Robust Stabilization Problem Research Articles

Robust Output Feedback Stabilization for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delay

This paper investigates the problem of robust exponential stabilization of uncertain discrete-time stochastic neural networks with time-varying delay based on output feedback control. By choosing an augmented Lyapunov–Krasovskii functional, we established the sufficient conditions of the delay-dependent asymptotical stabilization in the mean square for a class of discrete-time stochastic neural networks with time-varying delay. Furthermore, we obtain the criteria of robust global exponential stabilization in the mean square for uncertain discrete-time stochastic neural networks with time-varying delay. Finally, we give numerical examples to illustrate the effectiveness of the proposed results.

Distributed robust stabilization of networked multiagent systems with strict negative imaginary uncertainties

SummaryThis paper deals with the distributed robust stabilization problem for networked multiagent systems with strict negative imaginary (SNI) uncertainties. Communication among agents in the network is modelled by an undirected graph with at least one self‐loop. A protocol based on relative state measurements of neighbouring agents and absolute state measurements of a subset of agents is considered. This paper shows how to design the protocol parameters such that the uncertain closed‐loop networked multiagent system is robustly stable against any SNI uncertainty within a certain set for various different network topologies. Tools from negative imaginary (NI) theory are used as an aid to simplify the problem and synthesise the protocol parameters. We show that a state, input, and output transformation preserves the NI property of the network. Consequently, a necessary and sufficient condition for the transfer function matrix of the nominal closed‐loop networked system to be NI and satisfy a DC gain condition is that multiple reduced‐order equivalent systems be NI and satisfy a DC gain condition simultaneously. Based on the reduced‐order systems, we derive sufficient conditions in an LMI framework which ensure the existence of a protocol satisfying the desired objectives. A numerical example is given to confirm the effectivenesses of the proposed results.

Robust Stabilization of Memristor-based Coupled Neural Networks with Time-varying Delays

The robust stabilization problem of memristor-based coupled neural networks (MNNs) is addressed in this paper. Firstly, the fuzzy model of MNNs is obtained by considering the properties of memristor and corresponding circuit, some predictable assumptions on the boundedness and Lipschitz continuity of activation functions are formulated. Secondly, based on T-S fuzzy theory and Lyapunov-Krasovskii functional method, robust stabilization criteria are derived in form of linear matrix inequalities (LMIs). Finally a numerical example is presented to demonstrate the effectiveness of the proposed robust stabilization criteria, which well supports theoretical results.

On delay-interval-dependent robust stability of LPD discrete-time system with mixed time-varying delays and nonlinear uncertainties

In this work, a delay-interval-dependent robust stability problem for linear parameter dependent (LPD) discrete-time system with discrete and distributed time-varying delays and nonlinear uncertainties is addressed. By adopting combinations of mixed model transformation, various inequality expressions, utilization of zero equations, and new parameter dependent Lyapunov–Krasovskii functional, a new delay-interval-dependent asymptotic stability criterion is derived in the form of linear matrix inequalities. Moreover, an improved delay-interval-dependent asymptotic stability criterion of discrete-time linear system with discrete time-varying delay and nonlinear uncertainties is also achieved. Some numerical examples are also illustrated to exhibit the effectiveness with less conservatism of the proposed stability criterion.

Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays

In this paper, the robust stability problem for a class of uncertain stochastic complex-valued neural networks (USCVNNs) with additive time-varying delays (ATDs) is discussed. By constructing a suitable Lyapunov–Krasovskii functional (LKF), more time delay information is considered. By employing integral inequalities, some delay-dependent stability criteria are derived by converting USCVNNs into an equivalent real-valued uncertain stochastic neural networks. The obtained stability criterion is presented in the form of linear matrix inequalities (LMIs), which can be calculated through MATLAB LMI toolbox. Finally, the validity and feasibility of the proposed method are demonstrated by two numerical examples.

Robust of Interval Dynamic Systems

The frequency and algebraic directions of researches of robust stability are considered. Frequency or Tsypkin-Polyaka’s direction is considered briefly in a survey order. The algebraic or Kharitonov’s direction is considered more more widely, namely basic provisions and results of the Algebraic method of robust stability of interval dynamic systems developed within development algebraic or Kharitonov’s direction of robust stability are presented. Fundamental works of V. L. Kharitonov since issue have caused a huge flow of the publications connected with extreme relevance of the solution of problems of a robustness of systems. So far from a circle of problems of a robustness many issues of robust stability are resolved. Discrete analogs and versions of theorems of Kharitonov are received. Frequency conditions of robust stability are considered and solved in Ya. Z. Tsypkin, B. T. Polyak, Yu. I. Neymark works. However in a problem of robust stability not all issues are so far resolved, especially big contradictions have arisen in a continuous case. Also the tasks considered here for interval matrixes and polyhedrons of matrixes haven’t been solved. In work the theorem like the third theorem of Kharitonov which cancels counterexamples to former known results in this direction is formulated and proved and also on its basis the costal theorem for polyhedrons of matrixes is proved. The new costal theorem also cancels counterexamples for this case. To the main theorem of the considered algebraic method the specifying remark is formulated that in the absence of a full set of four angular polynoms of Kharitonov of a condition of this theorem are necessary, but can be insufficient for stability of system. Determination of angular separate coefficients of a characteristic polynom of system is generally carried out by means of use of methods of nonlinear programming. For a discrete case the discrete analog of the theorem of Kharitonov which is received on the basis of Schur’s theorem is presented. At the same time, the concepts of points and intervals of a variabless used for the theorem of an analog of a continuous case are entered. The algorithm of definition of a robustness of discrete systems is formulated. The main results, the Algebraic method of robust stability developed by the author are illustrated with cancellation of the counterexamples widely known from scientific literature.

Robust stabilisation of fractional-order interval systems via dynamic output feedback: an LMI approach

ABSTRACTThis paper addresses the problem of robust dynamic output stabilisation of FO-LTI interval systems with the fractional order , in terms of linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic output feedback controller that asymptotically stabilises interval fractional-order linear time-invariant (FO-LTI) systems. Sufficient conditions are obtained for designing a stabilising controller with a predetermined order, which can be chosen to be as low as possible. The LMI-based procedures of designing robust stabilising controllers are preserved in spite of the complexity of assuming the most complete model of linear controller, with direct feedthrough parameter. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.

Robust stability and robust stabilizability for periodically switched linear systems

In this paper, the problem of robust stability and robust stabilizability for periodically switched linear systems is studied. The stability radius involving structured perturbations acting on both coefficient matrices and switching moments is introduced and investigated. Some lower bounds for stability radii of periodically switched linear systems are provided. After that, we derive the notion of fast and slow stabilizability for these systems. Some characterizations for robust stabilizability under structured perturbations are established. Several examples are given to illustrate the obtained results.

Stability analysis for uncertain neutral-type stochastic nonlinear systems with mixed time-varying delays

This study investigates the robust stability problem in the presence of uncertain parameters for a class of stochastic neutral-type systems with mixed time-varying delays, where external disturbance and nonlinearity are considered together. The nonlinear function is assumed to satisfy the one-sided Lipschitz condition and the quadratic inner-boundedness condition. By constructing a modified Lyapunov–Krasovskii functional and using the free-weighting matrix technique, some new delay-dependent criteria for the stability of the problem are presented. In particular, the derivatives of the time-varying delays are no longer limited to being less than one. Finally, numerical examples are given to illustrate the effectiveness of the derived results.

Stabilization of uncertain nonlinear discrete-time switched systems with state delays: A constrained robust model predictive control approach

This paper studies the problem of robust stabilization for a class of nonlinear discrete-time switched systems with polytopic uncertainties and unknown state delay. Moreover, the control signal is assumed to be constrained. The objective of the proposed controller is to stabilize the switched system under arbitrary switching signals based on the switched Lyapunov function approach. Therefore, based on the constrained robust model predictive control method and an appropriate Lyapunov–Krasovskii functional, the sufficient conditions to guarantee the asymptotical stability of the switched system are developed as linear matrix inequalities. Through online solving an optimization problem, the predictive state-feedback controller is designed. Furthermore, in this delay-dependent approach, only the upper bound of time-delay should be known. Appropriate transient response, ability to handle constraints, and nonconstrained switching signal are the other advantages of the proposed method. Finally, the performance of the proposed approach is compared with a similar approach through a numerical example. As well as, to show the applicability of the proposed controller, it is applied to a drinking water supply network, as an application example.

An application of forward difference method in robust stability of discrete uncertainty system with delays

This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement technique, two conditions are developed to guarantee the robust stability of a class of discrete systems with uncertainty parameters in terms of the linear matrix inequality (LMI). By applying the forward difference method and via a quadratic cost function, the criteria of LMI are obtained by the input control u(k)=0 and u(k)=Kx(k); meanwhile, the bounds of cost function are established. The feedback control gain is designed to ensure the robust stability of the closed-loop system. A numerical example and simulation figures are provided to illustrate the effectiveness and potential of the proposed techniques and results.

НЕЛИНЕЙНАЯ МОДЕЛЬ СИСТЕМЫ ЭЛЕКТРОПИТАНИЯ ПОГРУЖНЫХ ОБЪЕКТОВ С УЧЕТОМ ИЗМЕНЕНИЯ ДЛИНЫ КАБЕЛЬ-ТРОСА

Актуальность работы определяется необходимостью создания адекватных математических моделей систем электропитания сложного погружного технологического оборудования, например электроцентробежных насосов и автономных подводных аппаратов, получающих энергию переменного тока по достаточно протяженной кабельной линии. Приемлемая адекватность характеристик модели и реальной системы электропитания данного класса объектов может быть достигнута в результате учета изменяемой длины кабельной линии и различных режимов работы погружного оборудования. Использование передаточных функций в качестве промежуточных моделей основных элементов системы электропитания и операторного метода является достаточно приемлемым решением для адекватного отражения процессов изменения напряжения на нагрузке. Далее путем преобразования передаточной функции записывается нелинейная математическая модель системы электропитания в пространстве переменных состояния, которая позволяет аналитическим образом решить задачу робастной стабилизации неизмеряемого напряжения на полезной электромеханической нагрузке. Цель работы: построение нелинейной математической модели системы электропитания с передачей энергии переменного тока по кабель-тросу с учетом изменения его длины в пространстве переменных состояния. Методы: операторный метод, методы пространства состояния и математического моделирования. Результаты. Разработана методика определения параметров устройства компенсации реактивной мощности в кабель-тросе для увеличения его пропускной способности при передаче мощности на дальние расстояния при повышенной частоте. Определена аналитическая зависимость, позволяющая рассчитать индуктивность компенсирующего устройства во всем диапазоне изменения длины кабель-троса. Для построения оптимального регулятора получены полиномы, позволяющие определять коэффициенты передаточных функций при изменении длины кабеля и сопротивления нагрузки системы электропитания. На основании передаточных функций, полученных для различных режимов работы системы электропитания, определены параметры схемы замещения, позволяющей записать нелинейную математическую модель системы электропитания пониженного порядка. Проведена сравнительная оценка результатов моделирования системы электропитания с передачей энергии переменного тока по кабель-тросу, подтверждающая возможность ее описания моделью пониженного порядка в пространстве состояний. Выводы. В работе предложена методика определения параметров устройства компенсации реактивной мощности, позволяющего увеличить пропускную способность кабель-троса. На основании передаточных функций, коэффициенты которых зависят от длины кабель-троса, записана упрощенная нелинейная математическая модель системы электропитания погружного технологического оборудования. В результате полученная модель системы электропитания может быть использована для последующего синтеза оптимального регулятора напряжения в классе нелинейных систем управления.

Evaluation of the Weighted Level of Damping of Bounded Disturbances in Descriptor Systems

We establish necessary and sufficient conditions for the realization of the upper bounds in the performance criteria for linear descriptor systems characterizing the weighted level of damping of the external and initial disturbances. The verification of these conditions is reduced to the solution of matrix equations and inequalities. The main statements are formulated with an aim of their subsequent application in the problems of robust stabilization and H∞-optimization of descriptor control systems.

Intelligent Critic Control With Robustness Guarantee of Disturbed Nonlinear Plants.

In this paper, the author focuses on establishing an intelligent critic control framework with robustness guarantee for disturbed nonlinear systems. Combining the neural network learning ability with adaptive critic designs, a general structure of intelligent critic control is developed to address the robustness problems, which broadens the application scope of adaptive dynamic programming and the related learning control methods. First, the problem transformation is conducted for changing the robust stabilization problem into optimal control design, where a special discounted cost function is well defined. Then, a recurrent neural network is constructed to learn the unknown nominal plant with stability proof. Moreover, the critic network implementation is presented with the help of the obtained neural identifier and the adaptive learning architecture. In addition, extension discussions and several simulation examples are provided to display the robustness verification results of the intelligent critic strategy.

Robust bounds for fractional-order systems with uncertain order and structured perturbations via Cylindrical Algebraic Decomposition method

This paper considers the robust stability problem of fractional-order systems with uncertain order and structured perturbations. A stability check procedure is proposed for determining the robust bounds of uncertain order and other uncertain parameters for fractional-order systems.The results are obtained in terms of Cylindrical Algebraic Decomposition which is first used for analyzing the robust stability problem of fractional-order systems with uncertain order. The method is non-conservative for fractional-order systems with the uncertain order α satisfying 0 < α < 2. Examples are given to demonstrate the effectiveness of proposed approach.

Robust Finite-Time Stabilizers for a Connected Chain of Nonlinear Double-Integrator Systems

In this paper, the robust finite-time stabilization problem is addressed for a wide group of fully actuated nonlinear systems containing dependent double-integrator subsystems in the presence of unbounded uncertainties. Based on the nonsingular terminal sliding mode control, three types of stabilizers are proposed to steer the system states to zero within adjustable convergence finite times. Moreover, several inequalities are obtained to determine the conservative upper bounds for these convergence finite times. To clarify the applicability of the suggested stabilization methods, a finite-time tracking problem for robotic manipulators is discussed and handled by applying three introduced stabilizers. Finally, a numerical simulation related to this tracking problem is provided.

Data-Driven Robust Control of Discrete-Time Uncertain Linear Systems via Off-Policy Reinforcement Learning.

This paper presents a model-free solution to the robust stabilization problem of discrete-time linear dynamical systems with bounded and mismatched uncertainty. An optimal controller design method is derived to solve the robust control problem, which results in solving an algebraic Riccati equation (ARE). It is shown that the optimal controller obtained by solving the ARE can robustly stabilize the uncertain system. To develop a model-free solution to the translated ARE, off-policy reinforcement learning (RL) is employed to solve the problem in hand without the requirement of system dynamics. In addition, the comparisons between on- and off-policy RL methods are presented regarding the robustness to probing noise and the dependence on system dynamics. Finally, a simulation example is carried out to validate the efficacy of the presented off-policy RL approach.

Robust analysis of discrete time noises for stochastic systems and application in neural networks

ABSTRACT Robust analysis in the stochastic sense, including robust boundedness and robust stability, has become a momentous problem of stochastic systems. Up to now, almost all existing works about robust boundedness and robust stability require that stochastic perturbations are rooted in continuous time observations of systems states. However, compared with the continuous time noises case, stochastic perturbations of discrete time noises are not only appropriate but also reasonable. Hence, this brief proposes and explores the problems of robust boundedness and robust stability of discrete time noises for stochastic systems satisfying the linear growth condition. The destination of this brief is to answer the question: how much stochastic perturbations of discrete time noises can a bounded or stable system tolerate guaranteeing stochastically perturbed system remains asymptotically bounded or stable. In addition, this brief discusses the application of our results in neural networks.

Global robust practical output regulation for nonlinear systems in output feedback form by output‐based event‐triggered control

SummaryIn this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems.

Robust Stabilization of Discrete‐Time Switched Periodic Systems with Time Delays

This paper studies the problems of robust stability and robust stabilization for discrete‐time switched periodic systems with time‐varying delays and parameter uncertainty. We obtain the novel sufficient conditions to ensure the switched system is robustly asymptotically stable in terms of linear matrix inequalities. To obtain these conditions, we utilize a descriptor system method and introduce a switched Lyapunov‐Krasovskii functional. The robust stability results are then extended to solve problems of robust stabilization via periodic state feedback. Novel sufficient conditions are established to ensure that the uncertain switched periodic system is robustly asymptotically stabilizable. Finally, we give two numerical examples to illustrate the effectiveness of our method.