to indicate the direction of a target arrow, flanked by distractors, presented either above or below the fixation following auditory signals or/and visual cue. Network scores were calculated using orthogonal subtractions of performance in selected conditions. All network scores remained highly significant even after nine previous sessions despite some practice effects in the executive and the alerting networks. Some lack of independence among the networks was found. The relatively poor reliability of network scores with one session of data rises to respectable levels as more data is added. PMID:22110440
Quantum properties of exponential states
Luis, Alfredo
2007-05-15
The use of Renyi entropy as an uncertainty measure alternative to variance leads to the study of states with quantum fluctuations below the levels established by Gaussian states, which are the position-momentum minimum uncertainty states according to variance. We examine the quantum properties of states with exponential wave functions, which combine reduced fluctuations with practical feasibility.
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
Approximating Functions with Exponential Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2005-01-01
The possibility of approximating a function with a linear combination of exponential functions of the form e[superscript x], e[superscript 2x], ... is considered as a parallel development to the notion of Taylor polynomials which approximate a function with a linear combination of power function terms. The sinusoidal functions sin "x" and cos "x"…
Punctuated evolution and robustness in morphogenesis
Grigoriev, D.; Reinitz, J.; Vakulenko, S.; Weber, A.
2014-01-01
This paper presents an analytic approach to the pattern stability and evolution problem in morphogenesis. The approach used here is based on the ideas from the gene and neural network theory. We assume that gene networks contain a number of small groups of genes (called hubs) controlling morphogenesis process. Hub genes represent an important element of gene network architecture and their existence is empirically confirmed. We show that hubs can stabilize morphogenetic pattern and accelerate the morphogenesis. The hub activity exhibits an abrupt change depending on the mutation frequency. When the mutation frequency is small, these hubs suppress all mutations and gene product concentrations do not change, thus, the pattern is stable. When the environmental pressure increases and the population needs new genotypes, the genetic drift and other effects increase the mutation frequency. For the frequencies that are larger than a critical amount the hubs turn off; and as a result, many mutations can affect phenotype. This effect can serve as an engine for evolution. We show that this engine is very effective: the evolution acceleration is an exponential function of gene redundancy. Finally, we show that the Eldredge-Gould concept of punctuated evolution results from the network architecture, which provides fast evolution, control of evolvability, and pattern robustness. To describe analytically the effect of exponential acceleration, we use mathematical methods developed recently for hard combinatorial problems, in particular, for so-called k-SAT problem, and numerical simulations. PMID:24996115
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-06-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA.
Dolev, Danny; Függer, Matthias; Posch, Markus; Schmid, Ulrich; Steininger, Andreas; Lenzen, Christoph
2014-01-01
We present the first implementation of a distributed clock generation scheme for Systems-on-Chip that recovers from an unbounded number of arbitrary transient faults despite a large number of arbitrary permanent faults. We devise self-stabilizing hardware building blocks and a hybrid synchronous/asynchronous state machine enabling metastability-free transitions of the algorithm's states. We provide a comprehensive modeling approach that permits to prove, given correctness of the constructed low-level building blocks, the high-level properties of the synchronization algorithm (which have been established in a more abstract model). We believe this approach to be of interest in its own right, since this is the first technique permitting to mathematically verify, at manageable complexity, high-level properties of a fault-prone system in terms of its very basic components. We evaluate a prototype implementation, which has been designed in VHDL, using the Petrify tool in conjunction with some extensions, and synthesized for an Altera Cyclone FPGA. PMID:26516290
Generalized exponential function and discrete growth models
NASA Astrophysics Data System (ADS)
Souto Martinez, Alexandre; Silva González, Rodrigo; Lauri Espíndola, Aquino
2009-07-01
Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamic models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards’ model (generalization of the Gompertz and Verhulst models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stabilities. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.
Exponential Approximations Using Fourier Series Partial Sums
NASA Technical Reports Server (NTRS)
Banerjee, Nana S.; Geer, James F.
1997-01-01
The problem of accurately reconstructing a piece-wise smooth, 2(pi)-periodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coefficients of f are used to approximate the locations and magnitudes of the discontinuities in f and its first M derivatives. This is accomplished by first finding initial estimates of these quantities based on certain properties of Gibbs phenomenon, and then refining these estimates by fitting the asymptotic form of the Fourier coefficients to the given coefficients using a least-squares approach. It is conjectured that the locations of the singularities are approximated to within O(N(sup -M-2), and the associated jump of the k(sup th) derivative of f is approximated to within O(N(sup -M-l+k), as N approaches infinity, and the method is robust. These estimates are then used with a class of singular basis functions, which have certain 'built-in' singularities, to construct a new sequence of approximations to f. Each of these new approximations is the sum of a piecewise smooth function and a new Fourier series partial sum. When N is proportional to M, it is shown that these new approximations, and their derivatives, converge exponentially in the maximum norm to f, and its corresponding derivatives, except in the union of a finite number of small open intervals containing the points of singularity of f. The total measure of these intervals decreases exponentially to zero as M approaches infinity. The technique is illustrated with several examples.
Exponential Formulae and Effective Operations
NASA Technical Reports Server (NTRS)
Mielnik, Bogdan; Fernandez, David J. C.
1996-01-01
One of standard methods to predict the phenomena of squeezing consists in splitting the unitary evolution operator into the product of simpler operations. The technique, while mathematically general, is not so simple in applications and leaves some pragmatic problems open. We report an extended class of exponential formulae, which yield a quicker insight into the laboratory details for a class of squeezing operations, and moreover, can be alternatively used to programme different type of operations, as: (1) the free evolution inversion; and (2) the soft simulations of the sharp kicks (so that all abstract results involving the kicks of the oscillator potential, become realistic laboratory prescriptions).
Teaching about Exponential Growth in Social Studies.
ERIC Educational Resources Information Center
Allen, Rodney F.; LaHart, David E.
1984-01-01
Characteristics of exponential growth which should be taught in social studies classes are listed, and learning activities dealing with exponential growth which can be used in secondary social studies classes are provided. (RM)
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
In ecological networks, network robustness should be large enough to confer intrinsic robustness for tolerating intrinsic parameter fluctuations, as well as environmental robustness for resisting environmental disturbances, so that the phenotype stability of ecological networks can be maintained, thus guaranteeing phenotype robustness. However, it is difficult to analyze the network robustness of ecological systems because they are complex nonlinear partial differential stochastic systems. This paper develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance sensitivity in ecological networks. We found that the phenotype robustness criterion for ecological networks is that if intrinsic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations and environmental disturbances. These results in robust ecological networks are similar to that in robust gene regulatory networks and evolutionary networks even they have different spatial-time scales.
Robust stability under additive perturbations
NASA Technical Reports Server (NTRS)
Bhaya, A.; Desoer, C. A.
1985-01-01
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
Robust controls with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1993-01-01
This final report summarizes the recent results obtained by the principal investigator and his coworkers on the robust stability and control of systems containing parametric uncertainty. The starting point is a generalization of Kharitonov's theorem obtained in 1989, and its generalization to the multilinear case, the singling out of extremal stability subsets, and other ramifications now constitutes an extensive and coherent theory of robust parametric stability that is summarized in the results contained here.
Observational constraints on exponential gravity
Yang, Louis; Lee, Chung-Chi; Luo, Ling-Wei; Geng, Chao-Qiang
2010-11-15
We study the observational constraints on the exponential gravity model of f(R)=-{beta}R{sub s}(1-e{sup -R/R}{sub s}). We use the latest observational data including Supernova Cosmology Project Union2 compilation, Two-Degree Field Galaxy Redshift Survey, Sloan Digital Sky Survey Data Release 7, and Seven-Year Wilkinson Microwave Anisotropy Probe in our analysis. From these observations, we obtain a lower bound on the model parameter {beta} at 1.27 (95% C.L.) but no appreciable upper bound. The constraint on the present matter density parameter is 0.245<{Omega}{sub m}{sup 0}<0.311 (95% C.L.). We also find out the best-fit value of model parameters on several cases.
Wang, Nianfang; Koh, Sungjun; Jeong, Byeong Guk; Lee, Dongkyu; Kim, Whi Dong; Park, Kyoungwon; Nam, Min Ki; Lee, Kangha; Kim, Yewon; Lee, Baek-Hee; Lee, Kangtaek; Bae, Wan Ki; Lee, Doh C
2017-05-05
We present facile synthesis of bright CdS/CdSe/CdS@SiO2 nanoparticles with 72% of quantum yields (QYs) retaining ca 80% of the original QYs. The main innovative point is the utilization of the highly luminescent CdS/CdSe/CdS seed/spherical quantum well/shell (SQW) as silica coating seeds. The significance of inorganic semiconductor shell passivation and structure design of quantum dots (QDs) for obtaining bright QD@SiO2 is demonstrated by applying silica encapsulation via reverse microemulsion method to three kinds of QDs with different structure: CdSe core and 2 nm CdS shell (CdSe/CdS-thin); CdSe core and 6 nm CdS shell (CdSe/CdS-thick); and CdS core, CdSe intermediate shell and 5 nm CdS outer shell (CdS/CdSe/CdS-SQW). Silica encapsulation inevitably results in lower photoluminescence quantum yield (PL QY) than pristine QDs due to formation of surface defects. However, the retaining ratio of pristine QY is different in the three silica coated samples; for example, CdSe/CdS-thin/SiO2 shows the lowest retaining ratio (36%) while the retaining ratio of pristine PL QY in CdSe/CdS-thick/SiO2 and SQW/SiO2 is over 80% and SQW/SiO2 shows the highest resulting PL QY. Thick outermost CdS shell isolates the excitons from the defects at surface, making PL QY relatively insensitive to silica encapsulation. The bright SiO2-coated SQW sample shows robustness against harsh conditions, such as acid etching and thermal annealing. The high luminescence and long-term stability highlights the potential of using the SQW/SiO2 nanoparticles in bio-labeling or display applications.
Guo, Zhenyuan; Yang, Shaofu; Wang, Jun
2015-06-01
This paper presents theoretical results on the global exponential synchronization of multiple memristive neural networks with time delays. A novel coupling scheme is introduced, in a general topological structure described by a directed or undirected graph, with a linear diffusive term and discontinuous sign term. Several criteria are derived based on the Lyapunov stability theory to ascertain the global exponential stability of synchronization manifold in the coupling scheme. Simulation results for several examples are given to substantiate the effectiveness of the theoretical results.
Robust interval-based regulation for anaerobic digestion processes.
Alcaraz-González, V; Harmand, J; Rapaport, A; Steyer, J P; González-Alvarez, V; Pelayo-Ortiz, C
2005-01-01
A robust regulation law is applied to the stabilization of a class of biochemical reactors exhibiting partially known highly nonlinear dynamic behavior. An uncertain environment with the presence of unknown inputs is considered. Based on some structural and operational conditions, this regulation law is shown to exponentially stabilize the aforementioned bioreactors around a desired set-point. This approach is experimentally applied and validated on a pilot-scale (1 m3) anaerobic digestion process for the treatment of raw industrial wine distillery wastewater where the objective is the regulation of the chemical oxygen demand (COD) by using the dilution rate as the manipulated variable. Despite large disturbances on the input COD and state and parametric uncertainties, this regulation law gave excellent performances leading the output COD towards its set-point and keeping it inside a pre-specified interval.
Robust reliable sampled-data control for switched systems with application to flight control
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Joby, Maya; Shi, P.; Mathiyalagan, K.
2016-11-01
This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov-Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.
A Spectral Lyapunov Function for Exponentially Stable LTV Systems
NASA Technical Reports Server (NTRS)
Zhu, J. Jim; Liu, Yong; Hang, Rui
2010-01-01
This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.
Simple robust control laws for robot manipulators. Part 1: Non-adaptive case
NASA Technical Reports Server (NTRS)
Wen, J. T.; Bayard, D. S.
1987-01-01
A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.
EXPONENTIAL GALAXY DISKS FROM STELLAR SCATTERING
Elmegreen, Bruce G.; Struck, Curtis E-mail: curt@iastate.edu
2013-10-01
Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly flat rotation curves and near-solid-body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.
Equivalences between nonuniform exponential dichotomy and admissibility
NASA Astrophysics Data System (ADS)
Zhou, Linfeng; Lu, Kening; Zhang, Weinian
2017-01-01
Relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems. It was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy. In this paper we find an appropriate admissible pair of classes of Lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half-lines R± separately, on both half-lines R± simultaneously, and on the whole line R. Additionally, the maximal admissibility is proved in the case on both half-lines R± simultaneously.
Giving Exponential Functions a Fair Shake
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2005-01-01
This article details an exploration of exponential decay and growth relationships using M&M's and dice. Students collect data for mathematical models and use graphing calculators to make sense of the general form of the exponential functions. (Contains 10 figures and 2 tables.)
The matrix exponential in transient structural analysis
NASA Technical Reports Server (NTRS)
Minnetyan, Levon
1987-01-01
The primary usefulness of the presented theory is in the ability to represent the effects of high frequency linear response with accuracy, without requiring very small time steps in the analysis of dynamic response. The matrix exponential contains a series approximation to the dynamic model. However, unlike the usual analysis procedure which truncates the high frequency response, the approximation in the exponential matrix solution is in the time domain. By truncating the series solution to the matrix exponential short, the solution is made inaccurate after a certain time. Yet, up to that time the solution is extremely accurate, including all high frequency effects. By taking finite time increments, the exponential matrix solution can compute the response very accurately. Use of the exponential matrix in structural dynamics is demonstrated by simulating the free vibration response of multi degree of freedom models of cantilever beams.
Exponential fitted Gauss, Radau and Lobatto methods of low order
NASA Astrophysics Data System (ADS)
Martín-Vaquero, J.; Vigo-Aguiar, J.
2008-08-01
Several exponential fitting Runge-Kutta methods of collocation type are derived as a generalization of the Gauss, Radau and Lobatto traditional methods of two steps. The new methods are capable of the exact integration (with only round-off errors) of differential equations whose solutions are linear combinations of an exponential and ordinary polynomials. Theorems of the truncation error reveal the good behavior of the new methods for stiff problems. Plots of their absolute stability regions that include the whole of the negative real axis are provided. A different procedure to find the parameter of the method is proposed. The variable step Radau method of two stages is derived. Finally, numerical examples underscore the efficiency of the proposed codes, especially when they are integrating stiff problems.
Exponential wave-packet spreading via self-interaction time modulation
NASA Astrophysics Data System (ADS)
Zhao, Wen-Lei; Gong, Jiangbin; Wang, Wen-Ge; Casati, Giulio; Liu, Jie; Fu, Li-Bin
2016-11-01
The time-periodic modulation of the self-interaction of a Bose-Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross-Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.
Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays.
Zheng, Song
2015-09-01
In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems.
A Simulation To Model Exponential Growth.
ERIC Educational Resources Information Center
Appelbaum, Elizabeth Berman
2000-01-01
Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties that are observed in biological systems at many different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be large enough to confer: intrinsic robustness for tolerating intrinsic parameter fluctuations; genetic robustness for buffering genetic variations; and environmental robustness for resisting environmental disturbances. Network robustness is needed so phenotype stability of biological network can be maintained, guaranteeing phenotype robustness. Synthetic biology is foreseen to have important applications in biotechnology and medicine; it is expected to contribute significantly to a better understanding of functioning of complex biological systems. This paper presents a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation for synthetic gene networks in synthetic biology. Further, from the unifying mathematical framework, we found that the phenotype robustness criterion for synthetic gene networks is the following: if intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness, then the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in synthetic biology can also be investigated through corresponding phenotype robustness criteria from the systematic point of view. Finally, a robust synthetic design that involves network evolution algorithms with desired behavior under intrinsic parameter fluctuations, genetic variations, and environmental
Jana, Sunit Kumar; Guo, Xiurong; Mei, Hui; Seela, Frank
2015-12-18
A new unprecedented metal-mediated base pair was designed that stabilizes reverse Watson-Crick DNA (parallel strand orientation, ps) as well as canonical Watson-Crick DNA (antiparallel strand orientation, aps). This base pair contains two imidazolo-dC units decorated with furan residues. Tm measurements and spectroscopic studies reveal that each silver-mediated furano-imidazolo-dC forms exceptionally stable duplexes with ps and aps chain orientation. This stability increase by a silver-mediated base pair is the highest reported so far for ps and aps DNA helices.
Phylogenetic Stochastic Mapping Without Matrix Exponentiation
Irvahn, Jan; Minin, Vladimir N.
2014-01-01
Abstract Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), because current methodology relies on exponentiating CTMC infinitesimal rate matrices—an operation whose computational complexity grows as the size of the CTMC state space cubed. In this work, we introduce a new approach, based on a CTMC technique called uniformization, which does not use matrix exponentiation for phylogenetic stochastic mapping. Our method is based on a new Markov chain Monte Carlo (MCMC) algorithm that targets the distribution of trait histories conditional on the trait data observed at the tips of the tree. The computational complexity of our MCMC method grows as the size of the CTMC state space squared. Moreover, in contrast to competing matrix exponentiation methods, if the rate matrix is sparse, we can leverage this sparsity and increase the computational efficiency of our algorithm further. Using simulated data, we illustrate advantages of our MCMC algorithm and investigate how large the state space needs to be for our method to outperform matrix exponentiation approaches. We show that even on the moderately large state space of codons our MCMC method can be significantly faster than currently used matrix exponentiation methods. PMID:24918812
Zhu, Zonglong; Bai, Yang; Liu, Xiao; Chueh, Chu -Chen; Yang, Shihe; Jen, Alex K. -Y.
2016-05-11
Here highly crystalline SnO_{2} is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO_{2} electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity.
Zhu, Zonglong; Bai, Yang; Liu, Xiao; ...
2016-05-11
Here highly crystalline SnO2 is demonstrated to serve as a stable and robust electron-transporting layer for high-performance perovskite solar cells. Benefiting from its high crystallinity, the relatively thick SnO2 electron-transporting layer (≈120 nm) provides a respectable electron-transporting property to yield a promising power conversion efficiency (PCE)(18.8%) Over 90% of the initial PCE can be retained after 30 d storage in ambient with ≈70% relative humidity.
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Decoherence and Exponential Law: A Solvable Model
NASA Technical Reports Server (NTRS)
Pascazio, Saverio; Namiki, Mikio
1996-01-01
We analyze a modified version of the 'AgBr' Hamiltonian, solve exactly the equations of motion in terms of SU(2) coherent states, and study the weak-coupling, macroscopic limit of the model, obtaining an exponential behavior at all times. The asymptotic dominance of the exponential behavior is representative of a purely stochastic evolution and can be derived quantum mechanically in the so-called van Hove's limit (which is a weak-coupling, macroscopic limit). At the same time, a temporal behavior of the exponential type, yielding a 'probability dissipation' is closely related to dephasing ('decoherence') effects and one can expect a close connection with a dissipative and irreversible behavior. We stress the central relevance of the problem of dissipation to the quantum measurement theory and to the general topic of decoherence.
Method for exponentiating in cryptographic systems
Brickell, Ernest F.; Gordon, Daniel M.; McCurley, Kevin S.
1994-01-01
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a preapproved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g.sup.e ; transmitting the value g.sup.e to a remote facility by a communications network; receiving the value g.sup.e at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g.sup.xi ; computi The United States Government has rights in this invention pursuant to Contract No. DE-AC04-76DP00789 between the Department of Energy and AT&T Company.
Modeling aftershocks as a stretched exponential relaxation
NASA Astrophysics Data System (ADS)
Mignan, A.
2015-11-01
The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.
Chen, Bor-Sen; Lin, Ying-Po
2013-01-01
Robust stabilization and environmental disturbance attenuation are ubiquitous systematic properties observed in biological systems at different levels. The underlying principles for robust stabilization and environmental disturbance attenuation are universal to both complex biological systems and sophisticated engineering systems. In many biological networks, network robustness should be enough to confer intrinsic robustness in order to tolerate intrinsic parameter fluctuations, genetic robustness for buffering genetic variations, and environmental robustness for resisting environmental disturbances. With this, the phenotypic stability of biological network can be maintained, thus guaranteeing phenotype robustness. This paper presents a survey on biological systems and then develops a unifying mathematical framework for investigating the principles of both robust stabilization and environmental disturbance attenuation in systems and evolutionary biology. Further, from the unifying mathematical framework, it was discovered that the phenotype robustness criterion for biological networks at different levels relies upon intrinsic robustness + genetic robustness + environmental robustness ≦ network robustness. When this is true, the phenotype robustness can be maintained in spite of intrinsic parameter fluctuations, genetic variations, and environmental disturbances. Therefore, the trade-offs between intrinsic robustness, genetic robustness, environmental robustness, and network robustness in systems and evolutionary biology can also be investigated through their corresponding phenotype robustness criterion from the systematic point of view.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
ERIC Educational Resources Information Center
Ellis, Amy B.; Ozgur, Zekiye; Kulow, Torrey; Dogan, Muhammed F.; Amidon, Joel
2016-01-01
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks…
Exponentially Fragile PT Symmetry in Lattices with Localized Eigenmodes
Bendix, Oliver; Fleischmann, Ragnar; Kottos, Tsampikos; Shapiro, Boris
2009-07-17
We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting deltaapproxexp{sup -N/x}i where xi is their localization length. The level 'evolution' with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gamma{sub PT}approxmin(delta), thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gamma{sub PT}approx1/N{sup 2} and the distribution P(gamma{sub PT}) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.
Graphical Models via Univariate Exponential Family Distributions
Yang, Eunho; Ravikumar, Pradeep; Allen, Genevera I.; Liu, Zhandong
2016-01-01
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions. PMID:27570498
A Simple Mechanical Experiment on Exponential Growth
ERIC Educational Resources Information Center
McGrew, Ralph
2015-01-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…
Exponential lifetime improvement in topological quantum memories
NASA Astrophysics Data System (ADS)
Bardyn, Charles-Edouard; Karzig, Torsten
2016-09-01
We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size L , up to an upper bound Lmax, which can increase exponentially with Δ /T , where T is the temperature and Δ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with Δ /T , which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.
A note on the Jackson exponentiality test
NASA Astrophysics Data System (ADS)
Caeiro, Frederico; Marques, Filipe J.; Mateus, Ayana; Atal, Serra
2016-12-01
In this paper we revisit the Jackson exponentiality test. We study and provide functions in R language to compute theoretical moments, the distribution function and quantiles of the statistic test. Approximations to the exact distribution function and quantiles are also provided and their precision discussed. In addition, we provide an application of the Jackson test to real data.
Intersection of the Exponential and Logarithmic Curves
ERIC Educational Resources Information Center
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Exponential examples of solving parity games
NASA Astrophysics Data System (ADS)
Lebedev, V. N.
2016-04-01
This paper is devoted to solving certain problems on the computational complexity of deciding the winner in cyclic games. The main result is the proof of the fact that the nondeterministic potential transformation algorithm designed for solving parity games is exponential in terms of computation time.
Hayes, Roger; LeLacheur, Richard; Dumont, Isabelle; Couerbe, Philippe; Safavi, Afshin; Islam, Rafiq; Pattison, Colin; Cape, Stephanie; Rocci, Mario; Briscoe, Chad; Cojocaru, Laura; Groeber, Elizabeth; Silvestro, Luigi; Bravo, Jennifer; Shoup, Ron; Verville, Manon; Zimmer, Jennifer; Caturla, Maria Cruz; Khadang, Ardeshir; Bourdage, James; Hughes, Nicola; Fatmi, Saadya; Di Donato, Lorella; Sheldon, Curtis; Keyhani, Anahita; Satterwhite, Christina; Yu, Mathilde; Fiscella, Michele; Hulse, James; Lin, Zhongping John; Garofolo, Wei; Savoie, Natasha; Xiao, Yi Qun; Kurylak, Kai; Harris, Sarah; Saxena, Manju; Buonarati, Mike; Lévesque, Ann; Boudreau, Nadine; Lin, Jenny; Khan, Masood U; Ray, Gene; Liu, Yansheng; Xu, Allan; Soni, Gunjan; Ward, Ian; Kingsley, Clare; Ritzén, Hanna; Tabler, Edward; Nicholson, Bob; Bennett, Patrick; van de Merbel, Nico; Karnik, Shane; Bouhajib, Mohammed; Wieling, Jaap; Mulvana, Daniel; Ingelse, Benno; Allen, Mike; Malone, Michele; Fang, Xinping
2016-03-01
The 9th GCCClosed Forum was held just prior to the 2015 Workshop on Recent Issues in Bioanalysis (WRIB) in Miami, FL, USA on 13 April 2015. In attendance were 58 senior-level participants, from eight countries, representing 38 CRO companies offering bioanalytical services. The objective of this meeting was for CRO bioanalytical representatives to meet and discuss scientific and regulatory issues specific to bioanalysis. The issues selected at this year's closed forum include CAPA, biosimilars, preclinical method validation, endogenous biomarkers, whole blood stability, and ELNs. A summary of the industry's best practices and the conclusions from the discussion of these topics is included in this meeting report.
Zhang, Xuming; Peng, Xiang; Li, Wan; Li, Limin; Gao, Biao; Wu, Guosong; Huo, Kaifu; Chu, Paul K
2015-04-17
A coaxial electrode structure composed of manganese oxide-decorated TiC/C core/shell nanofiber arrays is produced hydrothermally in a KMnO4 solution. The pristine TiC/C core/shell structure prepared on the Ti alloy substrate provides the self-sacrificing carbon shell and highly conductive TiC core, thus greatly simplifying the fabrication process without requiring an additional reduction source and conductive additive. The as-prepared electrode exhibits a high specific capacitance of 645 F g(-1) at a discharging current density of 1 A g(-1) attributable to the highly conductive TiC/C and amorphous MnO2 shell with fast ion diffusion. In the charging/discharging cycling test, the as-prepared electrode shows high stability and 99% capacity retention after 5000 cycles. Although the thermal treatment conducted on the as-prepared electrode decreases the initial capacitance, the electrode undergoes capacitance recovery through structural transformation from the crystalline cluster to layered birnessite type MnO2 nanosheets as a result of dissolution and further electrodeposition in the cycling. 96.5% of the initial capacitance is retained after 1000 cycles at high charging/discharging current density of 25 A g(-1). This study demonstrates a novel scaffold to construct MnO2 based SCs with high specific capacitance as well as excellent mechanical and cycling stability boding well for future design of high-performance MnO2-based SCs.
Global ?-exponential stabilisation of a class of nonlinear networked control systems
NASA Astrophysics Data System (ADS)
Shen, Yan-Jun; Zhang, Daoyuan; Huang, Yuehua; Liu, Yungang
2016-11-01
In this paper, we investigate global ?-exponential stabilisation of a class of nonlinear networked control systems. The network-induced delays are assumed to be random and significantly smaller than the sampling period. First, sufficient conditions are presented to ensure global ?-exponential stability for a class of hybrid systems with time delay. Then, the networked control systems are modelled as the hybrid systems with time delay. By the techniques of adding a power integrator and a recursive argument, a sampled-data state feedback control law is presented. Sufficient conditions are given to ensure global ?-exponential stability of the closed-loop system by constructing a Lyapunov-Krasovskii function. Finally, a numerical example is presented to show the validity of the new methods.
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.
1992-01-01
A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).
An exponential ESS model and its application to frequency-dependent selection.
Li, J; Liu, L
1989-10-01
A nonlinear ESS model is put forward, that is, a nonnegative exponential ESS model. For a simple case, we discuss the existence, uniqueness, and stability of an ESS. As an application of the model, we give a quantitative analysis of frequency-dependent selection in population genetics when the rare type has an advantage.
NASA Astrophysics Data System (ADS)
Tollaksen, Jeff; Aharonov, Yakir
2006-03-01
We introduce a new type of weak measurement which yields a quantum average of weak values that is robust, outside the range of eigenvalues, extends the valid regime for weak measurements, and for which the probability of obtaining the pre- and post-selected ensemble is not exponentially rare. This result extends the applicability of weak values, shifts the statistical interpretation previously attributed to weak values and suggests that the weak value is a property of every pre- and post-selected ensemble. We then apply this new weak measurement to Hardy's paradox. Usually the paradox is dismissed on grounds of counterfactuality, i.e., because the paradoxical effects appear only when one considers results of experiments which do not actually take place. We suggest a new set of measurements in connection with Hardy's scheme, and show that when they are actually performed, they yield strange and surprising outcomes. More generally, we claim that counterfactual paradoxes point to a deeper structure inherent to quantum mechanics characterized by weak values (Aharonov Y, Botero A, Popescu S, Reznik B, Tollaksen J, Physics Letters A, 301 (3-4): 130-138, 2002).
Moradi, Hojjatullah; Majd, Vahid Johari
2016-05-01
In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.
A Simple Mechanical Experiment on Exponential Growth
NASA Astrophysics Data System (ADS)
McGrew, Ralph
2015-04-01
With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the activity are accessible to students in physical science and environmental science courses.
Exponential integration algorithms applied to viscoplasticity
NASA Technical Reports Server (NTRS)
Freed, Alan D.; Walker, Kevin P.
1991-01-01
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps.
Likelihood Estimation for Generalized Mixed Exponential Distributions.
1984-07-01
specified beforehand. 23 S. . ... .- ~T§777 ~"~~ 7’.7 . -- ." F0 * 0 REFERENCES L. Armijo, "Minimization of Functions Having Lipschitz Continuous...and F. W. Fairman, Exponential Approximation via a Closed Form Gauss-Newton Method, IEEE Trans. Circuit Theory, CT-20 (1973), pp. 361-369. A. R...engineering disciplines of Chemical, Civil, Electrical , and Mechanical and Aerospace to newer, more specialized fields of Biomedical Engineering
Exponential DNA Replication by Laminar Convection
NASA Astrophysics Data System (ADS)
Braun, Dieter; Goddard, Noel L.; Libchaber, Albert
2003-10-01
It is shown that laminar thermal convection can drive a chain reaction of DNA replication. The convection is triggered by a constant horizontal temperature gradient, moving molecules along stationary paths between hot and cold regions. This implements the temperature cycling for the classical polymerase chain reaction (PCR). The amplification is shown to be exponential and reaches 100 000-fold gains within 25min. Besides direct applications, the mechanism might have implications for the molecular evolution of life.
Dynamo theory, vorticity generation, and exponential stretching.
Friedlander, Susan; Vishik, Misha M.
1991-08-01
A discussion is given of the analogy between the dynamo equation for the generation of a magnetic field by the motion of an electrically conducting fluid and the equation for the evolution of vorticity of a viscous fluid. In both cases exponential stretching is an important feature of the underlying instability problem. For the "fast" dynamo problem, the existence of exponential stretching (i.e., the positivity of the Lyapunov exponent) somewhere in the flow is a necessary condition when the flow is smooth. An example is presented of a flow with exponential stretching (an Anosov flow) that supports fast dynamo action. A parallel treatment is described for the linearized Navier-Stokes equations for the motion of a viscous fluid. In this problem the analogous necessary condition for "fast vorticity generation" is the existence of some instability in the corresponding Euler (i.e., inviscid) equation. Dynamo theory methods give a second related result, namely a universal geometric estimate from below on the growth rate of a small perturbation in an inviscid fluid. This bound gives an effective sufficient condition for local instability for Eulers equations. In particular, it is proved that a steady flow with a hyperbolic stagnation point is unstable. The growth rate of an infinitesimal perturbation in a metric with derivatives depends on this metric. This dependence is completely described.
Method for exponentiating in cryptographic systems
Brickell, E.F.; Gordon, D.M.; McCurley, K.S.
1992-12-31
An improved cryptographic method utilizing exponentiation is provided which has the advantage of reducing the number of multiplications required to determine the legitimacy of a message or user. The basic method comprises the steps of selecting a key from a pre-approved group of integer keys g; exponentiating the key by an integer value e, where e represents a digital signature, to generate a value g{sup e}; transmitting the value g{sup e} to a remote facility by a communications network; receiving the value g{sup e} at the remote facility; and verifying the digital signature as originating from the legitimate user. The exponentiating step comprises the steps of initializing a plurality of memory locations with a plurality of values g{sup xi}, computing a{sub i} representations for a integer base b, where a{sub i} represents the weighing factor of the ith digit of the integer e; computing the individual values of c{sub d} according to the rule: c{sub d}={product}a{sub i}=d g{sup x {sub i}}; and computing the product of {product}{sup h}/{sub d=1} c{sub d}{sup d} from the stored values of from the plurality of memory locations so as to determine a value for g{sup e}.
NASA Astrophysics Data System (ADS)
Chandrasekaran, Rajeswari; Bi, Wu; Fuller, Thomas F.
With increasing interest in energy storage and conversion devices for automobile applications, the necessity to understand and predict life behavior of rechargeable batteries, PEM fuel cells and super capacitors is paramount. These electrochemical devices are most beneficial when used in hybrid configurations rather than as individual components. A system model helps us to understand the interactions between components and enables us to determine the response of the system as a whole. However, system models that are available predict just the performance and neglect degradation. The objective of this research is to provide a framework to account for the durability phenomena that are prevalent in fuel cells and batteries in a hybrid system. Toward this end, the methodology for development of surrogate models is provided, and Pt catalyst dissolution in proton exchange membrane fuel cells (PEMFCs) is used as an example to demonstrate the approach. Surrogate models are more easily integrated into higher level system models than the detailed physics-based models. As an illustration, the effects of changes in control strategies and power management approaches in mitigating platinum instability in fuel cells are reported. A system model that includes a fuel cell stack, a storage battery, power-sharing algorithm, and dc/dc converter has been developed; and preliminary results have been presented. These results show that platinum stability can be improved with only a small impact on system efficiency. Thus, this research will elucidate the importance of degradation issues in system design and optimization as opposed to just initial performance metrics.
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N; Palomares, Emilio; Demadrille, Renaud
2014-02-07
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm(-2)) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability.
NASA Astrophysics Data System (ADS)
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-02-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm-2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability.
Joly, Damien; Pellejà, Laia; Narbey, Stéphanie; Oswald, Frédéric; Chiron, Julien; Clifford, John N.; Palomares, Emilio; Demadrille, Renaud
2014-01-01
Among the new photovoltaic technologies, the Dye-Sensitized Solar Cell (DSC) is becoming a realistic approach towards energy markets such as BIPV (Building Integrated PhotoVoltaics). In order to improve the performances of DSCs and to increase their commercial attractiveness, cheap, colourful, stable and highly efficient ruthenium-free dyes must be developed. Here we report the synthesis and complete characterization of a new purely organic sensitizer (RK1) that can be prepared and synthetically upscaled rapidly. Solar cells containing this orange dye show a power conversion efficiency of 10.2% under standard conditions (AM 1.5G, 1000 Wm−2) using iodine/iodide as the electrolyte redox shuttle in the electrolyte, which is among the few examples of DSC using an organic dyes and iodine/iodide red/ox pair to overcome the 10% efficiency barrier. We demonstrate that the combination of this dye with an ionic liquid electrolyte allows the fabrication of solar cells that show power conversion efficiencies of up to 7.36% that are highly stable with no measurable degradation of initial performances after 2200 h of light soaking at 65°C under standard irradiation conditions. RK1 achieves one of the best output power conversion efficiencies for a solar cell based on the iodine/iodide electrolyte, combining high efficiency and outstanding stability. PMID:24504344
On Using Exponential Parameter Estimators with an Adaptive Controller
NASA Technical Reports Server (NTRS)
Patre, Parag; Joshi, Suresh M.
2011-01-01
Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators.
Black hole as a magnetic monopole within exponential nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Kruglov, S. I.
2017-03-01
We perform the gauge covariant quantization of the exponential model of nonlinear electrodynamics. Magnetically charged black holes, in the framework of our model are considered, and the regular black hole solution is obtained in general relativity. The asymptotic black hole solution at r → ∞ is found. We calculate the magnetic mass of the black hole and the metric function which are expressed via the parameter β of the model and the magnetic charge. The thermodynamic properties and thermal stability of regular black holes are analysed. We calculate the Hawking temperature of black holes and their heat capacity at the constant magnetic charge. We find a point where the temperature changes the sign that corresponds to the first-order phase transition. It is shown that at critical point, where the heat capacity diverges, there is a phase transition of the second-order. We obtain the parameters of the model when the black hole is stable.
NASA Astrophysics Data System (ADS)
Sun, Xifang; Chen, Weisheng; Wu, Jian
2016-12-01
In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.
Exponential expansion: galactic destiny or technological hubris?
NASA Astrophysics Data System (ADS)
Finney, B. R.
Is it our destiny to expand exponentially to populate the galaxy, or is such a vision but an extreme example of technological hubris? The overall record of human evolution and dispersion over the Earth can be cited to support the view that we are a uniquely expansionary and technological animal bound for the stars, yet an examination of the fate of individual migrations and exploratory initiatives raises doubts. Although it may be in keeping with our hubristic nature to predict ultimate galactic expansion, there is no way to specify how far expansionary urges may drive our spacefaring descendants.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
Robustness enhancement of neurocontroller and state estimator
NASA Technical Reports Server (NTRS)
Troudet, Terry
1993-01-01
The feasibility of enhancing neurocontrol robustness, through training of the neurocontroller and state estimator in the presence of system uncertainties, is investigated on the example of a multivariable aircraft control problem. The performance and robustness of the newly trained neurocontroller are compared to those for an existing neurocontrol design scheme. The newly designed dynamic neurocontroller exhibits a better trade-off between phase and gain stability margins, and it is significantly more robust to degradations of the plant dynamics.
Global exponential almost periodicity of a delayed memristor-based neural networks.
Chen, Jiejie; Zeng, Zhigang; Jiang, Ping
2014-12-01
In this paper, the existence, uniqueness and stability of almost periodic solution for a class of delayed memristor-based neural networks are studied. By using a new Lyapunov function method, the neural network that has a unique almost periodic solution, which is globally exponentially stable is proved. Moreover, the obtained conclusion on the almost periodic solution is applied to prove the existence and stability of periodic solution (or equilibrium point) for delayed memristor-based neural networks with periodic coefficients (or constant coefficients). The obtained results are helpful to design the global exponential stability of almost periodic oscillatory memristor-based neural networks. Three numerical examples and simulations are also given to show the feasibility of our results.
Preconditioned implicit-exponential integrators (IMEXP) for stiff PDEs
NASA Astrophysics Data System (ADS)
Luan, Vu Thai; Tokman, Mayya; Rainwater, Greg
2017-04-01
We propose two new classes of time integrators for stiff DEs: the implicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational advantages when used with preconditioners. Any preconditioner can be used with any of these new schemes. This leads to a broader applicability of exponential methods. The proof of convergence of these integrators and numerical demonstration of their efficiency are presented.
The LEM exponential integrator for advection-diffusion-reaction equations
NASA Astrophysics Data System (ADS)
Caliari, Marco; Vianello, Marco; Bergamaschi, Luca
2007-12-01
We implement a second-order exponential integrator for semidiscretized advection-diffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja-Euler-Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.
Exponential Size Distribution of von Willebrand Factor
Lippok, Svenja; Obser, Tobias; Müller, Jochen P.; Stierle, Valentin K.; Benoit, Martin; Budde, Ulrich; Schneppenheim, Reinhard; Rädler, Joachim O.
2013-01-01
Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications. PMID:24010664
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Human-chimpanzee alignment: ortholog exponentials and paralog power laws.
Gao, Kun; Miller, Jonathan
2014-12-01
Genomic subsequences conserved between closely related species such as human and chimpanzee exhibit an exponential length distribution, in contrast to the algebraic length distribution observed for sequences shared between distantly related genomes. We find that the former exponential can be further decomposed into an exponential component primarily composed of orthologous sequences, and a truncated algebraic component primarily composed of paralogous sequences.
Aston, Elizabeth; Channon, Alastair; Day, Charles; Knight, Christopher G
2013-01-01
Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has
Robust control with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1988-01-01
Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.
NASA Astrophysics Data System (ADS)
Bég, O. Anwar; Khan, M. S.; Karim, Ifsana; Alam, Md. M.; Ferdows, M.
2013-10-01
A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (G r ), species Grashof number (G m ), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (E c ), Lewis number (L e ), Brownian motion parameter (N b) and thermophoresis parameter (N t). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.
Exponential-Krylov methods for ordinary differential equations
NASA Astrophysics Data System (ADS)
Tranquilli, Paul; Sandu, Adrian
2014-12-01
This paper develops a new family of exponential time discretization methods called exponential-Krylov (EXPK). The new schemes treat the time discretization and the Krylov-based approximation of exponential matrix-vector products as a single computational process. The classical order conditions theory developed herein accounts for both the temporal and the Krylov approximation errors. Unlike traditional exponential schemes, EXPK methods require the construction of only a single Krylov space at each timestep. The number of basis vectors that guarantee the temporal order of accuracy does not depend on the application at hand. Numerical results show favorable properties of EXPK methods when compared to current exponential schemes.
Fluctuation Bounds in the Exponential Bricklayers Process
NASA Astrophysics Data System (ADS)
Balázs, Márton; Komjáthy, Júlia; Seppäläinen, Timo
2012-04-01
This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.
Arsenic for the fool: an exponential connection.
Dani, Sergio U
2010-03-15
Anthropogenic arsenic is insidiously building up together with natural arsenic to a level unprecedented in the history of mankind. Arsenopyrite (FeAsS) is the principal ore of arsenic and gold in hard rock mines; it is formed by a coupled substitution of sulphur by arsenic in the structure of pyrite (FeS(2)) - nicknamed "fool's gold". Other important sources of anthropogenic arsenic are fossil fuels such as coal and oil. Here I report on the first indication that the environmental concentration of total arsenic in topsoils - in the 7-18ppm range - is exponentially related to the prevalence and mortality of Alzheimer's disease and other dementias in European countries. This evidence defies the imputed absence of verified cases of human morbidity or mortality resulting from exposure to low-level arsenic in topsoils.
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP.
A Robustly Stabilizing Model Predictive Control Algorithm
NASA Technical Reports Server (NTRS)
Ackmece, A. Behcet; Carson, John M., III
2007-01-01
A model predictive control (MPC) algorithm that differs from prior MPC algorithms has been developed for controlling an uncertain nonlinear system. This algorithm guarantees the resolvability of an associated finite-horizon optimal-control problem in a receding-horizon implementation.
Aggarwal, Ankush
2017-03-01
Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
Robust nonlinear control of vectored thrust aircraft
NASA Technical Reports Server (NTRS)
Doyle, John C.; Murray, Richard; Morris, John
1993-01-01
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.
NASA Technical Reports Server (NTRS)
Wen, John T.; Kreutz, Kenneth; Bayard, David S.
1988-01-01
A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator. PMID:26339793
Forecasting Financial Extremes: A Network Degree Measure of Super-Exponential Growth.
Yan, Wanfeng; van Tuyll van Serooskerken, Edgar
2015-01-01
Investors in stock market are usually greedy during bull markets and scared during bear markets. The greed or fear spreads across investors quickly. This is known as the herding effect, and often leads to a fast movement of stock prices. During such market regimes, stock prices change at a super-exponential rate and are normally followed by a trend reversal that corrects the previous overreaction. In this paper, we construct an indicator to measure the magnitude of the super-exponential growth of stock prices, by measuring the degree of the price network, generated from the price time series. Twelve major international stock indices have been investigated. Error diagram tests show that this new indicator has strong predictive power for financial extremes, both peaks and troughs. By varying the parameters used to construct the error diagram, we show the predictive power is very robust. The new indicator has a better performance than the LPPL pattern recognition indicator.
Easton, D M
1978-01-01
The conductance changes, gK(t) and gNa(t), of squid giant axon under voltage clamp (Hodgkin and Huxley, 1952) may be modeled by exponentiated exponential functions (Gompertz kinetics) from any holding potential VO to any membrane clamp potential V. The equation constants are set by the membrane potential V, and include, for any voltage step in the case of gK, the initial conductance, gO, the asymptote conductance g, and rate constant k: gK = g exp(-be-kt) where b = 1n g/gO. Equations of similar form relate g and k to the voltage V, and govern the corresponding parameters of the gNa system. For the gNa, the fast phase y = y exp (-be-kt) is cut down in proportion to a slow process p = (1 - p)e-k't + p, and thus gNa = py. The expo-exponential functions involve fewer constants than the Hodgkin-Huxley model. In particular, the role of the n, m, h parameters appears to be filled largely by 1n (g/gO) in the case of gK and by 1n (y/yO) in the case of gNa. Membrane action potentials during current clamp may be computed from the conductances generated by use of the appropriate differential forms of the equations; diverse other membrane behaviors may be predicted. PMID:638223
Stretched Exponential relaxation in pure Se glass
NASA Astrophysics Data System (ADS)
Dash, S.; Ravindren, S.; Boolchand, P.
A universal feature of glasses is the stretched exponential relaxation, f (t) = exp[ - t / τ ] β . The model of diffusion of excitations to randomly distributed traps in a glass by Phillips1 yields the stretched exponent β = d[d +2] where d, the effective dimensionality. We have measured the enthalpy of relaxation ΔHnr (tw) at Tg of Se glass in modulated DSC experiments as glasses age at 300K and find β = 0.43(2) for tw in the 0
Robust Inflation from fibrous strings
Burgess, C.P.; Cicoli, M.; Alwis, S. de; Quevedo, F.
2016-05-13
Successful inflationary models should (i) describe the data well; (ii) arise generically from sensible UV completions; (iii) be insensitive to detailed fine-tunings of parameters and (iv) make interesting new predictions. We argue that a class of models with these properties is characterized by relatively simple potentials with a constant term and negative exponentials. We here continue earlier work exploring UV completions for these models — including the key (though often ignored) issue of modulus stabilisation — to assess the robustness of their predictions. We show that string models where the inflaton is a fibration modulus seem to be robust due to an effective rescaling symmetry, and fairly generic since most known Calabi-Yau manifolds are fibrations. This class of models is characterized by a generic relation between the tensor-to-scalar ratio r and the spectral index n{sub s} of the form r∝(n{sub s}−1){sup 2} where the proportionality constant depends on the nature of the effects used to develop the inflationary potential and the topology of the internal space. In particular we find that the largest values of the tensor-to-scalar ratio that can be obtained by generalizing the original set-up are of order r≲0.01. We contrast this general picture with specific popular models, such as the Starobinsky scenario and α-attractors. Finally, we argue the self consistency of large-field inflationary models can strongly constrain non-supersymmetric inflationary mechanisms.
Exponential convergence rates for weighted sums in noncommutative probability space
NASA Astrophysics Data System (ADS)
Choi, Byoung Jin; Ji, Un Cig
2016-11-01
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
Density Estimation of Simulation Output Using Exponential EPI-Splines
2013-12-01
ak+1,1, k = 1, 2, ..., N − 1. Pointwise Fisher information. We define the pointwise Fisher information of an exponential epi-spline density h at x to...are required to obtain meaningful results. All exponential epi-splines are computed under the assumptions of continuity, smoothness, pointwise Fisher...Kernel 0.4310 0.3536 In the exponential epi-spline estimates, we include continuity, differentiability, and pointwise Fisher information constraints with
Using Differentials to Differentiate Trigonometric and Exponential Functions
ERIC Educational Resources Information Center
Dray, Tevian
2013-01-01
Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.
Exponentially Long Orbits in Hopfield Neural Networks.
Muscinelli, Samuel P; Gerstner, Wulfram; Brea, Johanni
2017-02-01
We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For [Formula: see text] units, these sequences have length [Formula: see text]; that is, they cover the full state space. We present a mathematical proof that maximal-length orbits exist for all [Formula: see text], and we provide a method to construct both the sequence and the weight matrix that allow its production. The orbit is relatively robust to dynamical noise, and perturbations of the optimal weights reveal other periodic orbits that are not maximal but typically still very long. We discuss how the resulting dynamics on slow time-scales can be used to generate desired output sequences.
Exponential and power-law contact distributions represent different atmospheric conditions.
Reynolds, A M
2011-12-01
It is well known that the dynamics of plant disease epidemics are very sensitive to the functional form of the contact distribution?the probability distribution function for the distance of viable fungal spore movement until deposition. Epidemics can take the form of a constant-velocity travelling wave when the contact distribution is exponentially bounded. Fat-tailed contact distributions, on the other hand, lead to epidemic spreads that accelerate over time. Some empirical data for contact distributions can be well represented by negative exponentials while other data are better represented by fat-tailed inverse power laws. Here we present data from numerical simulations that suggest that negative exponentials and inverse power laws are not competing candidate forms of the contact distribution but are instead representative of different atmospheric conditions. Contact distributions for atmospheric boundary-layers with stabilities ranging from strongly convective (a hot windless day time scenario) to stable stratification (a cold windy night time scenario) but without precipitation events are calculated using well-established state-of-the-art Lagrangian stochastic (particle tracking) dispersal models. Contact distributions are found to be well represented by exponentials for strongly convective conditions; a -3/2 inverse power law for convective boundary-layers with wind shear; and by a -2/3 inverse power law for stably stratified conditions.
NASA Astrophysics Data System (ADS)
Taller, Daniel; Go, David B.; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
Taller, Daniel; Go, David B; Chang, Hsueh-Chia
2013-05-01
The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.
Robust lateral control of highway vehicles
Byrne, R.H.; Abdallah, C.
1994-08-01
Vehicle lateral dynamics are affected by vehicle mass, longitudinal velocity, vehicle inertia, and the cornering stiffness of the tires. All of these parameters are subject to variation, even over the course of a single trip. Therefore, a practical lateral control system must guarantee stability, and hopefully ride comfort, over a wide range of parameter changes. This paper describes a robust controller which theoretically guarantees stability over a wide range of parameter changes. The robust controller is designed using a frequency domain transfer function approach. An uncertainty band in the frequency domain is determined using simulations over the range of expected parameter variations. Based on this bound, a robust controller is designed by solving the Nevanlinna-Pick interpolation problem. The performance of the robust controller is then evaluated over the range of parameter variations through simulations.
Computer-aided-analysis of linear control system robustness
NASA Technical Reports Server (NTRS)
Stengel, Robert F.; Ray, Laura R.
1990-01-01
Stochastic robustness is a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems. The use of high-speed graphics workstations and control system design software in stochastic robustness analysis is discussed and demonstrated. It is shown that stochastic robustness makes good use of modern computational and graphic tools, and it is easily implemented using commercial control system design and analysis software.
Review of "Going Exponential: Growing the Charter School Sector's Best"
ERIC Educational Resources Information Center
Garcia, David
2011-01-01
This Progressive Policy Institute report argues that charter schools should be expanded rapidly and exponentially. Citing exponential growth organizations, such as Starbucks and Apple, as well as the rapid growth of molds, viruses and cancers, the report advocates for similar growth models for charter schools. However, there is no explanation of…
Exponential Correlation of IQ and the Wealth of Nations
ERIC Educational Resources Information Center
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
A Learning Cycle on Exponential Growth and the Energy Crises.
ERIC Educational Resources Information Center
Dykstra, D. I., Jr.
1982-01-01
Describes nature and logistics of a learning cycle approach to teaching exponential growth and the energy crisis. Used with both science and nonscience majors, the cycle uses no algebra, never mentions the terms exponential or logarithmic, and requires a calculator. Instructions for obtaining student and instructor materials are provided.…
Flows induced by exponential stretching and shearing plate motions
NASA Astrophysics Data System (ADS)
Weidman, Patrick
2016-11-01
Boundary-layer solutions for the flow induced by an exponentially stretching surface also sheared in its own plane are given. Prior to this study no similarity solutions have been reported for flows generated by exponentially sheared surfaces concomitant with surface stretching in any form. The method of solution is self-similarity. The results found here are intimately related to those of Magyari and Keller ["Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface," J. Phys. D: Appl. Phys. 32, 577-585 (1999)] who studied the motion and heat transfer induced by an exponentially stretching plate. In addition to two particular cases reported here, a third situation is found where an exponentially stretching surface admits a concomitant arbitrary streamwise shearing motion.
NASA Astrophysics Data System (ADS)
Hsiao, Feng-Hsiag
2016-10-01
In this study, a novel approach via improved genetic algorithm (IGA)-based fuzzy observer is proposed to realise exponential optimal H∞ synchronisation and secure communication in multiple time-delay chaotic (MTDC) systems. First, an original message is inserted into the MTDC system. Then, a neural-network (NN) model is employed to approximate the MTDC system. Next, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion derived in terms of Lyapunov's direct method, thus ensuring that the trajectories of the slave system approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to GA's random global optimisation search capabilities, the lower and upper bounds of the search space can be set so that the GA will seek better fuzzy observer feedback gains, accelerating feedback gain-based synchronisation via the LMI-based approach. IGA, which exhibits better performance than traditional GA, is used to synthesise a fuzzy observer to not only realise the exponential synchronisation, but also achieve optimal H∞ performance by minimizing the disturbance attenuation level and recovering the transmitted message. Finally, a numerical example with simulations is given in order to demonstrate the effectiveness of our approach.
Modeling and robust control of wind turbine
NASA Astrophysics Data System (ADS)
Gilev, Bogdan
2016-12-01
In this paper a model of a wind turbine is evaluated, consisting of: wind speed model, mechanical and electrical model of generator and tower oscillation model. This model is linearized around of a nominal point. By using the linear model with uncertainties is synthesized a uncertain model. By using the uncertain model and robust control theory is developed a robust controller, which provide mode of stabilizing the rotor frequency and damping the tower oscillations. Finally is simulated work of nonlinear system and robust controller
NASA Astrophysics Data System (ADS)
Emam, Mahmoud; Han, Qi; Yu, Liyang; Zhang, Ye; Niu, Xiamu
2015-07-01
Copy-move is one of the most common methods for image manipulation. Several methods have been proposed to detect and locate the tampered regions, while many methods failed when the copied regions are rotated before being pasted. A rotational invariant detecting method using Polar Complex Exponential Transform (PCET) is proposed in this paper. Firstly, the original image is divided into overlapping circular blocks, and PCET is employed to each block to extract the rotation-invariant robust features. Secondly, the Approximate Nearest Neighbors (ANN) of each feature vector are collected by Locality Sensitive Hashing (LSH). Experimental results show that the proposed technique is robust to rotation.
Correcting Partial Volume Effect in Bi-exponential T2 Estimation of Small Lesions
Huang, Chuan; Galons, Jean-Philippe; Graff, Christian G.; Clarkson, Eric W.; Bilgin, Ali; Kalb, Bobby; Martin, Diego R.; Altbach, Maria I.
2014-01-01
Purpose T2 mapping provides a quantitative approach for focal liver lesion characterization. For small lesions a bi-exponential model should be used to account for partial volume effects (PVE). However, conventional bi-exponential fitting suffers from large uncertainty of the fitted parameters when noise is present. The purpose of this work is to develop a more robust method to correct for PVE affecting small lesions. Methods We developed a ROI-based joint bi-exponential fitting (JBF) algorithm to estimate the T2 of lesions affected by PVE. JBF takes advantage of the lesion fraction variation among voxels within an ROI. JBF is compared to conventional approaches using Cramér-Rao lower bound analysis, numerical simulations, phantom and -vivo data. Results JBF provides more accurate and precise T2 estimates in the presence of PVE. Furthermore, JBF is less sensitive to ROI drawing. Phantom and in-vivo results show that JBF can be combined with a reconstruction method for highly undersampled data, enabling the characterization of small abdominal lesions from data acquired in a single breath-hold. Conclusion The JBF algorithm provides more accurate and stable T2 estimates for small structures than conventional techniques when PVE is present. It should be particularly useful for the characterization of small abdominal lesions. PMID:24753061
NASA Astrophysics Data System (ADS)
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.
Kaneko, Kunihiko
2011-06-01
Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.
Exponential synchronization of memristive Cohen-Grossberg neural networks with mixed delays.
Yang, Xinsong; Cao, Jinde; Yu, Wenwu
2014-06-01
This paper concerns the problem of global exponential synchronization for a class of memristor-based Cohen-Grossberg neural networks with time-varying discrete delays and unbounded distributed delays. The drive-response set is discussed. A novel controller is designed such that the response (slave) system can be controlled to synchronize with the drive (master) system. Through a nonlinear transformation, we get an alternative system from the considered memristor-based Cohen-Grossberg neural networks. By investigating the global exponential synchronization of the alternative system, we obtain the corresponding synchronization criteria of the considered memristor-based Cohen-Grossberg neural networks. Moreover, the conditions established in this paper are easy to be verified and improve the conditions derived in most of existing papers concerning stability and synchronization for memristor-based neural networks. Numerical simulations are given to show the effectiveness of the theoretical results.
Scalar-fluid interacting dark energy: Cosmological dynamics beyond the exponential potential
NASA Astrophysics Data System (ADS)
Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola
2017-01-01
We extend the dynamical systems analysis of scalar-fluid interacting dark energy models performed in C. G. Boehmer et al., Phys. Rev. D 91, 123002 (2015), 10.1103/PhysRevD.91.123002 by considering scalar field potentials beyond the exponential type. The properties and stability of critical points are examined using a combination of linear analysis, computational methods and advanced mathematical techniques, such as center manifold theory. We show that the interesting results obtained with an exponential potential can generally be recovered also for more complicated scalar field potentials. In particular, employing power law and hyperbolic potentials as examples, we find late time accelerated attractors, transitions from dark matter to dark energy domination with specific distinguishing features, and accelerated scaling solutions capable of solving the cosmic coincidence problem.
NASA Astrophysics Data System (ADS)
Mohammadi, Reza
2014-03-01
In this study, the exponential spline scheme is implemented to find a numerical solution of the nonlinear Schrödinger equations with constant and variable coefficients. The method is based on the Crank-Nicolson formulation for time integration and exponential spline functions for space integration. The error analysis, existence, stability, uniqueness and convergence properties of the method are investigated using the energy method. We show that the method is unconditionally stable and accurate of orders O(k+kh+h2) and O(k+kh+h4). This method is tested on three examples by using the cubic nonlinear Schrödinger equation with constant and variable coefficients and the Gross-Pitaevskii equation. The computed results are compared wherever possible with those already available in the literature. The results show that the derived method is easily implemented and approximate the exact solution very well.
Derivation of stretched exponential tap density equations of granular powders.
Hao, Tian
2015-04-21
The tap density of granular powders was found to be better fitted with the stretched exponential law. In our previous work, the stretched exponential tap density equations were derived with the rate process theory and free volume concept, under the assumption that the particle packing rate during the tapping process obeys the stretched Arrhenius equation, which, however, has an empirical origin. In this article, the above assumption is eliminated and attempts are made to obtain the stretched exponential tap density equations from very fundamental bases. In a vertical tapping process, the probability of particles attaining certain energy states is assumed to obey the Boltzmann distribution and particles traveling from one site to another are assumed to follow a very common memoryless random exponential law. The stretched exponential tap density equations are thus derived and all parameters acquire clear physical meanings. The most important parameter, the stretched exponential, is demonstrated to correlate with the interparticle forces: a small value may indicate a strong adhesive or cohesive interaction. Therefore, the stretched exponential could be a better indicator for powder flowability correlated with particle interactions as well.
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.; Ernazarov, K. K.
2017-01-01
A (n + 1)-dimensional gravitational model with cosmological constant and Gauss-Bonnet term is studied. The ansatz with diagonal cosmological metrics is adopted and solutions with exponential dependence of scale factors: ai ∼ exp (vit), i = 1, …, n, are considered. The stability analysis of the solutions with non-static volume factor is presented. We show that the solutions with v 1 = v 2 = v 3 = H > 0 and small enough variation of the effective gravitational constant G are stable if certain restriction on (vi ) is obeyed. New examples of stable exponential solutions with zero variation of G in dimensions D = 1 + m + 2 with m > 2 are presented.
NASA Technical Reports Server (NTRS)
Narendra, K. S.; Annaswamy, A. M.
1985-01-01
Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known.
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.
Exponential Functions, Rates of Change, and the Multiplicative Unit.
ERIC Educational Resources Information Center
Confrey, Jere; Smith, Erick
1994-01-01
Describes a covariational, rather than correspondence, approach to functions that emphasizes rate of change. Proposes three ways of understanding rate of change in relation to exponential functions. (Contains 41 references.) (Author/MKR)
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1985-01-01
Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Exponential order statistic models of software reliability growth
NASA Technical Reports Server (NTRS)
Miller, D. R.
1986-01-01
Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.
Demonstration of the exponential decay law using beer froth
NASA Astrophysics Data System (ADS)
Leike, A.
2002-01-01
The volume of beer froth decays exponentially with time. This property is used to demonstrate the exponential decay law in the classroom. The decay constant depends on the type of beer and can be used to differentiate between different beers. The analysis shows in a transparent way the techniques of data analysis commonly used in science - consistency checks of theoretical models with the data, parameter estimation and determination of confidence intervals.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Robust H ∞ Filtering for a Class of Complex Networks with Stochastic Packet Dropouts and Time Delays
Lyu, Ming; Guo, Pengfei; Bo, Yuming
2014-01-01
The robust H ∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the H ∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method. PMID:24987738
Robust flight control of rotorcraft
NASA Astrophysics Data System (ADS)
Pechner, Adam Daniel
With recent design improvement in fixed wing aircraft, there has been a considerable interest in the design of robust flight control systems to compensate for the inherent instability necessary to achieve desired performance. Such systems are designed for maximum available retention of stability and performance in the presence of significant vehicle damage or system failure. The rotorcraft industry has shown similar interest in adopting these reconfigurable flight control schemes specifically because of their ability to reject disturbance inputs and provide a significant amount of robustness for all but the most catastrophic of situations. The research summarized herein focuses on the extension of the pseudo-sliding mode control design procedure interpreted in the frequency domain. Application of the technique is employed and simulated on two well known helicopters, a simplified model of a hovering Sikorsky S-61 and the military's Black Hawk UH-60A also produced by Sikorsky. The Sikorsky helicopter model details are readily available and was chosen because it can be limited to pitch and roll motion reducing the number of degrees of freedom and yet contains two degrees of freedom, which is the minimum requirement in proving the validity of the pseudo-sliding control technique. The full order model of a hovering Black Hawk system was included both as a comparison to the S-61 helicopter design system and as a means to demonstrate the scaleability and effectiveness of the control technique on sophisticated systems where design robustness is of critical concern.
Can distributed delays perfectly stabilize dynamical networks?
NASA Astrophysics Data System (ADS)
Omi, Takahiro; Shinomoto, Shigeru
2008-04-01
Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integrodifferential equation that describes the collective dynamics of a neural network with distributed signal delays. With the Γ distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.
NASA Astrophysics Data System (ADS)
Johnson, Y.; Dasgupta, S.
2014-07-01
Multiple unmanned aerial vehicle (UAV) control in formation flight is comparatively a new research area in the field of aerospace engineering. In the proposed work, robust control techniques are implemented to maintain a fixed relative distance in horizontal and vertical direction with uniform pitch orientation in an uncertain leader-follower pattern of close formation flight platform. The forward velocity dynamics is of focal interest in this paper. H-infinity controllers are designed for leader control and its tracking. The robustness of the H-infinity controller is validated with Kharitonov related bounded phase conditions by forming interval polynomials.
Average-cost based robust structural control
NASA Technical Reports Server (NTRS)
Hagood, Nesbitt W.
1993-01-01
A method is presented for the synthesis of robust controllers for linear time invariant structural systems with parameterized uncertainty. The method involves minimizing quantities related to the quadratic cost (H2-norm) averaged over a set of systems described by real parameters such as natural frequencies and modal residues. Bounded average cost is shown to imply stability over the set of systems. Approximations for the exact average are derived and proposed as cost functionals. The properties of these approximate average cost functionals are established. The exact average and approximate average cost functionals are used to derive dynamic controllers which can provide stability robustness. The robustness properties of these controllers are demonstrated in illustrative numerical examples and tested in a simple SISO experiment on the MIT multi-point alignment testbed.
Robust Critical Point Detection
Bhatia, Harsh
2016-07-28
Robust Critical Point Detection is a software to compute critical points in a 2D or 3D vector field robustly. The software was developed as a part of the author's work at the lab as a Phd student under Livermore Scholar Program (now called Livermore Graduate Scholar Program).
Mechanisms for Robust Cognition
ERIC Educational Resources Information Center
Walsh, Matthew M.; Gluck, Kevin A.
2015-01-01
To function well in an unpredictable environment using unreliable components, a system must have a high degree of robustness. Robustness is fundamental to biological systems and is an objective in the design of engineered systems such as airplane engines and buildings. Cognitive systems, like biological and engineered systems, exist within…
On long-time algebraic and exponential instabilities found in linear dispersive flows
NASA Astrophysics Data System (ADS)
Barlow, Nathaniel; King, Kristina; Zaretzky, Paula; Cromer, Michael; Weinstein, Steven
2016-11-01
A physically-motivated class of partial differential equations that describes the response of a system to disturbances is examined. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. Specifically, the propagation characteristics of the response are examined in the context of spatio-temporal hydrodynamic stability theory. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.
NASA Astrophysics Data System (ADS)
Liu, Yurong; Alsaadi, Fuad E.; Yin, Xiaozhou; Wang, Yamin
2015-02-01
In this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribed ? disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived.
Berthelot, Geoffroy; Len, Stéphane; Hellard, Philippe; Tafflet, Muriel; Guillaume, Marion; Vollmer, Jean-Claude; Gager, Bruno; Quinquis, Laurent; Marc, Andy; Toussaint, Jean-François
2012-08-01
The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes' careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.
Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised
NASA Technical Reports Server (NTRS)
Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.
1995-01-01
The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.
NASA Technical Reports Server (NTRS)
Ryan, Robert
1993-01-01
The concept of rubustness includes design simplicity, component and path redundancy, desensitization to the parameter and environment variations, control of parameter variations, and punctual operations. These characteristics must be traded with functional concepts, materials, and fabrication approach against the criteria of performance, cost, and reliability. The paper describes the robustness design process, which includes the following seven major coherent steps: translation of vision into requirements, definition of the robustness characteristics desired, criteria formulation of required robustness, concept selection, detail design, manufacturing and verification, operations.
NASA Astrophysics Data System (ADS)
Lu, Y.; Chatterjee, S.
2014-11-01
Exponential family statistical distributions, including the well-known normal, binomial, Poisson, and exponential distributions, are overwhelmingly used in data analysis. In the presence of covariates, an exponential family distributional assumption for the response random variables results in a generalized linear model. However, it is rarely ensured that the parameters of the assumed distributions are stable through the entire duration of the data collection process. A failure of stability leads to nonsmoothness and nonlinearity in the physical processes that result in the data. In this paper, we propose testing for stability of parameters of exponential family distributions and generalized linear models. A rejection of the hypothesis of stable parameters leads to change detection. We derive the related likelihood ratio test statistic. We compare the performance of this test statistic to the popular normal distributional assumption dependent cumulative sum (Gaussian CUSUM) statistic in change detection problems. We study Atlantic tropical storms using the techniques developed here, so to understand whether the nature of these tropical storms has remained stable over the last few decades.
Non-exponential and oscillatory decays in quantum mechanics
Peshkin, Murray; Volya, Alexander; Zelevinsky, Vladimir
2014-08-07
The quantum-mechanical theory of the decay of unstable states is revisited. We show that the decay is non-exponential both in the short-time and long-time limits using a more physical definition of the decay rate than the one usually used. We report results of numerical studies based on Winter's model that may elucidate qualitative features of exponential and non-exponential decay more generally. The main exponential stage is related to the formation of a radiating state that maintains the shape of its wave function with exponentially diminishing normalization. We discuss situations where the radioactive decay displays several exponents. The transient stages between different regimes are typically accompanied by interference of various contributions and resulting oscillations in the decay curve. The decay curve can be fully oscillatory in a two-flavor generalization of Winter's model with some values of the parameters. We consider the implications of that result for models of the oscillations reported by GSI.
Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles
Warshaw, S I
2001-07-15
In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resulted from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.
NASA Technical Reports Server (NTRS)
Pratt, D. T.
1984-01-01
Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.
Design of a 9-loop quasi-exponential waveform generator.
Banerjee, Partha; Shukla, Rohit; Shyam, Anurag
2015-12-01
We know in an under-damped L-C-R series circuit, current follows a damped sinusoidal waveform. But if a number of sinusoidal waveforms of decreasing time period, generated in an L-C-R circuit, be combined in first quarter cycle of time period, then a quasi-exponential nature of output current waveform can be achieved. In an L-C-R series circuit, quasi-exponential current waveform shows a rising current derivative and thereby finds many applications in pulsed power. Here, we have described design and experiment details of a 9-loop quasi-exponential waveform generator. In that, design details of magnetic switches have also been described. In the experiment, output current of 26 kA has been achieved. It has been shown that how well the experimentally obtained output current profile matches with the numerically computed output.
Exponential rise of dynamical complexity in quantum computing through projections.
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-10-10
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.
Exponential rise of dynamical complexity in quantum computing through projections
Burgarth, Daniel Klaus; Facchi, Paolo; Giovannetti, Vittorio; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya
2014-01-01
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once ‘observed’ as outlined above. Conversely, we show that any complex quantum dynamics can be ‘purified’ into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics. PMID:25300692
Exponential Sensitivity and its Cost in Quantum Physics.
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-02-10
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed.
Rotational stretched exponential relaxation in random trap-barrier model
NASA Astrophysics Data System (ADS)
Aydiner, Ekrem
2015-07-01
The relaxation behavior of complex-disordered systems, such as spin glasses, polymers, colloidal suspensions, structural glasses,and granular media, has not been clarified. Theoretical studies show that relaxation in these systems has a topological origin. In this paper, we focus on the rotational stretched exponential relaxation behavior in complex-disordered systems and introduce a simple phase space model to understand the mechanism of the non-exponential relaxation of these systems. By employing the Monte Carlo simulation method to the model, we obtain the rotational relaxation function as a function of temperature. We show that the relaxation function has a stretched exponential form under the critical temperature while it obeys the Debye law above the critical temperature. Project supported by Istanbul University (Grant Nos. 28432 and 45662).
Exponential Sensitivity and its Cost in Quantum Physics
Gilyén, András; Kiss, Tamás; Jex, Igor
2016-01-01
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate that chaotic behaviour is a rather generic feature in state selective protocols: exponential sensitivity can exist for all initial states in an experimentally realisable optical scheme. Moreover, any complex rational polynomial map, including the example of the Mandelbrot set, can be directly realised. In state selective protocols, one needs an ensemble of initial states, the size of which decreases with each iteration. We prove that exponential sensitivity to initial states in any quantum system has to be related to downsizing the initial ensemble also exponentially. Our results show that magnifying initial differences of quantum states (a Schrödinger microscope) is possible; however, there is a strict bound on the number of copies needed. PMID:26861076
On the performance of exponential integrators for problems in magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Einkemmer, Lukas; Tokman, Mayya; Loffeld, John
2017-02-01
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin-Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.
Chowell, Gerardo; Viboud, Cécile
2016-10-01
The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.
Exponential time-differencing with embedded Runge–Kutta adaptive step control
Whalen, P.; Brio, M.; Moloney, J.V.
2015-01-01
We have presented the first embedded Runge–Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In our stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations: the shock-fronts of Burgers equation, interacting KdV solitons, KS controlled chaos, and critical collapse of two-dimensional NLS.
Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay
NASA Astrophysics Data System (ADS)
Chunodkar, Apurva A.; Akella, Maruthi R.
2013-12-01
This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Dehyadegari, A.; Sheykhi, A.; Dehghani, M. H.
2016-03-01
In this paper, we construct a new class of topological black hole Lifshitz solutions in the presence of nonlinear exponential electrodynamics for Einstein-dilaton gravity. We show that the reality of Lifshitz supporting Maxwell matter fields exclude the negative horizon curvature solutions except for the asymptotic AdS case. Calculating the conserved and thermodynamical quantities, we obtain a Smarr type formula for the mass and confirm that thermodynamics first law is satisfied on the black hole horizon. Afterward, we study the thermal stability of our solutions and figure out the effects of different parameters on the stability of solutions under thermal perturbations. Next, we apply the gauge/gravity duality in order to calculate the ratio of shear viscosity to entropy for a three-dimensional hydrodynamic system by using the pole method. Furthermore, we study the behavior of holographic conductivity for two-dimensional systems such as graphene. We consider linear Maxwell and nonlinear exponential electrodynamics separately and disclose the effect of nonlinearity on holographic conductivity. We indicate that holographic conductivity vanishes for z > 3 in the case of nonlinear electrodynamics while it does not in the linear Maxwell case. Finally, we solve perturbative additional field equations numerically and plot the behaviors of real and imaginary parts of conductivity for asymptotic AdS and Lifshitz cases. We present experimental results match with our numerical ones.
Engineering bright solitons to enhance the stability of two-component Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Radha, R.; Vinayagam, P. S.; Sudharsan, J. B.; Liu, Wu-Ming; Malomed, Boris A.
2015-12-01
We consider a system of coupled Gross-Pitaevskii (GP) equations describing a binary quasi-one-dimensional Bose-Einstein condensate (BEC) with intrinsic time-dependent attractive interactions, placed in a time-dependent expulsive parabolic potential, in a special case when the system is integrable (a deformed Manakov's system). Since the nonlinearity in the integrable system which represents binary attractive interactions exponentially decays with time, solitons are also subject to decay. Nevertheless, it is shown that the robustness of bright solitons can be enhanced in this system, making their respective lifetime longer, by matching the time dependence of the interaction strength (adjusted with the help of the Feshbach-resonance management) to the time modulation of the strength of the parabolic potential. The analytical results, and their stability, are corroborated by numerical simulations. In particular, we demonstrate that the addition of random noise does not impact the stability of the solitons.
Numerical Studies of Non-Exponential Decay of Wavefunctions
NASA Astrophysics Data System (ADS)
Vermedahl, Jon; Petridis, Athanasios; Luban, Marshall; Staunton, Lawrence
2002-04-01
We use the staggered-leap-frog algorithm to numerically solve the time-dependent Schrödinger equation. This algorithm is particularly accurate and stable as demonstrated in a number of cases whose solutions are analytically known. Deviations from exponential decay have been established for short times for a wavefunction initially set within finite depth potential wells. The survival probability has been fit with analytical functions that reproduce exponential decay at long times. Various time scales characterizing the decay are thus extracted.
Stretched-exponential Doppler spectra in underwater acoustic communication channels.
van Walree, P A; Jenserud, T; Otnes, R
2010-11-01
The theory of underwater sound interacting with the sea surface predicts a Gaussian-spread frequency spectrum in the case of a large Rayleigh parameter. However, recent channel soundings reveal more sharply peaked spectra with heavier tails. The measured Doppler spread increases with the frequency and differs between multipath arrivals. The overall Doppler spectrum of a broadband waveform is the sum of the spectra of all constituent paths and frequencies, and is phenomenologically described by a stretched or compressed exponential. The stretched exponential also fits well to the broadband spectrum of a single propagation path, and narrowband spectra summed over all paths.
Exponential model for option prices: Application to the Brazilian market
NASA Astrophysics Data System (ADS)
Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.
2016-03-01
In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
Jingshan, Zhong; Claus, Rene A; Dauwels, Justin; Tian, Lei; Waller, Laura
2014-05-05
We propose an alternative method for solving the Transport of Intensity equation (TIE) from a stack of through-focus intensity images taken by a microscope or lensless imager. Our method enables quantitative phase and amplitude imaging with improved accuracy and reduced data capture, while also being computationally efficient and robust to noise. We use prior knowledge of how intensity varies with propagation in the spatial frequency domain in order to constrain a fitting algorithm [Gaussian process (GP) regression] for estimating the axial intensity derivative. Solving the problem in the frequency domain inspires an efficient measurement scheme which captures images at exponentially spaced focal steps, significantly reducing the number of images required. Low-frequency artifacts that plague traditional TIE methods can be suppressed without an excessive number of captured images. We validate our technique experimentally by recovering the phase of human cheek cells in a brightfield microscope.
1985-12-01
schemes involving more general perturbations. Also Desoer et al [8] have established conditions for stability robustness of linear multivarible...address regulators with quadratic performance indices. Desoer et al [8] have established conditions for stability robust- ness of linear...p. 45-46. 8. Desoer , C.A., Callier, F.M. and Chan, W.S., "Robustness of Stability Conditions for Linear Time Invariant Feedback Systems," IEEE
Engineering robust intelligent robots
NASA Astrophysics Data System (ADS)
Hall, E. L.; Ali, S. M. Alhaj; Ghaffari, M.; Liao, X.; Cao, M.
2010-01-01
The purpose of this paper is to discuss the challenge of engineering robust intelligent robots. Robust intelligent robots may be considered as ones that not only work in one environment but rather in all types of situations and conditions. Our past work has described sensors for intelligent robots that permit adaptation to changes in the environment. We have also described the combination of these sensors with a "creative controller" that permits adaptive critic, neural network learning, and a dynamic database that permits task selection and criteria adjustment. However, the emphasis of this paper is on engineering solutions which are designed for robust operations and worst case situations such as day night cameras or rain and snow solutions. This ideal model may be compared to various approaches that have been implemented on "production vehicles and equipment" using Ethernet, CAN Bus and JAUS architectures and to modern, embedded, mobile computing architectures. Many prototype intelligent robots have been developed and demonstrated in terms of scientific feasibility but few have reached the stage of a robust engineering solution. Continual innovation and improvement are still required. The significance of this comparison is that it provides some insights that may be useful in designing future robots for various manufacturing, medical, and defense applications where robust and reliable performance is essential.
Exponential dichotomy for hyperbolic systems with periodic boundary conditions
NASA Astrophysics Data System (ADS)
Klyuchnyk, R.; Kmit, I.; Recke, L.
2017-02-01
We investigate evolution families generated by general linear first-order hyperbolic systems in one space dimension with periodic boundary conditions. We state explicit conditions on the coefficient functions that are sufficient for the existence of exponential dichotomies on R in the space of continuous periodic functions.
Exponentially Fitted Variants of Euler's Method for ODEs
ERIC Educational Resources Information Center
Kanwar, V.; Tomar, S. K.
2008-01-01
A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and…
Teaching Exponential Growth and Decay: Examples from Medicine
ERIC Educational Resources Information Center
Hobbie, Russell K.
1973-01-01
A treatment of exponential growth and decay is sketched which does not require knowledge of calculus, and hence, it can be applied to many cases in the biological and medical sciences. Some examples are bacterial growth, sterilization, clearance, and drug absorption. (DF)
Min and Max Exponential Extreme Interval Values and Statistics
ERIC Educational Resources Information Center
Jance, Marsha; Thomopoulos, Nick
2009-01-01
The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…
Concept of the Exponential Law Prior to 1900
ERIC Educational Resources Information Center
Curtis, Lorenzo J.
1978-01-01
Presents the historical development of perceptions and applications of the exponential law, tracing it from its ancient origins until the year 1900. Shows that many concepts such as mean life and half life and their relationships to differential equations were known long before their application to nuclear radioactivity. (GA)
Weight Factor Selection in Double Exponential Smoothing Enrollment Forecasts.
ERIC Educational Resources Information Center
Gardner, Don E.
1981-01-01
The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The basic assumptions and formulas for its use are outlined. The difficulties associated with selecting an appropriate weight factor are discussed, and the potential effect on prediction results is illustrated.…
Extreme rainfall distribution tails: Exponential, subexponential or hyperexponential?
NASA Astrophysics Data System (ADS)
Nerantzaki, Sofia; Papalexiou, Simon Michael; Koutsoyiannis, Demetris
2013-04-01
The upper tail of a probability distribution controls the behavior of both the magnitude and the frequency of extreme events. In general, based on their tail behavior, probability distributions can be categorized into two families (with reference to the exponential distribution): subexponential and hyperexponential. The latter corresponds to milder and less frequent extremes. In order to evaluate the behavior of rainfall extremes, we examine data from 3 477 stations from all over the world with sample size over 100 years. We apply the Mean Excess Function (MEF) which is a common graphical method that results in a zero slope line when applied to exponentially distributed data and in a positive slope in the case of subexponential distributions. To implement the method, we constructed confidence intervals for the slope of the Exponential distribution as functions of the sample size. The validation of the method using Monte Carlo techniques reveals that it performs well especially for large samples. The analysis shows that subexponential distributions are generally in better agreement with rainfall extremes compared to the commonly used exponential ones.
Double Exponential Relativity Theory Coupled Theoretically with Quantum Theory?
Montero Garcia, Jose de la Luz; Novoa Blanco, Jesus Francisco
2007-04-28
Here the problem of special relativity is analyzed into the context of a new theoretical formulation: the Double Exponential Theory of Special Relativity with respect to which the current Special or Restricted Theory of Relativity (STR) turns to be a particular case only.
Modelling income data using two extensions of the exponential distribution
NASA Astrophysics Data System (ADS)
Calderín-Ojeda, Enrique; Azpitarte, Francisco; Gómez-Déniz, Emilio
2016-11-01
In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT-Lognormal models discussed in this paper preserve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT-Lognormal models to study the distribution of incomes in Australia for the period 2001-2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Exponential passivity for output feedback stabilisation of nonlinear uncertain systems
NASA Astrophysics Data System (ADS)
Benabdallah, Amel
2010-11-01
In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.
Looking for Connections between Linear and Exponential Functions
ERIC Educational Resources Information Center
Lo, Jane-Jane; Kratky, James L.
2012-01-01
Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…
'Glocal' robustness analysis and model discrimination for circadian oscillators.
Hafner, Marc; Koeppl, Heinz; Hasler, Martin; Wagner, Andreas
2009-10-01
To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This 'global' analysis is then supplemented by a 'local' analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our 'glocal' combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets.
Exponentially localized Wannier functions in periodic zero flux magnetic fields
NASA Astrophysics Data System (ADS)
De Nittis, G.; Lein, M.
2011-11-01
In this work, we investigate conditions which ensure the existence of an exponentially localized Wannier basis for a given periodic hamiltonian. We extend previous results [Panati, G., Ann. Henri Poincare 8, 995-1011 (2007), 10.1007/s00023-007-0326-8] to include periodic zero flux magnetic fields which is the setting also investigated by Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. The new notion of magnetic symmetry plays a crucial rôle; to a large class of symmetries for a non-magnetic system, one can associate "magnetic" symmetries of the related magnetic system. Observing that the existence of an exponentially localized Wannier basis is equivalent to the triviality of the so-called Bloch bundle, a rank m hermitian vector bundle over the Brillouin zone, we prove that magnetic time-reversal symmetry is sufficient to ensure the triviality of the Bloch bundle in spatial dimension d = 1, 2, 3. For d = 4, an exponentially localized Wannier basis exists provided that the trace per unit volume of a suitable function of the Fermi projection vanishes. For d > 4 and d ⩽ 2m (stable rank regime) only the exponential localization of a subset of Wannier functions is shown; this improves part of the analysis of Kuchment [J. Phys. A: Math. Theor. 42, 025203 (2009), 10.1088/1751-8113/42/2/025203]. Finally, for d > 4 and d > 2m (unstable rank regime) we show that the mere analysis of Chern classes does not suffice in order to prove triviality and thus exponential localization.
Robust control for snake maneuver design of missile
NASA Astrophysics Data System (ADS)
Kun, Ya; Chen, Xin; Li, Chuntao
2017-01-01
For the performance of missile with high Mach number and strongly nonlinear dynamics, this paper uses robust control to design maneuver controller. Robust servomechanism linear quadratic regulator (RSLQR) control is used to form the inner loop and proportional-plus-integral (PI) control is used to provide yawing tracking with no error. Contrast simulations under three types of deviation have been done to confirm robustness of the RSLQR-plus-PI control. Simulation results shows that RSLQR-plus-PI control would resist the disturbance and maintain the properties of the controller, guarantee the robustness and stability of missile more effectively than pure PI control.
Identification and robust control of an experimental servo motor.
Adam, E J; Guestrin, E D
2002-04-01
In this work, the design of a robust controller for an experimental laboratory-scale position control system based on a dc motor drive as well as the corresponding identification and robust stability analysis are presented. In order to carry out the robust design procedure, first, a classic closed-loop identification technique is applied and then, the parametrization by internal model control is used. The model uncertainty is evaluated under both parametric and global representation. For the latter case, an interesting discussion about the conservativeness of this description is presented by means of a comparison between the uncertainty disk and the critical perturbation radius approaches. Finally, conclusions about the performance of the experimental system with the robust controller are discussed using comparative graphics of the controlled variable and the Nyquist stability margin as a robustness measurement.
Strain-Dependent Transcriptome Signatures for Robustness in Lactococcus lactis
Dijkstra, Annereinou R.; Alkema, Wynand; Starrenburg, Marjo J. C.; van Hijum, Sacha A. F. T.; Bron, Peter A.
2016-01-01
Recently, we demonstrated that fermentation conditions have a strong impact on subsequent survival of Lactococcus lactis strain MG1363 during heat and oxidative stress, two important parameters during spray drying. Moreover, employment of a transcriptome-phenotype matching approach revealed groups of genes associated with robustness towards heat and/or oxidative stress. To investigate if other strains have similar or distinct transcriptome signatures for robustness, we applied an identical transcriptome-robustness phenotype matching approach on the L. lactis strains IL1403, KF147 and SK11, which have previously been demonstrated to display highly diverse robustness phenotypes. These strains were subjected to an identical fermentation regime as was performed earlier for strain MG1363 and consisted of twelve conditions, varying in the level of salt and/or oxygen, as well as fermentation temperature and pH. In the exponential phase of growth, cells were harvested for transcriptome analysis and assessment of heat and oxidative stress survival phenotypes. The variation in fermentation conditions resulted in differences in heat and oxidative stress survival of up to five 10-log units. Effects of the fermentation conditions on stress survival of the L. lactis strains were typically strain-dependent, although the fermentation conditions had mainly similar effects on the growth characteristics of the different strains. By association of the transcriptomes and robustness phenotypes highly strain-specific transcriptome signatures for robustness towards heat and oxidative stress were identified, indicating that multiple mechanisms exist to increase robustness and, as a consequence, robustness of each strain requires individual optimization. However, a relatively small overlap in the transcriptome responses of the strains was also identified and this generic transcriptome signature included genes previously associated with stress (ctsR and lplL) and novel genes, including nan
Strain-Dependent Transcriptome Signatures for Robustness in Lactococcus lactis.
Dijkstra, Annereinou R; Alkema, Wynand; Starrenburg, Marjo J C; Hugenholtz, Jeroen; van Hijum, Sacha A F T; Bron, Peter A
2016-01-01
Recently, we demonstrated that fermentation conditions have a strong impact on subsequent survival of Lactococcus lactis strain MG1363 during heat and oxidative stress, two important parameters during spray drying. Moreover, employment of a transcriptome-phenotype matching approach revealed groups of genes associated with robustness towards heat and/or oxidative stress. To investigate if other strains have similar or distinct transcriptome signatures for robustness, we applied an identical transcriptome-robustness phenotype matching approach on the L. lactis strains IL1403, KF147 and SK11, which have previously been demonstrated to display highly diverse robustness phenotypes. These strains were subjected to an identical fermentation regime as was performed earlier for strain MG1363 and consisted of twelve conditions, varying in the level of salt and/or oxygen, as well as fermentation temperature and pH. In the exponential phase of growth, cells were harvested for transcriptome analysis and assessment of heat and oxidative stress survival phenotypes. The variation in fermentation conditions resulted in differences in heat and oxidative stress survival of up to five 10-log units. Effects of the fermentation conditions on stress survival of the L. lactis strains were typically strain-dependent, although the fermentation conditions had mainly similar effects on the growth characteristics of the different strains. By association of the transcriptomes and robustness phenotypes highly strain-specific transcriptome signatures for robustness towards heat and oxidative stress were identified, indicating that multiple mechanisms exist to increase robustness and, as a consequence, robustness of each strain requires individual optimization. However, a relatively small overlap in the transcriptome responses of the strains was also identified and this generic transcriptome signature included genes previously associated with stress (ctsR and lplL) and novel genes, including nan
Designing for Reliability and Robustness
NASA Technical Reports Server (NTRS)
Svetlik, Randall G.; Moore, Cherice; Williams, Antony
2017-01-01
Long duration spaceflight has a negative effect on the human body, and exercise countermeasures are used on-board the International Space Station (ISS) to minimize bone and muscle loss, combatting these effects. Given the importance of these hardware systems to the health of the crew, this equipment must continue to be readily available. Designing spaceflight exercise hardware to meet high reliability and availability standards has proven to be challenging throughout the time the crewmembers have been living on ISS beginning in 2000. Furthermore, restoring operational capability after a failure is clearly time-critical, but can be problematic given the challenges of troubleshooting the problem from 220 miles away. Several best-practices have been leveraged in seeking to maximize availability of these exercise systems, including designing for robustness, implementing diagnostic instrumentation, relying on user feedback, and providing ample maintenance and sparing. These factors have enhanced the reliability of hardware systems, and therefore have contributed to keeping the crewmembers healthy upon return to Earth. This paper will review the failure history for three spaceflight exercise countermeasure systems identifying lessons learned that can help improve future systems. Specifically, the Treadmill with Vibration Isolation and Stabilization System (TVIS), Cycle Ergometer with Vibration Isolation and Stabilization System (CEVIS), and the Advanced Resistive Exercise Device (ARED) will be reviewed, analyzed, and conclusions identified so as to provide guidance for improving future exercise hardware designs. These lessons learned, paired with thorough testing, offer a path towards reduced system down-time.
Robustness of mission plans for unmanned aircraft
NASA Astrophysics Data System (ADS)
Niendorf, Moritz
This thesis studies the robustness of optimal mission plans for unmanned aircraft. Mission planning typically involves tactical planning and path planning. Tactical planning refers to task scheduling and in multi aircraft scenarios also includes establishing a communication topology. Path planning refers to computing a feasible and collision-free trajectory. For a prototypical mission planning problem, the traveling salesman problem on a weighted graph, the robustness of an optimal tour is analyzed with respect to changes to the edge costs. Specifically, the stability region of an optimal tour is obtained, i.e., the set of all edge cost perturbations for which that tour is optimal. The exact stability region of solutions to variants of the traveling salesman problems is obtained from a linear programming relaxation of an auxiliary problem. Edge cost tolerances and edge criticalities are derived from the stability region. For Euclidean traveling salesman problems, robustness with respect to perturbations to vertex locations is considered and safe radii and vertex criticalities are introduced. For weighted-sum multi-objective problems, stability regions with respect to changes in the objectives, weights, and simultaneous changes are given. Most critical weight perturbations are derived. Computing exact stability regions is intractable for large instances. Therefore, tractable approximations are desirable. The stability region of solutions to relaxations of the traveling salesman problem give under approximations and sets of tours give over approximations. The application of these results to the two-neighborhood and the minimum 1-tree relaxation are discussed. Bounds on edge cost tolerances and approximate criticalities are obtainable likewise. A minimum spanning tree is an optimal communication topology for minimizing the cumulative transmission power in multi aircraft missions. The stability region of a minimum spanning tree is given and tolerances, stability balls
Robustness of spatial micronetworks
NASA Astrophysics Data System (ADS)
McAndrew, Thomas C.; Danforth, Christopher M.; Bagrow, James P.
2015-04-01
Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure.
1981-12-01
106 A. 13 XSU ......................................... 108 A.14 DDTCON...................................... 108 A.15 DKFTR...operation is preserved. Although some papers (Refs 6 and 13 ) deal with robustness only in regard to parameter variations within the basic controlled...since these can ofter be neglected in actual implementation, a constant-gain time 13 ........................................ invariant solution with
Robustness of spatial micronetworks.
McAndrew, Thomas C; Danforth, Christopher M; Bagrow, James P
2015-04-01
Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure.
Matlab as a robust control design tool
NASA Technical Reports Server (NTRS)
Gregory, Irene M.
1994-01-01
This presentation introduces Matlab as a tool used in flight control research. The example used to illustrate some of the capabilities of this software is a robust controller designed for a single stage to orbit air breathing vehicles's ascent to orbit. The global requirements of the controller are to stabilize the vehicle and follow a trajectory in the presence of atmospheric disturbances and strong dynamic coupling between airframe and propulsion.
Robust Control Design for Systems With Probabilistic Uncertainty
NASA Technical Reports Server (NTRS)
Crespo, Luis G.; Kenny, Sean P.
2005-01-01
This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.
Networked Robust Predictive Control Systems Design with Packet Loss
NASA Astrophysics Data System (ADS)
Nguyen, Quang T.; Veselý, Vojtech; Kozáková, Alena; Pakshin, Pavel
2014-01-01
The paper addresses problem of designing a robust output feedback model predictive control for uncertain linear systems over networks with packet-loss. The packet-loss process is arbitrary and bounded by the control horizon of model predictive control. Networked predictive control systems with packet loss are modeled as switched linear systems. This enables us to apply the theory of switched systems to establish the stability condition. The stabilizing controller design is based on sufficient robust stability conditions formulated as a solution of bilinear matrix inequality. Finally, a benchmark numerical example-double integrator is given to illustrate the effectiveness of the proposed method.
Can a first-order exponential decay model fit heart rate recovery after resistance exercise?
Bartels-Ferreira, Rhenan; de Sousa, Élder D; Trevizani, Gabriela A; Silva, Lilian P; Nakamura, Fábio Y; Forjaz, Cláudia L M; Lima, Jorge Roberto P; Peçanha, Tiago
2015-03-01
The time-constant of postexercise heart rate recovery (HRRτ ) obtained by fitting heart rate decay curve by a first-order exponential fitting has being used to assess cardiac autonomic recovery after endurance exercise. The feasibility of this model was not tested after resistance exercise (RE). The aim of this study was to test the goodness of fit of the first-order exponential decay model to fit heart rate recovery (HRR) after RE. Ten healthy subjects participated in the study. The experimental sessions occurred in two separated days and consisted of performance of 1 set of 10 repetitions at 50% or 80% of the load achieved on the one-repetition maximum test [low-intensity (LI) and high-intensity (HI) sessions, respectively]. Heart rate (HR) was continuously registered before and during exercise and also for 10 min of recovery. A monoexponential equation was used to fit the HRR curve during the postexercise period using different time windows (i.e. 30, 60, 90, … 600 s). For each time window, (i) HRRτ was calculated and (ii) variation of HR explained by the model (R(2) goodness of fit index) was assessed. The HRRτ showed stabilization from 360 and 420 s on LI and HI, respectively. Acceptable R(2) values were observed from the 360 s on LI (R(2) > 0.65) and at all tested time windows on HI (R(2) > 0.75). In conclusion, this study showed that using a minimum length of monitoring (~420 s) HRR after RE can be adequately modelled by a first-order exponential fitting.
Exponential time-dependent perturbation theory in rotationally inelastic scattering
NASA Astrophysics Data System (ADS)
Cross, R. J.
1983-08-01
An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error.
Exponentials and Laplace transforms on nonuniform time scales
NASA Astrophysics Data System (ADS)
Ortigueira, Manuel D.; Torres, Delfim F. M.; Trujillo, Juan J.
2016-10-01
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla and delta exponentials, computed. With these exponentials, two generalised discrete-time Laplace transforms are deduced and their properties studied. These transforms are compatible with the standard Laplace and Z transforms. They are used to study discrete-time linear systems defined by difference equations. These equations mimic the usual continuous-time equations that are uniformly approximated when the sampling interval becomes small. Impulse response and transfer function notions are introduced. This implies a unified mathematical framework that allows us to approximate the classic continuous-time case when the sampling rate is high or to obtain the standard discrete-time case, based on difference equations, when the time grid becomes uniform.
The scaling of human mobility by taxis is exponential
NASA Astrophysics Data System (ADS)
Liang, Xiao; Zheng, Xudong; Lv, Weifeng; Zhu, Tongyu; Xu, Ke
2012-03-01
As a significant factor in urban planning, traffic forecasting and prediction of epidemics, modeling patterns of human mobility draws intensive attention from researchers for decades. Power-law distribution and its variations are observed from quite a few real-world human mobility datasets such as the movements of banking notes, trackings of cell phone users' locations and trajectories of vehicles. In this paper, we build models for 20 million trajectories with fine granularity collected from more than 10 thousand taxis in Beijing. In contrast to most models observed in human mobility data, the taxis' traveling displacements in urban areas tend to follow an exponential distribution instead of a power-law. Similarly, the elapsed time can also be well approximated by an exponential distribution. Worth mentioning, analysis of the interevent time indicates the bursty nature of human mobility, similar to many other human activities.
Historical remarks on exponential product and quantum analysis
Suzuki, Masuo
2015-03-10
The exponential product formula [1, 2] was substantially introduced in physics by the present author [2]. Its systematic applications to quantum Monte Carlo Methods [3] were preformed [4, 5] first in 1977. Many interesting applications [6] of the quantum-classical correspondence (namely S-T transformation) have been reported. Systematic higher-order decomposition formulae were also discovered by the present author [7-11], using the recursion scheme [7, 9]. Physically speaking, these exponential product formulae play a conceptual role of separation of procedures [3,14]. Mathematical aspects of these formulae have been integrated in quantum analysis [15], in which non-commutative differential calculus is formulated and a general quantum Taylor expansion formula is given. This yields many useful operator expansion formulae such as the Feynman expansion formula and the resolvent expansion. Irreversibility and entropy production are also studied using quantum analysis [15].
Tachyonic matter cosmology with exponential and hyperbolic potentials
NASA Astrophysics Data System (ADS)
Pourhassan, B.; Naji, J.
In this paper, we consider tachyonic matter in spatially flat Friedmann-Robertson-Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.
The Exponential Function, the Human Race, and Scientists
NASA Astrophysics Data System (ADS)
Bartlett, Albert A.
2004-05-01
"The greatest shortcoming of the human race is our inability to understand the exponential function." This is the opening line of a talk I have given over 1500 times since 1969. In this context, the exponential function is used to give a quantitative description of steady growth of, for example, a population. As we all know, quantities that grow steadily, at even modest rates, quickly become impossibly large. Yet non-scientists in the business and government communities continue to fight for "sustainable growth" of the U.S. economy and population. What are scientists doing to increase public comprehension of the impossibility of "sustainable growth?" The main role of scientists seems to be to avoid calling attention to the impossibility of continued growth of populations and of rates of consumption of resources and, instead, to focus on minor aspects of the related problems. In so doing, we are complicit in making the problems worse. For scientists, this opening line should be revised to read: "The greatest shortcoming of scientists is our unwillingness to apply our knowledge of the exponential function to the great problems that are facing the human race."
The Exponential Decay Law, Bell's Inequality, and Nonlinear Dynamics
NASA Astrophysics Data System (ADS)
McHarris, Wm. C.
2002-10-01
What do the exponential decay law and Bell's inequality have in common? And with nonlinear dynamics? Simply that they both are among the puzzles at the heart of quantum mechanics, puzzles which can have parallel explanations in terms of chaos or nonlinear dynamics. The statistical nature of the exponential decay law, which at first glance is incompatible with the quantum mechanical concept of indistinguishabe particles, can be mocked up by the extreme sensitivity of chaotic systems to initial conditions. In accord with Ockham's Razor, iteration of a simple unimodal (e.g., quadratic) map in its chaotic region and keeping track of the number of iterations required for a trajectory starting from a point chosen at random within a small interval to escape into another small small interval reproduces the observed exponential behavior. Similarly, Bell's inequality derived using classical mechanics (with an underlying assumption of classical statistics) places an upper limit on numbers derived from measurements on entangled states, whereas quantum mechanics implies that this upper limit no longer holds. Experiments have shown the inequality to be violated, upholding quantum mechanics. However, nonlinear dynamics, with its correlated statistics, can yield results overlapping with the quantum mechanical predictions. Whether or not the experiments rule out "local realism" is thus a moot point. Nonlinear determinism just might exist within quantum mechanics.
A kernel representation for exponential splines with global tension
NASA Astrophysics Data System (ADS)
Barendt, Sven; Fischer, Bernd; Modersitzki, Jan
2009-02-01
Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
Comparing dependent robust correlations.
Wilcox, Rand R
2016-11-01
Let r1 and r2 be two dependent estimates of Pearson's correlation. There is a substantial literature on testing H0 : ρ1 = ρ2 , the hypothesis that the population correlation coefficients are equal. However, it is well known that Pearson's correlation is not robust. Even a single outlier can have a substantial impact on Pearson's correlation, resulting in a misleading understanding about the strength of the association among the bulk of the points. A way of mitigating this concern is to use a correlation coefficient that guards against outliers, many of which have been proposed. But apparently there are no results on how to compare dependent robust correlation coefficients when there is heteroscedasicity. Extant results suggest that a basic percentile bootstrap will perform reasonably well. This paper reports simulation results indicating the extent to which this is true when using Spearman's rho, a Winsorized correlation or a skipped correlation.
NASA Astrophysics Data System (ADS)
Rider, William; Witkowski, Walt; Kamm, James R.; Wildey, Tim
2016-02-01
We introduce a new methodology for inferring the accuracy of computational simulations through the practice of solution verification. We demonstrate this methodology on examples from computational heat transfer, fluid dynamics and radiation transport. Our methodology is suited to both well- and ill-behaved sequences of simulations. Our approach to the analysis of these sequences of simulations incorporates expert judgment into the process directly via a flexible optimization framework, and the application of robust statistics. The expert judgment is systematically applied as constraints to the analysis, and together with the robust statistics guards against over-emphasis on anomalous analysis results. We have named our methodology Robust Verification. Our methodology is based on utilizing multiple constrained optimization problems to solve the verification model in a manner that varies the analysis' underlying assumptions. Constraints applied in the analysis can include expert judgment regarding convergence rates (bounds and expectations) as well as bounding values for physical quantities (e.g., positivity of energy or density). This approach then produces a number of error models, which are then analyzed through robust statistical techniques (median instead of mean statistics). This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations.
Rider, William; Witkowski, Walt; Kamm, James R.; Wildey, Tim
2016-02-15
We introduce a new methodology for inferring the accuracy of computational simulations through the practice of solution verification. We demonstrate this methodology on examples from computational heat transfer, fluid dynamics and radiation transport. Our methodology is suited to both well- and ill-behaved sequences of simulations. Our approach to the analysis of these sequences of simulations incorporates expert judgment into the process directly via a flexible optimization framework, and the application of robust statistics. The expert judgment is systematically applied as constraints to the analysis, and together with the robust statistics guards against over-emphasis on anomalous analysis results. We have named our methodology Robust Verification. Our methodology is based on utilizing multiple constrained optimization problems to solve the verification model in a manner that varies the analysis' underlying assumptions. Constraints applied in the analysis can include expert judgment regarding convergence rates (bounds and expectations) as well as bounding values for physical quantities (e.g., positivity of energy or density). This approach then produces a number of error models, which are then analyzed through robust statistical techniques (median instead of mean statistics). This provides self-contained, data and expert informed error estimation including uncertainties for both the solution itself and order of convergence. Our method produces high quality results for the well-behaved cases relatively consistent with existing practice. The methodology can also produce reliable results for ill-behaved circumstances predicated on appropriate expert judgment. We demonstrate the method and compare the results with standard approaches used for both code and solution verification on well-behaved and ill-behaved simulations.
Robustness in bacterial chemotaxis
NASA Astrophysics Data System (ADS)
Alon, U.; Surette, M. G.; Barkai, N.; Leibler, S.
1999-01-01
Networks of interacting proteins orchestrate the responses of living cells to a variety of external stimuli, but how sensitive is the functioning of these protein networks to variations in theirbiochemical parameters? One possibility is that to achieve appropriate function, the reaction rate constants and enzyme concentrations need to be adjusted in a precise manner, and any deviation from these `fine-tuned' values ruins the network's performance. An alternative possibility is that key properties of biochemical networks are robust; that is, they are insensitive to the precise values of the biochemical parameters. Here we address this issue in experiments using chemotaxis of Escherichia coli, one of the best-characterized sensory systems,. We focus on how response and adaptation to attractant signals vary with systematic changes in the intracellular concentration of the components of the chemotaxis network. We find that some properties, such as steady-state behaviour and adaptation time, show strong variations in response to varying protein concentrations. In contrast, the precision of adaptation is robust and does not vary with the protein concentrations. This is consistent with a recently proposed molecular mechanism for exact adaptation, where robustness is a direct consequence of the network's architecture.
Robustness of metabolic networks
NASA Astrophysics Data System (ADS)
Jeong, Hawoong
2009-03-01
We investigated the robustness of cellular metabolism by simulating the system-level computational models, and also performed the corresponding experiments to validate our predictions. We address the cellular robustness from the ``metabolite''-framework by using the novel concept of ``flux-sum,'' which is the sum of all incoming or outgoing fluxes (they are the same under the pseudo-steady state assumption). By estimating the changes of the flux-sum under various genetic and environmental perturbations, we were able to clearly decipher the metabolic robustness; the flux-sum around an essential metabolite does not change much under various perturbations. We also identified the list of the metabolites essential to cell survival, and then ``acclimator'' metabolites that can control the cell growth were discovered. Furthermore, this concept of ``metabolite essentiality'' should be useful in developing new metabolic engineering strategies for improved production of various bioproducts and designing new drugs that can fight against multi-antibiotic resistant superbacteria by knocking-down the enzyme activities around an essential metabolite. Finally, we combined a regulatory network with the metabolic network to investigate its effect on dynamic properties of cellular metabolism.
Robustness of Interdependent Networks
NASA Astrophysics Data System (ADS)
Havlin, Shlomo
2011-03-01
In interdependent networks, when nodes in one network fail, they cause dependent nodes in other networks to also fail. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of many interdependent networks. We will present a framework for understanding the robustness of interacting networks subject to such cascading failures and provide a basic analytic approach that may be useful in future studies. We present exact analytical solutions for the critical fraction of nodes that upon removal will lead to a failure cascade and to a complete fragmentation of two interdependent networks in a first order transition. Surprisingly, analyzing complex systems as a set of interdependent networks may alter a basic assumption that network theory has relied on: while for a single network a broader degree distribution of the network nodes results in the network being more robust to random failures, for interdependent networks, the broader the distribution is, the more vulnerable the networks become to random failure. We also show that reducing the coupling between the networks leads to a change from a first order percolation phase transition to a second order percolation transition at a critical point. These findings pose a significant challenge to the future design of robust networks that need to consider the unique properties of interdependent networks.
NASA Astrophysics Data System (ADS)
Guardia, Marcel; Seara, Tere M.
2012-05-01
In this paper, we study the splitting of separatrices phenomenon which arises when one considers a Hamiltonian system of one degree of freedom with a fast periodic or quasiperiodic and meromorphic in the state variables perturbation. The obtained results are different from the previous ones in the literature, which mainly assume algebraic or trigonometric polynomial dependence on the state variables. As a model, we consider the pendulum equation with several meromorphic perturbations and we show the sensitivity of the size of the splitting on the width of the analyticity strip of the perturbation with respect to the state variables. We show that the size of the splitting is exponentially small if the strip of analyticity is wide enough. Furthermore, we see that the splitting grows as the width of the analyticity strip shrinks, even becoming non-exponentially small for very narrow strips. Our results prevent use of polynomial truncations of the meromorphic perturbation to compute the size of the splitting of separatrices.
Exponential and logarithmic f(T) wormhole solutions in Lorentzian noncommutative background
NASA Astrophysics Data System (ADS)
Rani, Shamaila; Bilal Amin, M.; Jawad, Abdul
2016-12-01
In this paper, we take noncommutative geometry under Lorentzian distribution and explore static spherically symmetric wormhole solutions in the extended teleparallel gravity by taking exponential and logarithmic f ( T) models. For matter components, we use effective energy-momentum tensor for a nondiagonal tetrad and develop field equations. We work to explore solutions by considering various viable f( T) models and conclude that there exists a possibility of physically acceptable wormhole solutions under noncommutative background for these models. We observe that the effective energy-momentum tensor is responsible for the violation of the energy conditions. Also, we check the stability for these solutions by equilibrium condition. The equilibrium condition does not meet properly for any obtained solutions. Therefore solutions are in less equilibrium situation.
Exponential H ∞ Synchronization of Chaotic Cryptosystems Using an Improved Genetic Algorithm
Hsiao, Feng-Hsiag
2015-01-01
This paper presents a systematic design methodology for neural-network- (NN-) based secure communications in multiple time-delay chaotic (MTDC) systems with optimal H ∞ performance and cryptography. On the basis of the Improved Genetic Algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a model-based fuzzy controller is then synthesized to stabilize the MTDC systems. A fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H ∞ performance by minimizing the disturbance attenuation level. Furthermore, the error of the recovered message is stated by using the n-shift cipher and key. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. PMID:26366432
Practical robustness measures in multivariable control system analysis. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.
1981-01-01
The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.
Exponential integrators for a Markov chain model of the fast sodium channel of cardiomyocytes.
Starý, Tomás; Biktashev, Vadim N
2015-04-01
The modern Markov chain models of ionic channels in excitable membranes are numerically stiff. The popular numerical methods for these models require very small time steps to ensure stability. Our objective is to formulate and test two methods addressing this issue, so that the timestep can be chosen based on accuracy rather than stability. Both proposed methods extend Rush-Larsen technique, which was originally developed to Hogdkin-Huxley type gate models. One method, "matrix Rush-Larsen" (MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix exponentials are calculated using precomputed tables of eigenvalues and eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits asymptotic properties of a particular Markov chain model, allowing explicit analytical expressions for the substeps. We test both methods on the Clancy and Rudy (2002) I(Na)Markov chain model. With precomputed tables for functions of the transmembrane voltage, both methods are comparable to the forward Euler method in accuracy and computational cost, but allow longer time steps without numerical instability. We conclude that both methods are of practical interest. MRL requires more computations than HOS, but is formulated in general terms which can be readily extended to other Markov chain channel models, whereas the utility of HOS depends on the asymptotic properties of a particular model. The significance of the methods is that they allow a considerable speed-up of large-scale computations of cardiac excitation models by increasing the time step, while maintaining acceptable accuracy and preserving numerical stability.
Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares
NASA Technical Reports Server (NTRS)
Dorobantu, Andrei; Crespo, Luis G.; Seiler, Peter J.
2012-01-01
A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.
On Ideal Stability of Cylindrical Localized Interchange Modes
Umansky, M V
2007-05-15
Stability of cylindrical localized ideal pressure-driven interchange plasma modes is revisited. Converting the underlying eigenvalue problem into the form of the Schroedinger equation gives a new simple way of deriving the Suydam stability criterion and calculating the growth rates of unstable modes. Near the marginal stability limit the growth rate is exponentially small and the mode has a double-peak structure.
Robust reconstruction of the rate constant distribution using the phase function method.
Zhou, Yajun; Zhuang, Xiaowei
2006-12-01
Many biological processes exhibit complex kinetic behavior that involves a nontrivial distribution of rate constants. Characterization of the rate constant distribution is often critical for mechanistic understandings of these processes. However, it is difficult to extract a rate constant distribution from data measured in the time domain. This is due to the numerical instability of the inverse Laplace transform, a long-standing mathematical challenge that has hampered data analysis in many disciplines. Here, we present a method that allows us to reconstruct the probability distribution of rate constants from decay data in the time domain, without fitting to specific trial functions or requiring any prior knowledge of the rate distribution. The robustness (numerical stability) of this reconstruction method is numerically illustrated by analyzing data with realistic noise and theoretically proved by the continuity of the transformations connecting the relevant function spaces. This development enhances our ability to characterize kinetics and dynamics of biological processes. We expect this method to be useful in a broad range of disciplines considering the prevalence of complex exponential decays in many experimental systems.
Bayer, T.; Wollenhaupt, M.; Sarpe-Tudoran, C.; Baumert, T.
2009-01-16
We experimentally demonstrate a strong-field coherent control mechanism that combines the advantages of photon locking (PL) and rapid adiabatic passage (RAP). Unlike earlier implementations of PL and RAP by pulse sequences or chirped pulses, we use shaped pulses generated by phase modulation of the spectrum of a femtosecond laser pulse with a generalized phase discontinuity. The novel control scenario is characterized by a high degree of robustness achieved via adiabatic preparation of a state of maximum coherence. Subsequent phase control allows for efficient switching among different target states. We investigate both properties by photoelectron spectroscopy on potassium atoms interacting with the intense shaped light field.
Robust Kriged Kalman Filtering
Baingana, Brian; Dall'Anese, Emiliano; Mateos, Gonzalo; Giannakis, Georgios B.
2015-11-11
Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.
Carlson, J. M.; Doyle, John
2002-01-01
Highly optimized tolerance (HOT) was recently introduced as a conceptual framework to study fundamental aspects of complexity. HOT is motivated primarily by systems from biology and engineering and emphasizes, (i) highly structured, nongeneric, self-dissimilar internal configurations, and (ii) robust yet fragile external behavior. HOT claims these are the most important features of complexity and not accidents of evolution or artifices of engineering design but are inevitably intertwined and mutually reinforcing. In the spirit of this collection, our paper contrasts HOT with alternative perspectives on complexity, drawing on real-world examples and also model systems, particularly those from self-organized criticality. PMID:11875207
Robustness of Cantor diffractals.
Verma, Rupesh; Sharma, Manoj Kumar; Banerjee, Varsha; Senthilkumaran, Paramasivam
2013-04-08
Diffractals are electromagnetic waves diffracted by a fractal aperture. In an earlier paper, we reported an important property of Cantor diffractals, that of redundancy [R. Verma et. al., Opt. Express 20, 8250 (2012)]. In this paper, we report another important property, that of robustness. The question we address is: How much disorder in the Cantor grating can be accommodated by diffractals to continue to yield faithfully its fractal dimension and generator? This answer is of consequence in a number of physical problems involving fractal architecture.
Synthesis Methods for Robust Passification and Control
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M. (Technical Monitor)
2000-01-01
The research effort under this cooperative agreement has been essentially the continuation of the work from previous grants. The ongoing work has primarily focused on developing passivity-based control techniques for Linear Time-Invariant (LTI) systems. During this period, there has been a significant progress made in the area of passivity-based control of LTI systems and some preliminary results have also been obtained for nonlinear systems, as well. The prior work has addressed optimal control design for inherently passive as well as non- passive linear systems. For exploiting the robustness characteristics of passivity-based controllers the passification methodology was developed for LTI systems that are not inherently passive. Various methods of passification were first proposed in and further developed. The robustness of passification was addressed for multi-input multi-output (MIMO) systems for certain classes of uncertainties using frequency-domain methods. For MIMO systems, a state-space approach using Linear Matrix Inequality (LMI)-based formulation was presented, for passification of non-passive LTI systems. An LMI-based robust passification technique was presented for systems with redundant actuators and sensors. The redundancy in actuators and sensors was used effectively for robust passification using the LMI formulation. The passification was designed to be robust to an interval-type uncertainties in system parameters. The passification techniques were used to design a robust controller for Benchmark Active Control Technology wing under parametric uncertainties. The results on passive nonlinear systems, however, are very limited to date. Our recent work in this area was presented, wherein some stability results were obtained for passive nonlinear systems that are affine in control.
Exponential frequency spectrum and Lorentzian pulses in magnetized plasmas
Pace, D. C.; Shi, M.; Maggs, J. E.; Morales, G. J.; Carter, T. A.
2008-12-15
Two different experiments involving pressure gradients across the confinement magnetic field in a large plasma column are found to exhibit a broadband turbulence that displays an exponential frequency spectrum for frequencies below the ion cyclotron frequency. The exponential feature has been traced to the presence of solitary pulses having a Lorentzian temporal signature. These pulses arise from nonlinear interactions of drift-Alfven waves driven by the pressure gradients. In both experiments the width of the pulses is narrowly distributed resulting in exponential spectra with a single characteristic time scale. The temporal width of the pulses is measured to be a fraction of a period of the drift-Alfven waves. The experiments are performed in the Large Plasma Device (LAPD-U) [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] operated by the Basic Plasma Science Facility at the University of California, Los Angeles. One experiment involves a controlled, pure electron temperature gradient associated with a microscopic (6 mm gradient length) hot electron temperature filament created by the injection a small electron beam embedded in the center of a large, cold magnetized plasma. The other experiment is a macroscopic (3.5 cm gradient length) limiter-edge experiment in which a density gradient is established by inserting a metallic plate at the edge of the nominal plasma column of the LAPD-U. The temperature filament experiment permits a detailed study of the transition from coherent to turbulent behavior and the concomitant change from classical to anomalous transport. In the limiter experiment the turbulence sampled is always fully developed. The similarity of the results in the two experiments strongly suggests a universal feature of pressure-gradient driven turbulence in magnetized plasmas that results in nondiffusive cross-field transport. This may explain previous observations in helical confinement devices, research tokamaks, and arc plasmas.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Exponential Methods for the Time Integration of Schroedinger Equation
Cano, B.; Gonzalez-Pachon, A.
2010-09-30
We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.
A Mixed Exponential Time Series Model. NMEARMA(p,q).
1980-03-01
AD-AO85 316 NAVAL POSTGRADUATE SCHOOL MONTEREY CA F/G 12/1 A MIXED EXPONENTIAL TIME SERIES MODEL. NMEARMA(P,Q).(U MAR GO A .J LAWRANCE , P A LEWIS...This report was prepared by: A. J. Lawrance University of Birmingham Birmingham, England Reviewed by: Released by- Michael G. Sover’ign, Chirman...MODEL, NMEARMA(p,q) by A. J. Lawrance P. A. W. Lewis University of Birmingham Naval Postgraduate School Birmingham, England Monterey, California, USA
A conditionally exponential decay approach to scaling in finance
NASA Astrophysics Data System (ADS)
Weron, Rafal; Weron, Karina; Weron, Aleksander
We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency data from the foreign exchange market. For this purpose, we adopt the conditionally exponential decay model, which describes asymptotic behaviour of general complex systems. We also discuss the overall rationale for why one might expect such scaling laws to hold for financial data.
An Exponential Finite Difference Technique for Solving Partial Differential Equations.
1987-06-01
density , kg/N 3 (lbm/ft 3) 91.*,e separation variables (At dimensionless timelAX) 2 vi -W sNiv W- NiW.4%1 1. INTRODUCTION Partial differential equations...competing numerical analysis were run in double precision on either the IBM-3033 or the Cray X-MP mainframes. The computer codes developed for the...is increased. - R P~p~ 15 Effect of Initial and Boundary Conditions on the Exponential Finite Difference Method In this section the effect of
Asymptotic Structure of Constrained Exponential Random Graph Models
NASA Astrophysics Data System (ADS)
Zhu, Lingjiong
2017-03-01
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.
On the function inverse to the exponential integral function
NASA Astrophysics Data System (ADS)
Pecina, P.
1986-01-01
The paper deals briefly with one integral of the basic equations of meteoric physics which includes the exponential integral function Ei(x). It is further shown that the approximation of the function inverse to Ei(x), Ei-1(x), is also required. The construction of this function, using series expansion by means of Chebyshev polynomials, is described. Computer programs, written in Fortran IV G, which serve to compute the values of Ei(x) and Ei-1(x), accurate to 13 decimal figures, are included.
Polar exponential sensor arrays unify iconic and Hough space representation
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1990-01-01
The log-polar coordinate system, inherent in both polar exponential sensor arrays and log-polar remapped video imagery, is identical to the coordinate system of its corresponding Hough transform parameter space. The resulting unification of iconic and Hough domains simplifies computation for line recognition and eliminates the slope quantization problems inherent in the classical Cartesian Hough transform. The geometric organization of the algorithm is more amenable to massively parallel architectures than that of the Cartesian version. The neural architecture of the human visual cortex meets the geometric requirements to execute 'in-place' log-Hough algorithms of the kind described here.
Curve fitting of aeroelastic transient response data with exponential functions
NASA Technical Reports Server (NTRS)
Bennett, R. M.; Desmarais, R. N.
1976-01-01
The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.
Exponential integrators for the incompressible Navier-Stokes equations.
Newman, Christopher K.
2004-07-01
We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size. Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step. Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L{sup 2} inner product. We examine this L{sup 2} projection and an H{sup 1} projection induced by the H{sup 1} semi-inner product. The H
Stretched exponential survival statistics for microorganisms in radiation field
NASA Astrophysics Data System (ADS)
Plonka, Andrzej; Bogus, Wlodzimierz
1999-11-01
The so-called concave or tailed survival curves are reported both for multi and single species bacterial populations. Taking as an example Bacillus pumilus, frequently encountered in decontamination studies, it is shown that the tailed survival curves are adequately described by stretched (0< α<1) exponential SF=exp[-( D/ D0) α], where SF denotes the fraction of species surviving the irradiation dose D, D0 is the effective dose, and α is the dispersion parameter interpreted phenomenologically in terms of radiation sensivity distribution for single species population under the given experimental conditions.
Incomplete exponential sums and Diffie-Hellman triples
NASA Astrophysics Data System (ADS)
Banks, William D.; Friedlander, John B.; Konyagin, Sergei V.; Shparlinski, Igor E.
2006-03-01
Let p be a prime and vartheta an integer of order t in the multiplicative group modulo p. In this paper, we continue the study of the distribution of Diffie-Hellman triples (vartheta(x,) vartheta(y,) vartheta(xy) ) by considering the closely related problem of estimating exponential sums formed from linear combinations of the entries in such triples. We show that the techniques developed earlier for complete sums can be combined, modified and developed further to treat incomplete sums as well. Our bounds imply uniformity of distribution results for Diffie-Hellman triples as the pair (x,y) varies over small boxes.
Solving Point-Reactor Kinetics Equations Using Exponential Moment Methods
2013-03-21
equations of the following form: ( ) ( ) ( ) ( ) ( )i i i dn t t n t c t S t dt (2) ( ) ( ) ( )i ii i dc t c t n...presented in the function. Exponential moment functions are orderless; that is, the value of the function is invariant under permutations of its...turned into an integral equation by ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i i i i dn
Stretched Exponential Relaxation of Glasses at Low Temperature.
Yu, Yingtian; Wang, Mengyi; Zhang, Dawei; Wang, Bu; Sant, Gaurav; Bauchy, Mathieu
2015-10-16
The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent β=3/5, as predicted by Phillips's diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but it is rather a manifestation of the mixed alkali effect.
Hermite-Padé approximation of exponential functions
NASA Astrophysics Data System (ADS)
Astafyeva, A. V.; Starovoitov, A. P.
2016-06-01
The paper is concerned with diagonal Hermite-Padé polynomials of the first kind for the system of exponentials \\{eλ_jz\\}j=0^k with arbitrary distinct complex parameters \\{λ_k\\}j=0^k. An asymptotic formula for the remainder term is established and the location of the zeros is described. For real parameters the asymptotics are found and the extremal properties are described. The theorems obtained supplement the well-known results due to Borwein, Wielonsky, Saff, Varga and Stahl. Bibliography: 43 titles.
Species interactions differ in their genetic robustness
Chubiz, Lon M.; Granger, Brian R.; Segre, Daniel; ...
2015-04-14
Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S.more » enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.« less
Influence of annular boundaries on Thomson's vortex polygon stability
Kurakin, L. G.
2014-06-15
The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle inside an annulus is presented. The problem is reduced to one of the equilibrium stability of the Hamiltonian system with a cyclic variable. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The stability of the stationary motion is interpreted as a Routh stability. The exponential instability is shown always to take place if N ≥ 7. For N = 2, 4, and 6, the parameter space is divided in two: a Routh stability domain in an exact nonlinear setting and an exponential instability domain. For N = 3 and 5, the parameter space consists of three domains. The stability of the third in an exact nonlinear setting is sandwiched between the Routh and exponential domains. Its analysis remains an open problem with its solution requiring nonlinear analysis.
Influence of annular boundaries on Thomson's vortex polygon stability
NASA Astrophysics Data System (ADS)
Kurakin, L. G.
2014-06-01
The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle inside an annulus is presented. The problem is reduced to one of the equilibrium stability of the Hamiltonian system with a cyclic variable. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The stability of the stationary motion is interpreted as a Routh stability. The exponential instability is shown always to take place if N ≥ 7. For N = 2, 4, and 6, the parameter space is divided in two: a Routh stability domain in an exact nonlinear setting and an exponential instability domain. For N = 3 and 5, the parameter space consists of three domains. The stability of the third in an exact nonlinear setting is sandwiched between the Routh and exponential domains. Its analysis remains an open problem with its solution requiring nonlinear analysis.
Influence of annular boundaries on Thomson's vortex polygon stability.
Kurakin, L G
2014-06-01
The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle inside an annulus is presented. The problem is reduced to one of the equilibrium stability of the Hamiltonian system with a cyclic variable. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The stability of the stationary motion is interpreted as a Routh stability. The exponential instability is shown always to take place if N ≥ 7. For N = 2, 4, and 6, the parameter space is divided in two: a Routh stability domain in an exact nonlinear setting and an exponential instability domain. For N = 3 and 5, the parameter space consists of three domains. The stability of the third in an exact nonlinear setting is sandwiched between the Routh and exponential domains. Its analysis remains an open problem with its solution requiring nonlinear analysis.
Vehicle active steering control research based on two-DOF robust internal model control
NASA Astrophysics Data System (ADS)
Wu, Jian; Liu, Yahui; Wang, Fengbo; Bao, Chunjiang; Sun, Qun; Zhao, Youqun
2016-07-01
Because of vehicle's external disturbances and model uncertainties, robust control algorithms have obtained popularity in vehicle stability control. The robust control usually gives up performance in order to guarantee the robustness of the control algorithm, therefore an improved robust internal model control(IMC) algorithm blending model tracking and internal model control is put forward for active steering system in order to reach high performance of yaw rate tracking with certain robustness. The proposed algorithm inherits the good model tracking ability of the IMC control and guarantees robustness to model uncertainties. In order to separate the design process of model tracking from the robustness design process, the improved 2 degree of freedom(DOF) robust internal model controller structure is given from the standard Youla parameterization. Simulations of double lane change maneuver and those of crosswind disturbances are conducted for evaluating the robust control algorithm, on the basis of a nonlinear vehicle simulation model with a magic tyre model. Results show that the established 2-DOF robust IMC method has better model tracking ability and a guaranteed level of robustness and robust performance, which can enhance the vehicle stability and handling, regardless of variations of the vehicle model parameters and the external crosswind interferences. Contradiction between performance and robustness of active steering control algorithm is solved and higher control performance with certain robustness to model uncertainties is obtained.
Tuteja, Anish; Choi, Wonjae; Mabry, Joseph M.; McKinley, Gareth H.; Cohen, Robert E.
2008-01-01
Superhydrophobic surfaces display water contact angles greater than 150° in conjunction with low contact angle hysteresis. Microscopic pockets of air trapped beneath the water droplets placed on these surfaces lead to a composite solid-liquid-air interface in thermodynamic equilibrium. Previous experimental and theoretical studies suggest that it may not be possible to form similar fully-equilibrated, composite interfaces with drops of liquids, such as alkanes or alcohols, that possess significantly lower surface tension than water (γlv = 72.1 mN/m). In this work we develop surfaces possessing re-entrant texture that can support strongly metastable composite solid-liquid-air interfaces, even with very low surface tension liquids such as pentane (γlv = 15.7 mN/m). Furthermore, we propose four design parameters that predict the measured contact angles for a liquid droplet on a textured surface, as well as the robustness of the composite interface, based on the properties of the solid surface and the contacting liquid. These design parameters allow us to produce two different families of re-entrant surfaces— randomly-deposited electrospun fiber mats and precisely fabricated microhoodoo surfaces—that can each support a robust composite interface with essentially any liquid. These omniphobic surfaces display contact angles greater than 150° and low contact angle hysteresis with both polar and nonpolar liquids possessing a wide range of surface tensions. PMID:19001270
Robust Flutter Margin Analysis that Incorporates Flight Data
NASA Technical Reports Server (NTRS)
Lind, Rick; Brenner, Martin J.
1998-01-01
An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.
Data assimilation on the exponentially accurate slow manifold.
Cotter, Colin
2013-05-28
I describe an approach to data assimilation making use of an explicit map that defines a coordinate system on the slow manifold in the semi-geostrophic scaling in Lagrangian coordinates, and apply the approach to a simple toy system that has previously been proposed as a low-dimensional model for the semi-geostrophic scaling. The method can be extended to Lagrangian particle methods such as Hamiltonian particle-mesh and smooth-particle hydrodynamics applied to the rotating shallow-water equations, and many of the properties will remain for more general Eulerian methods. Making use of Hamiltonian normal-form theory, it has previously been shown that, if initial conditions for the system are chosen as image points of the map, then the fast components of the system have exponentially small magnitude for exponentially long times as ε→0, and this property is preserved if one uses a symplectic integrator for the numerical time stepping. The map may then be used to parametrize initial conditions near the slow manifold, allowing data assimilation to be performed without introducing any fast degrees of motion (more generally, the precise amount of fast motion can be selected).
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
NASA Astrophysics Data System (ADS)
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
Freddi: Fast Rise Exponential Decay accretion Disk model Implementation
NASA Astrophysics Data System (ADS)
Malanchev, K. L.; Lipunova, G. V.
2016-10-01
Freddi (Fast Rise Exponential Decay: accretion Disk model Implementation) solves 1-D evolution equations of the Shakura-Sunyaev accretion disk. It simulates fast rise exponential decay (FRED) light curves of low mass X-ray binaries (LMXBs). The basic equation of the viscous evolution relates the surface density and viscous stresses and is of diffusion type; evolution of the accretion rate can be found on solving the equation. The distribution of viscous stresses defines the emission from the source. The standard model for the accretion disk is implied; the inner boundary of the disk is at the ISCO or can be explicitely set. The boundary conditions in the disk are the zero stress at the inner boundary and the zero accretion rate at the outer boundary. The conditions are suitable during the outbursts in X-ray binary transients with black holes. In a binary system, the accretion disk is radially confined. In Freddi, the outer radius of the disk can be set explicitely or calculated as the position of the tidal truncation radius.
A stochastic evolutionary model generating a mixture of exponential distributions
NASA Astrophysics Data System (ADS)
Fenner, Trevor; Levene, Mark; Loizou, George
2016-02-01
Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.
Arima model and exponential smoothing method: A comparison
NASA Astrophysics Data System (ADS)
Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri
2013-04-01
This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.
Exponentially more precise quantum simulation of fermions in second quantization
NASA Astrophysics Data System (ADS)
Babbush, Ryan; Berry, Dominic W.; Kivlichan, Ian D.; Wei, Annie Y.; Love, Peter J.; Aspuru-Guzik, Alán
2016-03-01
We introduce novel algorithms for the quantum simulation of fermionic systems which are dramatically more efficient than those based on the Lie-Trotter-Suzuki decomposition. We present the first application of a general technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The key difficulty in applying algorithms for general sparse Hamiltonian simulation to fermionic simulation is that a query, corresponding to computation of an entry of the Hamiltonian, is costly to compute. This means that the gate complexity would be much higher than quantified by the query complexity. We solve this problem with a novel quantum algorithm for on-the-fly computation of integrals that is exponentially faster than classical sampling. While the approaches presented here are readily applicable to a wide class of fermionic models, we focus on quantum chemistry simulation in second quantization, perhaps the most studied application of Hamiltonian simulation. Our central result is an algorithm for simulating an N spin-orbital system that requires \\tilde{{ O }}({N}5t) gates. This approach is exponentially faster in the inverse precision and at least cubically faster in N than all previous approaches to chemistry simulation in the literature.
Truncated γ-exponential models for tidal stellar systems
NASA Astrophysics Data System (ADS)
Gomez-Leyton, Y. J.; Velazquez, L.
2016-05-01
We introduce a parametric family of models to characterize the properties of astrophysical systems in a quasi-stationary evolution under the incidence evaporation. We start from an one-particle distribution fγ (q, p|β,ɛs) that considers an appropriate deformation of Maxwell-Boltzmann form with inverse temperature β, in particular, a power-law truncation at the scape energy ɛs with exponent γ > 0. This deformation is implemented using a generalized γ-exponential function obtained from the fractional integration of ordinary exponential. As shown in this work, this proposal generalizes models of tidal stellar systems that predict particles distributions with isothermal cores and polytropic haloes, e.g.: Michie-King models. We perform the analysis of thermodynamic features of these models and their associated distribution profiles. A nontrivial consequence of this study is that profiles with isothermal cores and polytropic haloes are only obtained for low energies whenever deformation parameter γ < γc ≃ 2.13. This study is a first approximation to characterize a self- gravitating system, so we consider equal to all the particles that constitute the system.
Properties of branching exponential flights in bounded domains
NASA Astrophysics Data System (ADS)
Zoia, A.; Dumonteil, E.; Mazzolo, A.
2012-11-01
In a series of recent works, important results have been reported concerning the statistical properties of exponential flights evolving in bounded domains, a widely adopted model for finite-speed transport phenomena (Blanco S. and Fournier R., Europhys. Lett., 61 (2003) 168; Mazzolo A., Europhys. Lett., 68 (2004) 350; Bénichou O. et al., Europhys. Lett., 70 (2005) 42). Motivated by physical and biological systems where random spatial displacements are coupled with Galton-Watson birth-death mechanisms, such as neutron multiplication, diffusion of reproducing bacteria or spread of epidemics, in this letter we extend those results in two directions, via a Feynman-Kac formalism. First, we characterize the occupation statistics of exponential flights in the presence of absorption and branching, and give explicit moment formulas for the total length travelled by the walker and the number of performed collisions in a given domain. Then, we show that the survival and escape probability can be derived as well by resorting to a similar approach.
Evolving Robust Gene Regulatory Networks
Noman, Nasimul; Monjo, Taku; Moscato, Pablo; Iba, Hitoshi
2015-01-01
Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of ‘parts’ and ‘devices’. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems. PMID:25616055
Facilitating Understanding of a Catch-22 Concept: Teaching Exponential Change with Logo.
ERIC Educational Resources Information Center
Weller, Herman G.; Johnson, Vivian
1992-01-01
Describes a unit for teaching exponential change in a noncalculus physics course by having students write recursive procedures in LOGO to graphically represent linear and exponential change. Summarizes the experience of implementing the unit in a segment on radioactive decay. Modifications to the unit are suggested for teaching exponential change…
Robust automated knowledge capture.
Stevens-Adams, Susan Marie; Abbott, Robert G.; Forsythe, James Chris; Trumbo, Michael Christopher Stefan; Haass, Michael Joseph; Hendrickson, Stacey M. Langfitt
2011-10-01
This report summarizes research conducted through the Sandia National Laboratories Robust Automated Knowledge Capture Laboratory Directed Research and Development project. The objective of this project was to advance scientific understanding of the influence of individual cognitive attributes on decision making. The project has developed a quantitative model known as RumRunner that has proven effective in predicting the propensity of an individual to shift strategies on the basis of task and experience related parameters. Three separate studies are described which have validated the basic RumRunner model. This work provides a basis for better understanding human decision making in high consequent national security applications, and in particular, the individual characteristics that underlie adaptive thinking.
Robustness in Digital Hardware
NASA Astrophysics Data System (ADS)
Woods, Roger; Lightbody, Gaye
The growth in electronics has probably been the equivalent of the Industrial Revolution in the past century in terms of how much it has transformed our daily lives. There is a great dependency on technology whether it is in the devices that control travel (e.g., in aircraft or cars), our entertainment and communication systems, or our interaction with money, which has been empowered by the onset of Internet shopping and banking. Despite this reliance, there is still a danger that at some stage devices will fail within the equipment's lifetime. The purpose of this chapter is to look at the factors causing failure and address possible measures to improve robustness in digital hardware technology and specifically chip technology, giving a long-term forecast that will not reassure the reader!
NASA Technical Reports Server (NTRS)
Lorenzo, Carl F.
1995-01-01
The potential for a revolutionary step in the durability of reusable rocket engines is made possible by the combination of several emerging technologies. The recent creation and analytical demonstration of life extending (or damage mitigating) control technology enables rapid rocket engine transients with minimum fatigue and creep damage. This technology has been further enhanced by the formulation of very simple but conservative continuum damage models. These new ideas when combined with recent advances in multidisciplinary optimization provide the potential for a large (revolutionary) step in reusable rocket engine durability. This concept has been named the robust rocket engine concept (RREC) and is the basic contribution of this paper. The concept also includes consideration of design innovations to minimize critical point damage.
NASA Astrophysics Data System (ADS)
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-03-01
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-03-15
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Dynamics robustness of cascading systems.
Young, Jonathan T; Hatakeyama, Tetsuhiro S; Kaneko, Kunihiko
2017-03-01
A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade's kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a
Dynamics robustness of cascading systems
Kaneko, Kunihiko
2017-01-01
A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade’s kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a
Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design
NASA Technical Reports Server (NTRS)
Whorton, Mark
2003-01-01
Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.
Iterative exponential growth of stereo- and sequence-controlled polymers
NASA Astrophysics Data System (ADS)
Barnes, Jonathan C.; Ehrlich, Deborah J. C.; Gao, Angela X.; Leibfarth, Frank A.; Jiang, Yivan; Zhou, Erica; Jamison, Timothy F.; Johnson, Jeremiah A.
2015-10-01
Chemists have long sought sequence-controlled synthetic polymers that mimic nature's biopolymers, but a practical synthetic route that enables absolute control over polymer sequence and structure remains a key challenge. Here, we report an iterative exponential growth plus side-chain functionalization (IEG+) strategy that begins with enantiopure epoxides and facilitates the efficient synthesis of a family of uniform >3 kDa macromolecules of varying sequence and stereoconfiguration that are coupled to produce unimolecular polymers (>6 kDa) with sequences and structures that cannot be obtained using traditional polymerization techniques. Selective side-chain deprotection of three hexadecamers is also demonstrated, which imbues each compound with the ability to dissolve in water. We anticipate that these new macromolecules and the general IEG+ strategy will find broad application as a versatile platform for the scalable synthesis of sequence-controlled polymers.
Exponential-family random graph models for valued networks
Krivitsky, Pavel N.
2013-01-01
Exponential-family random graph models (ERGMs) provide a principled and flexible way to model and simulate features common in social networks, such as propensities for homophily, mutuality, and friend-of-a-friend triad closure, through choice of model terms (sufficient statistics). However, those ERGMs modeling the more complex features have, to date, been limited to binary data: presence or absence of ties. Thus, analysis of valued networks, such as those where counts, measurements, or ranks are observed, has necessitated dichotomizing them, losing information and introducing biases. In this work, we generalize ERGMs to valued networks. Focusing on modeling counts, we formulate an ERGM for networks whose ties are counts and discuss issues that arise when moving beyond the binary case. We introduce model terms that generalize and model common social network features for such data and apply these methods to a network dataset whose values are counts of interactions. PMID:24678374
Auxiliary Parameter MCMC for Exponential Random Graph Models
NASA Astrophysics Data System (ADS)
Byshkin, Maksym; Stivala, Alex; Mira, Antonietta; Krause, Rolf; Robins, Garry; Lomi, Alessandro
2016-11-01
Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.
Atomic shell structure from the Single-Exponential Decay Detector
Silva, Piotr de; Korchowiec, Jacek; Wesolowski, Tomasz A.
2014-04-28
The density of atomic systems is analysed via the Single-Exponential Decay Detector (SEDD). SEDD is a scalar field designed to explore mathematical, rather than physical, properties of electron density. Nevertheless, it has been shown that SEDD can serve as a descriptor of bonding patterns in molecules as well as an indicator of atomic shells [P. de Silva, J. Korchowiec, and T. A. Wesolowski, ChemPhysChem 13, 3462 (2012)]. In this work, a more detailed analysis of atomic shells is done for atoms in the Li–Xe series. Shell populations based on SEDD agree with the Aufbau principle even better than those obtained from the Electron Localization Function, which is a popular indicator of electron localization. A link between SEDD and the local wave vector is given, which provides a physical interpretation of SEDD.
Predicting jet radius in electrospinning by superpositioning exponential functions
NASA Astrophysics Data System (ADS)
Widartiningsih, P. M.; Iskandar, F.; Munir, M. M.; Viridi, S.
2016-08-01
This paper presents an analytical study of the correlation between viscosity and fiber diameter in electrospinning. Control over fiber diameter in electrospinning process was important since it will determine the performance of resulting nanofiber. Theoretically, fiber diameter was determined by surface tension, solution concentration, flow rate, and electric current. But experimentally it had been proven that significantly viscosity had an influence to fiber diameter. Jet radius equation in electrospinning process was divided into three areas: near the nozzle, far from the nozzle, and at jet terminal. There was no correlation between these equations. Superposition of exponential series model provides the equations combined into one, thus the entire of working parameters on electrospinning take a contribution to fiber diameter. This method yields the value of solution viscosity has a linear relation to jet radius. However, this method works only for low viscosity.
Exponentially small splitting of separatrices beyond Melnikov analysis: Rigorous results
NASA Astrophysics Data System (ADS)
Baldomá, Inmaculada; Fontich, Ernest; Guardia, Marcel; Seara, Tere M.
We study the problem of exponentially small splitting of separatrices of one degree of freedom classical Hamiltonian systems with a non-autonomous perturbation fast and periodic in time. We provide a result valid for general systems which are algebraic or trigonometric polynomials in the state variables. It consists on obtaining a rigorous proof of the asymptotic formula for the measure of the splitting. We obtain that the splitting has the asymptotic behavior Kɛβe, identifying the constants K, β, a in terms of the system features. We consider several cases. In some cases, assuming the perturbation is small enough, the values of K, β coincide with the classical Melnikov approach. We identify the limit size of the perturbation for which this theory holds true. However for the limit cases, which appear naturally both in averaging and bifurcation theories, we encounter that, generically, K and β are not well predicted by Melnikov theory.
Statistical modelling of agrometeorological time series by exponential smoothing
NASA Astrophysics Data System (ADS)
Murat, Małgorzata; Malinowska, Iwona; Hoffmann, Holger; Baranowski, Piotr
2016-01-01
Meteorological time series are used in modelling agrophysical processes of the soil-plant-atmosphere system which determine plant growth and yield. Additionally, long-term meteorological series are used in climate change scenarios. Such studies often require forecasting or projection of meteorological variables, eg the projection of occurrence of the extreme events. The aim of the article was to determine the most suitable exponential smoothing models to generate forecast using data on air temperature, wind speed, and precipitation time series in Jokioinen (Finland), Dikopshof (Germany), Lleida (Spain), and Lublin (Poland). These series exhibit regular additive seasonality or non-seasonality without any trend, which is confirmed by their autocorrelation functions and partial autocorrelation functions. The most suitable models were indicated by the smallest mean absolute error and the smallest root mean squared error.
Non-exponential decay of dark localized surface plasmons.
Ginzburg, Pavel; Zayats, Anatoly V
2012-03-12
It is shown that the decay of the weakly coupled to radiation (dark) modes of subwavelength plasmonic nanostructures is strongly nonexponential. Their lifetime is overestimated by conventional exponential relaxation time obtained in the standard Markovian approximation. These effects are manifestations of the strong dispersion and near-field feedback. The developed theoretical framework introduces an ensemble of local relaxation degrees of freedom coupled to plasmonic mode in order to describe its decay due to material losses. The macroscopic description of the decay process leads to the specific memory function of the system, evaluated from the modal and material dispersions of the plasmonic nanostructure. Proper knowledge of the relaxation behavior is vital for various applications relying on light-matter interactions of emitters with nanoscale objects, such as fluorescence manipulation, bio-imaging, sensing, spasers, sub-diffraction optics, Raman scattering, and quantum optics.
Income inequality in Romania: The exponential-Pareto distribution
NASA Astrophysics Data System (ADS)
Oancea, Bogdan; Andrei, Tudorel; Pirjol, Dan
2017-03-01
We present a study of the distribution of the gross personal income and income inequality in Romania, using individual tax income data, and both non-parametric and parametric methods. Comparing with official results based on household budget surveys (the Family Budgets Survey and the EU-SILC data), we find that the latter underestimate the income share of the high income region, and the overall income inequality. A parametric study shows that the income distribution is well described by an exponential distribution in the low and middle incomes region, and by a Pareto distribution in the high income region with Pareto coefficient α = 2.53. We note an anomaly in the distribution in the low incomes region (∼9,250 RON), and present a model which explains it in terms of partial income reporting.
Exponential protection of zero modes in Majorana islands
NASA Astrophysics Data System (ADS)
Albrecht, S. M.; Higginbotham, A. P.; Madsen, M.; Kuemmeth, F.; Jespersen, T. S.; Nygård, J.; Krogstrup, P.; Marcus, C. M.
2016-03-01
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a ‘Majorana island’) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Exponential protection of zero modes in Majorana islands.
Albrecht, S M; Higginbotham, A P; Madsen, M; Kuemmeth, F; Jespersen, T S; Nygård, J; Krogstrup, P; Marcus, C M
2016-03-10
Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, with the departure from zero expected to be exponentially small as the modes become spatially separated. Following theoretical proposals, several experiments have identified signatures of Majorana modes in nanowires with proximity-induced superconductivity and atomic chains, with small amounts of mode splitting potentially explained by hybridization of Majorana modes. Here, we use Coulomb-blockade spectroscopy in an InAs nanowire segment with epitaxial aluminium, which forms a proximity-induced superconducting Coulomb island (a 'Majorana island') that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometres, sub-gap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometre of increased wire length. For devices longer than about one micrometre, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.
Exponential and power-law mass distributions in brittle fragmentation
NASA Astrophysics Data System (ADS)
Åström, J. A.; Linna, R. P.; Timonen, J.; Møller, Peder Friis; Oddershede, Lene
2004-08-01
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size s scales as s-(2D-1)/Df1(-(2/λ)Ds)+f2(-s0-1(λ+s1/D)D) , where D is the Euclidean dimension of the space, λ is the penetration depth, and f1 and f2 can be approximated by exponential functions. Simulation results and experiments can both be described by this theoretical fragment-size distribution. The typical largest fragment size s0 was found to diverge at the minimum strain required for fragmentation as it is inversely related to the density of initially formed cracks. Our results also indicate that scaling of s0 close to this divergence depends on, e.g., loading conditions, and thus is not universal. At the same time, the density of fragment surface vanishes as L-1 , L being the linear dimension of the brittle solid. The results obtained provide an explanation as to why the fragment-size distributions found in nature can have two components, an exponential as well as a power-law component, with varying relative weights.
Subglacial bedforms reveal an exponential size-frequency distribution
NASA Astrophysics Data System (ADS)
Hillier, J. K.; Smith, M. J.; Clark, C. D.; Stokes, C. R.; Spagnolo, M.
2013-05-01
Subglacial bedforms preserved in deglaciated landscapes record characteristics of past ice-sediment flow regimes, providing insight into subglacial processes and ice sheet dynamics. Individual forms vary considerably, but they can often be grouped into coherent fields, typically called flow-sets, that reflect discrete episodes of ice flow. Within these, bedform size-frequency distributions (predominantly height, width and length) are currently described by several statistics (e.g., mean, median, and standard deviation) that, arguably, do not best capture the defining characteristics of these populations. This paper seeks to create a better description based upon semi-log plots, which reveal that the frequency distributions of bedform dimensions (drumlin, mega-scale glacial lineation, and ribbed moraine) plot as straight lines above the mode (ϕ). This indicates, by definition, an exponential distribution, for which a simple and easily calculated, yet statistically rigorous, description is designed. Three descriptive parameters are proposed: gradient (λ; the exponent, characterising bedforms likely least affected by non-glacial factors), area-normalised y-intercept (β0; quantifying spatial density), and the mode (ϕ). Below ϕ, small features are less prevalent due to i) measurement: data, sampling and mapping fidelity; ii) possible post-glacial degradation; or iii) genesis: not being created sub-glacially. This new description has the benefit of being insensitive to the impact of potentially unmapped or degraded smaller features and better captures properties relating to ice flow. Importantly, using λ, flow sets can now be more usefully compared with each other across all deglaciated regions and with the output of numerical ice sheet models. Applications may also exist for analogous fluvial and aeolian bedforms. Identifying the characteristic exponential and that it is typical of 'emergent' subglacial bedforms is a new and potentially powerful constraint on
Mitigation of Remedial Action Schemes by Decentralized Robust Governor Control
Elizondo, Marcelo A.; Marinovici, Laurentiu D.; Lian, Jianming; Kalsi, Karanjit; Du, Pengwei
2014-04-15
This paper presents transient stability improvement by a new distributed hierarchical control architecture (DHC). The integration of remedial action schemes (RAS) to the distributed hierarchical control architecture is studied. RAS in power systems are designed to maintain stability and avoid undesired system conditions by rapidly switching equipment and/or changing operating points according to predetermined rules. The acceleration trend relay currently in use in the US western interconnection is an example of RAS that trips generators to maintain transient stability. The link between RAS and DHC is through fast acting robust turbine/governor control that can also improve transient stability. In this paper, the influence of the decentralized robust turbine/governor control on the design of RAS is studied. Benefits of combining these two schemes are increasing power transfer capability and mitigation of RAS generator tripping actions; the later benefit is shown through simulations.
Amsler, C D; Cho, M; Matsumura, P
1993-01-01
Motility and chemotaxis allow cells to move away from stressful microenvironments. Motility of Escherichia coli in batch cultures, as measured by cell swimming speed, was low in early-exponential-phase cells, peaked as the cells entered post-exponential phase, and declined into early stationary phase. Transcription from the flhB operon and synthesis of flagellin protein similarly peaked in late exponential and early post-exponential phases, respectively. The increase in swimming speed between early-exponential and post-exponential phases was correlated with twofold increases in both flagellar length and flagellar density per cell volume. This increased investment in flagella probably reflects the increased adaptive value of motility in less favorable environments. The decrease in speed between post-exponential and stationary phases was correlated with a threefold decrease in torque produced by the flagellar motors and presumably reflects decreased proton motive force available to stationary-phase cells. Images PMID:8407796
Robust relativistic bit commitment
NASA Astrophysics Data System (ADS)
Chakraborty, Kaushik; Chailloux, André; Leverrier, Anthony
2016-12-01
Relativistic cryptography exploits the fact that no information can travel faster than the speed of light in order to obtain security guarantees that cannot be achieved from the laws of quantum mechanics alone. Recently, Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015), 10.1103/PhysRevLett.115.030502] presented a bit-commitment scheme where each party uses two agents that exchange classical information in a synchronized fashion, and that is both hiding and binding. A caveat is that the commitment time is intrinsically limited by the spatial configuration of the players, and increasing this time requires the agents to exchange messages during the whole duration of the protocol. While such a solution remains computationally attractive, its practicality is severely limited in realistic settings since all communication must remain perfectly synchronized at all times. In this work, we introduce a robust protocol for relativistic bit commitment that tolerates failures of the classical communication network. This is done by adding a third agent to both parties. Our scheme provides a quadratic improvement in terms of expected sustain time compared with the original protocol, while retaining the same level of security.
NASA Astrophysics Data System (ADS)
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Mañas, Pilar; Mackey, Bernard M
2004-03-01
The relationship between a loss of viability and several morphological and physiological changes was examined with Escherichia coli strain J1 subjected to high-pressure treatment. The pressure resistance of stationary-phase cells was much higher than that of exponential-phase cells, but in both types of cell, aggregation of cytoplasmic proteins and condensation of the nucleoid occurred after treatment at 200 MPa for 8 min. Although gross changes were detected in these cellular structures, they were not related to cell death, at least for stationary-phase cells. In addition to these events, exponential-phase cells showed changes in their cell envelopes that were not seen for stationary-phase cells, namely physical perturbations of the cell envelope structure, a loss of osmotic responsiveness, and a loss of protein and RNA to the extracellular medium. Based on these observations, we propose that exponential-phase cells are inactivated under high pressure by irreversible damage to the cell membrane. In contrast, stationary-phase cells have a cytoplasmic membrane that is robust enough to withstand pressurization up to very intense treatments. The retention of an intact membrane appears to allow the stationary-phase cell to repair gross changes in other cellular structures and to remain viable at pressures that are lethal to exponential-phase cells.
Robust Control Feedback and Learning
2002-11-30
98-1-0026 5b. GRANT NUMBER Robust Control, Feedback and Learning F49620-98-1-0026 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Michael G...Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39.18 Final Report: ROBUST CONTROL FEEDBACK AND LEARNING AFOSR Grant F49620-98-1-0026 October 1...Philadelphia, PA, 2000. [16] M. G. Safonov. Recent advances in robust control, feedback and learning . In S. 0. R. Moheimani, editor, Perspectives in Robust
Robustness surfaces of complex networks
NASA Astrophysics Data System (ADS)
Manzano, Marc; Sahneh, Faryad; Scoglio, Caterina; Calle, Eusebi; Marzo, Jose Luis
2014-09-01
Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the R*-value and introducing the concept of robustness surface (Ω). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.
Stability Analysis of Uncertain Switched Delay Systems: A Time-Varying Lyapunov Function Approach
NASA Astrophysics Data System (ADS)
Huang, Ganji; Luo, Shixian; Chen, Wu-Hua
Exponential stability for switched systems with uncertain parameters and time-varying delay is considered in this paper. The parametric uncertainties are assumed to be time-varying and norm-bounded. By introducing a novel piecewise time-varying Lyapunov function and using Razumikhin techniques, some linear matrix inequalities (LMIs) stability criteria are derived to guarantee the exponential stability of the switched delay systems. A numerical example is presented to demonstrate the effectiveness of the proposed method.
Robust transition control of a Martian coaxial tiltrotor aerobot
NASA Astrophysics Data System (ADS)
Zhao, Wei; Underwood, Craig
2014-06-01
Hyperion is an autonomous solar-electric powered coaxial tiltrotor aerobot proposed to investigate the Isidis Planitia region on Mars. The objective of this paper is to propose a robust control strategy for transition flight between hover and cruise based on the supervisory control method and the linear robust control method. The proposed transition controller has two levels. The lower level is a series of candidate controllers for the subproblems, which are obtained by the operation of divide and conquer. The higher level uses the state variables to determine which lower level candidate controller should be used. The candidate controllers are solved using the μ synthesis and the conventional longitudinal and lateral control loops. The robustness of the candidate controllers is guaranteed by the robust control theory. The stability and robustness of the transition controller is determined by the switch logic in the higher level. The stability of the proposed control strategy is analyzed. A 6 Degree of Freedom simulation with uncertain aerodynamic model is used to show the robustness and the performance of the proposed controller.
Robust hopping based on virtual pendulum posture control.
Sharbafi, Maziar A; Maufroy, Christophe; Ahmadabadi, Majid Nili; Yazdanpanah, Mohammad J; Seyfarth, Andre
2013-09-01
A new control approach to achieve robust hopping against perturbations in the sagittal plane is presented in this paper. In perturbed hopping, vertical body alignment has a significant role for stability. Our approach is based on the virtual pendulum concept, recently proposed, based on experimental findings in human and animal locomotion. In this concept, the ground reaction forces are pointed to a virtual support point, named virtual pivot point (VPP), during motion. This concept is employed in designing the controller to balance the trunk during the stance phase. New strategies for leg angle and length adjustment besides the virtual pendulum posture control are proposed as a unified controller. This method is investigated by applying it on an extension of the spring loaded inverted pendulum (SLIP) model. Trunk, leg mass and damping are added to the SLIP model in order to make the model more realistic. The stability is analyzed by Poincaré map analysis. With fixed VPP position, stability, disturbance rejection and moderate robustness are achieved, but with a low convergence speed. To improve the performance and attain higher robustness, an event-based control of the VPP position is introduced, using feedback of the system states at apexes. Discrete linear quartic regulator is used to design the feedback controller. Considerable enhancements with respect to stability, convergence speed and robustness against perturbations and parameter changes are achieved.
Robust Neural Sliding Mode Control of Robot Manipulators
NASA Astrophysics Data System (ADS)
Hiep, Nguyen Tran; cat, Pham Thuong
2009-03-01
This paper proposes a robust neural sliding mode control method for robot tracking problem to overcome the noises and large uncertainties in robot dynamics. The Lyapunov direct method has been used to prove the stability of the overall system. Simulation results are given to illustrate the applicability of the proposed method
Robustness with observers. [linear optimal feedback control systems
NASA Technical Reports Server (NTRS)
Doyle, J. C.; Stein, G.
1979-01-01
The paper describes an adjustment procedure for observer-based linear control systems which asymptotically achieves the same loop transfer functions (and hence the same relative stability, robustness, and disturbance rejection properties) as full-state feedback control implementations. Full-state loop-transfer properties can be recovered asymptotically if the plant is minimum phase; this occurs at the expense of noise performance.
Robust Neural Sliding Mode Control of Robot Manipulators
Nguyen Tran Hiep; Pham Thuong Cat
2009-03-05
This paper proposes a robust neural sliding mode control method for robot tracking problem to overcome the noises and large uncertainties in robot dynamics. The Lyapunov direct method has been used to prove the stability of the overall system. Simulation results are given to illustrate the applicability of the proposed method.
The exponential eigenmodes of the carbon-climate system
NASA Astrophysics Data System (ADS)
Raupach, M. R.
2012-09-01
Several basic ratios describing the carbon-climate system are observed to adopt relatively steady values. Examples include the CO2 airborne fraction (the fraction of the total anthropogenic CO2 emission flux that accumulates in the atmosphere) and the ratio T/QE of warming (T) to cumulative total CO2 emissions (QE). This paper explores the reason for such near-constancy in the past, and its likely limitations in future. The contemporary carbon-climate system is often approximated as a first-order linear system, for example in response-function descriptions. All such linear systems have exponential eigenfunctions in time (an eigenfunction being one that, if applied to the system as a forcing, produces a response of the same shape). This implies that, if the carbon-climate system is idealised as a linear system (Lin) forced by exponentially growing CO2 emissions (Exp), then all ratios among fluxes and perturbation state variables are constant. Important cases are the CO2 airborne fraction (AF), the cumulative airborne fraction (CAF), other CO2 partition fractions and cumulative partition fractions into land and ocean stores, the CO2 sink uptake rate (kS, the combined land and ocean CO2 sink flux per unit excess atmospheric CO2), and the ratio T/QE. Further, the AF and the CAF are equal. The Lin and Exp idealisations apply approximately (but not exactly) to the carbon-climate system in the period from the start of industrialisation (nominally 1750) to the present, consistent with the observed near-constancy of the AF, CAF and T/QE in this period. A nonlinear carbon-climate model is used to explore how the likely future breakdown of both the Lin and Exp idealisations will cause the AF, CAF and kS to depart significantly from constancy, in ways that depend on CO2 emissions scenarios. However, T/QE remains approximately constant in typical scenarios, because of compensating interactions between emissions trajectories, carbon-cycle dynamics and non-CO2 gases. This theory
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David Albert; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Robust Understanding of Statistical Variation
ERIC Educational Resources Information Center
Peters, Susan A.
2011-01-01
This paper presents a framework that captures the complexity of reasoning about variation in ways that are indicative of robust understanding and describes reasoning as a blend of design, data-centric, and modeling perspectives. Robust understanding is indicated by integrated reasoning about variation within each perspective and across…
Robust, Optimal Subsonic Airfoil Shapes
NASA Technical Reports Server (NTRS)
Rai, Man Mohan
2014-01-01
A method has been developed to create an airfoil robust enough to operate satisfactorily in different environments. This method determines a robust, optimal, subsonic airfoil shape, beginning with an arbitrary initial airfoil shape, and imposes the necessary constraints on the design. Also, this method is flexible and extendible to a larger class of requirements and changes in constraints imposed.
Facial symmetry in robust anthropometrics.
Kalina, Jan
2012-05-01
Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.
Species interactions differ in their genetic robustness
Chubiz, Lon M.; Granger, Brian R.; Segre, Daniel; Harcombe, William R.
2015-04-14
Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S. enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.
NASA Technical Reports Server (NTRS)
Westall, F.; Steele, A.; Toporski, J.; Walsh, M. M.; Allen, C. C.; Guidry, S.; McKay, D. S.; Gibson, E. K.; Chafetz, H. S.
2000-01-01
containing fossil biofilm, including the 3.5 b.y..-old carbonaceous cherts from South Africa and Australia. As a result of the unique compositional, structural and "mineralisable" properties of bacterial polymer and biofilms, we conclude that bacterial polymers and biofilms constitute a robust and reliable biomarker for life on Earth and could be a potential biomarker for extraterrestrial life.
Generalized internal model robust control for active front steering intervention
NASA Astrophysics Data System (ADS)
Wu, Jian; Zhao, Youqun; Ji, Xuewu; Liu, Yahui; Zhang, Lipeng
2015-03-01
Because of the tire nonlinearity and vehicle's parameters' uncertainties, robust control methods based on the worst cases, such as H ∞, µ synthesis, have been widely used in active front steering control, however, in order to guarantee the stability of active front steering system (AFS) controller, the robust control is at the cost of performance so that the robust controller is a little conservative and has low performance for AFS control. In this paper, a generalized internal model robust control (GIMC) that can overcome the contradiction between performance and stability is used in the AFS control. In GIMC, the Youla parameterization is used in an improved way. And GIMC controller includes two sections: a high performance controller designed for the nominal vehicle model and a robust controller compensating the vehicle parameters' uncertainties and some external disturbances. Simulations of double lane change (DLC) maneuver and that of braking on split- µ road are conducted to compare the performance and stability of the GIMC control, the nominal performance PID controller and the H ∞ controller. Simulation results show that the high nominal performance PID controller will be unstable under some extreme situations because of large vehicle's parameters variations, H ∞ controller is conservative so that the performance is a little low, and only the GIMC controller overcomes the contradiction between performance and robustness, which can both ensure the stability of the AFS controller and guarantee the high performance of the AFS controller. Therefore, the GIMC method proposed for AFS can overcome some disadvantages of control methods used by current AFS system, that is, can solve the instability of PID or LQP control methods and the low performance of the standard H ∞ controller.
Robust stability of linear systems: Some computational considerations
NASA Technical Reports Server (NTRS)
Laub, A. J.
1979-01-01
The cases of both additive and multiplicative perturbations were discussed and a number of relationships between the two cases were given. A number of computational aspects of the theory were also discussed, including a proposed new method for evaluating general transfer or frequency response matrices. The new method is numerically stable and efficient, requiring only operations to update for new values of the frequency parameter.
Self-Stabilizing and Efficient Robust Uncertainty Management
2011-10-01
Orientation of Bees. Cambridge, Mass.: The Belknap Press of Harvard University Press. 24 Aristotle, Historia animalium, IX, 40, Becker 624b; modified... University Department of Communication Systems Engineering Ben-Gurion Boulevard Beer-Sheva, Israel 84751 October 2011 Final Report for 15...Segal 5d. PROJECT NUMBER 5d. TASK NUMBER 5e. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Ben Gurion University
Amplitude death in coupled robust-chaos oscillators
NASA Astrophysics Data System (ADS)
Palazzi, M. J.; Cosenza, M. G.
2014-12-01
We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.
Structured Robust Loop shaping control for HIMAT System Using PSO
NASA Astrophysics Data System (ADS)
Kaitwanidvilai, Somyot; Jangwanitlert, Anuwat; Parnichkun, Manukid
2009-01-01
Robust loop shaping control is a feasible method for designing a robust controller; however, the controller designed by this method is complicated and difficult to implement practically. To overcome this problem, in this paper, a new design technique of a fixed-structure robust loop shaping controller for a highly maneuverable airplane, HIMAT, is proposed. The performance and robust stability conditions of the designed system satisfying H∞ loop shaping control are formulated as the objective function in the optimization problem. Particle Swarm Optimization (PSO) technique is adopted to solve this problem and to achieve the control parameters of the proposed controller. Simulation results demonstrate that the proposed approach is numerically efficient and leads to performance comparable to that of the other method.
Predictors of the peak width for networks with exponential links
Troutman, B.M.; Karlinger, M.R.
1989-01-01
We investigate optimal predictors of the peak (S) and distance to peak (T) of the width function of drainage networks under the assumption that the networks are topologically random with independent and exponentially distributed link lengths. Analytical results are derived using the fact that, under these assumptions, the width function is a homogeneous Markov birth-death process. In particular, exact expressions are derived for the asymptotic conditional expectations of S and T given network magnitude N and given mainstream length H. In addition, a simulation study is performed to examine various predictors of S and T, including N, H, and basin morphometric properties; non-asymptotic conditional expectations and variances are estimated. The best single predictor of S is N, of T is H, and of the scaled peak (S divided by the area under the width function) is H. Finally, expressions tested on a set of drainage basins from the state of Wyoming perform reasonably well in predicting S and T despite probable violations of the original assumptions. ?? 1989 Springer-Verlag.
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, W. R.; Moser, D. E.; Suggs, R. M.; Cooke, W. J.
2011-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, eta, is a unique function of velocity with an extremely large variation in the laboratory range of under 6 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from both laboratory impacts and from lunar impact observations. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors. Keywords hypervelocity impact impact flash luminous efficiency lunar impact meteoroid 1
Mutant number distribution in an exponentially growing population
NASA Astrophysics Data System (ADS)
Keller, Peter; Antal, Tibor
2015-01-01
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrück (1943 Genetics 28 491-511) 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to grow exponentially in a deterministic fashion. Proportional to the wild-type population size, mutants arrive randomly and initiate new sub-populations of mutants that grow stochastically according to a supercritical birth and death process. We give an exact expression for the generating function of the total number of mutants at a given wild-type population size. We present a simple expression for the probability of finding no mutants, and a recursion formula for the probability of finding a given number of mutants. In the ‘large population-small mutation’ limit we recover recent results of Kessler and Levine (2014 J. Stat. Phys. doi:10.1007/s10955-014-1143-3) for a fully stochastic version of the process.
Exponential flux-controlled memristor model and its floating emulator
NASA Astrophysics Data System (ADS)
Liu, Wei; Wang, Fa-Qiang; Ma, Xi-Kui
2015-11-01
As commercial memristors are still unavailable in the market, mathematic models and emulators which can imitate the features of the memristor are meaningful for further research. In this paper, based on the analyses of characteristics of the q-φ curve, an exponential flux-controlled model, which has the quality that its memductance (memristance) will keep monotonically increasing or decreasing unless the voltage’s polarity reverses (if not approach the boundaries), is constructed. A new approach to designing the floating emulator of the memristor is also proposed. This floating structure can flexibly meet various demands for the current through the memristor (especially the demand for a larger current). The simulations and experiments are presented to confirm the effectiveness of this model and its floating emulator. Project supported by the National Natural Science Foundation of China (Grant Nos. 51377124 and 51221005), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201337), the Program for New Century Excellent Talents in University of China (Grant No. NCET-13-0457), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2012JQ7026).
Exponential 6 parameterization for the JCZ3-EOS
McGee, B.C.; Hobbs, M.L.; Baer, M.R.
1998-07-01
A database has been created for use with the Jacobs-Cowperthwaite-Zwisler-3 equation-of-state (JCZ3-EOS) to determine thermochemical equilibrium for detonation and expansion states of energetic materials. The JCZ3-EOS uses the exponential 6 intermolecular potential function to describe interactions between molecules. All product species are characterized by r*, the radius of the minimum pair potential energy, and {var_epsilon}/k, the well depth energy normalized by Boltzmann`s constant. These parameters constitute the JCZS (S for Sandia) EOS database describing 750 gases (including all the gases in the JANNAF tables), and have been obtained by using Lennard-Jones potential parameters, a corresponding states theory, pure liquid shock Hugoniot data, and fit values using an empirical EOS. This database can be used with the CHEETAH 1.40 or CHEETAH 2.0 interface to the TIGER computer program that predicts the equilibrium state of gas- and condensed-phase product species. The large JCZS-EOS database permits intermolecular potential based equilibrium calculations of energetic materials with complex elemental composition.
An Exponential Luminous Efficiency Model for Hypervelocity Impact into Regolith
NASA Technical Reports Server (NTRS)
Swift, Wesley R.; Moser, D.E.; Suggs, Robb M.; Cooke, W.J.
2010-01-01
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, Eta is a unique function of velocity with an extremely large variation in the laboratory range of under 8 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from laboratory impacts and from astronomical determinations and scaling factors are estimated. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors
Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions
Ostrovsky, V. N.
2003-07-01
The nonstationary Schroedinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic {approx}1/t time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schroedinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as t{yields}{infinity} in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time t{yields}+0). The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.
Absence of exponential clustering in quantum Coulomb fluids
NASA Astrophysics Data System (ADS)
Alastuey, A.; Martin, Ph. A.
1989-12-01
We show that the quantum corrections to the classical correlations of a Coulomb fluid do not decay exponentially fast for all values of the thermodynamical parameters. Specifically, the ħ4 term in the Wigner-Kirkwood expansion of the equilibrium charge-charge correlations of the quantum one-component plasma is found to decay like ||r||-10. More generally, using functional integration, we present a diagrammatic representation of the ħ expansion of the correlations in a multicomponent fluid with a locally regularized Coulomb potential and Maxwell-Boltzmann statistics. The ħ2n terms are found to decay algebraically for all n>=2. Furthermore, an analysis of the hierarchy equations for the correlations provides upper bounds that are compatible with the findings of the perturbative expansion. Except for the monopole, all higher-order multipole sum rules do not hold, in general, in the quantum system. This violation of the multipole sum rules as well as the related algebraic tails are due to the intrinsic quantum fluctuations that prevent a perfect organization of the screening clouds. This phenomenon is illustrated in a simpler model where the large-distance correlations between two quantum particles embedded in a classical plasma can be exactly computed.
Analysis of preloaded bolted joints under exponentially decaying pressure
Esmailzadeh, E.; Chorashi, M.; Ohadi, A.R.
1996-11-01
Dynamic properties of joints must be considered when designing complex structures. A good deal of investigation has been carried out for a better understanding of the dynamic behavior of mechanical joints. It is suitable initially to identify the parameters of a mechanical joint by using either experimental modal analysis or accurate finite element model, and then predicating the behavior of closure bolting system by means of spring-mass-damper model. The effect of bolt prestress on the maximum bolt displacement and stress has been treated. The loading is assumed to be initially peaked, exponentially decaying internal pressure pulse acting on the closure. The dependence of peak bolt stresses and deflections on the bolt prestress level and system damping is investigated. It has been shown that the derived formulas, if damping is neglected, reduce to those reported in the literature. Furthermore, the damping effect is shown to be most important, especially for large natural frequencies, longer loading duration, and lower levels of prestress. Existence of damping, which results in the reduction of maximum bolt displacement and stress, was shown to be beneficial, especially for longer loading duration. The importance of bolt displacement reduction from the viewpoint of fatigue life, vibration loosening, and sealing, especially for lower values of prestress, has been fully emphasized.
/q-exponential, Weibull, and /q-Weibull distributions: an empirical analysis
NASA Astrophysics Data System (ADS)
Picoli, S.; Mendes, R. S.; Malacarne, L. C.
2003-06-01
In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law ( q-exponential with q>1) controversy.