In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust ag...In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level ( cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the filter are simultaneously optimized through LMI multiobjective optimization.展开更多
This paper investigates the problem of dynamic output-feedback control for a class of Lipschitz nonlinear systems.First,a continuous-time controller is constructed and sufficient conditions for stability of the nonlin...This paper investigates the problem of dynamic output-feedback control for a class of Lipschitz nonlinear systems.First,a continuous-time controller is constructed and sufficient conditions for stability of the nonlinear systems are presented.Then,a novel event-triggered mechanism is proposed for the Lipschitz nonlinear systems in which new event-triggered conditions are introduced.Consequently,a closed-loop hybrid system is obtained using the event-triggered control strategy.Sufficient conditions for stability of the closed-loop system are established in the framework of hybrid systems.In addition,an upper bound of a minimum inter-event interval is provided to avoid the Zeno phenomenon.Finally,numerical examples of a neural network system and a genetic regulatory network system are provided to verify the theoretical results and to show the superiority of the proposed method.展开更多
This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping...This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.展开更多
This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced ...This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua＇s circuits and for obtaining identical behavior between the modified Chua＇s circuit and the R6ssler system.展开更多
This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral s...This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral system with multiple delays is obtained. Uniform asymptotic Lipschitz stability. Obviously, the above system is a generalization of the traditional differential system. The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability. The author uses the method of integral inequality to establish a double stability criterion. As a result, the local stability of differential equations is widely used in theory and practice, such as dynamic systems and control systems.展开更多
文摘In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level ( cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the filter are simultaneously optimized through LMI multiobjective optimization.
基金supported by the Jiangsu Provincial Natural Science Foundation of China(No.BK20201340)the 333 High-level Talents Training Pro ject of Jiangsu Provincethe China Postdoctoral Science Foundation(No.2018M642160)。
文摘This paper investigates the problem of dynamic output-feedback control for a class of Lipschitz nonlinear systems.First,a continuous-time controller is constructed and sufficient conditions for stability of the nonlinear systems are presented.Then,a novel event-triggered mechanism is proposed for the Lipschitz nonlinear systems in which new event-triggered conditions are introduced.Consequently,a closed-loop hybrid system is obtained using the event-triggered control strategy.Sufficient conditions for stability of the closed-loop system are established in the framework of hybrid systems.In addition,an upper bound of a minimum inter-event interval is provided to avoid the Zeno phenomenon.Finally,numerical examples of a neural network system and a genetic regulatory network system are provided to verify the theoretical results and to show the superiority of the proposed method.
文摘This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.
基金supported by the Higher Education Commission of Pakistan through the Indigenous 5000 Ph.D.Fellowship Program(Phase II,Batch II)
文摘This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua＇s circuits and for obtaining identical behavior between the modified Chua＇s circuit and the R6ssler system.
文摘This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral system with multiple delays is obtained. Uniform asymptotic Lipschitz stability. Obviously, the above system is a generalization of the traditional differential system. The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability. The author uses the method of integral inequality to establish a double stability criterion. As a result, the local stability of differential equations is widely used in theory and practice, such as dynamic systems and control systems.
