Global tracking of nonlinear systems with simultaneous unknown time‐varying state and input delays

This paper presents the design of a robust control law for a class of nonlinear dynamical systems subjected to parametric uncertainty and simultaneous unknown, variable state and input delays. A novel controller is developed, which consists of a filtered tracking error and the integral of previous values of control input where the limits of integration are dependent on the known bound of the input delay. Lyapunov‐Krasovskii functionals–based stability analysis guarantees a global uniformly ultimately bounded tracking result where sufficient conditions on controller gains and maximum allowable delay are derived. The performance and robustness of the controller are evaluated by simulation on a two‐link robot manipulator for different combinations of time‐varying state and input delays.     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

带有状态和输入时滞的不确定广义系统的鲁棒预测控制

针对一类同时具有状态和输入时滞的不确定广义系统, 研究其鲁棒预测控制问题, 给出了鲁棒预测控制器的综合方法. 运用Lyapunov稳定性理论和线性矩阵不等式方法, 近似求解无穷时域二次性能指标优化问题, 从而得到鲁棒预测控制器存在的充分条件和显式表达式. 证明了优化问题在初始时刻的可行解, 可以保证广义闭环时滞系统是渐近稳定且正则无脉冲的. 仿真算例验证了所提出方法的有效性.     

灰色随机线性时滞系统的渐近稳定性

首先提出了灰色随机线性时滞系统及其渐近稳定性的概念;然后,利用矩阵理论和随机微分时滞方程解的渐近收敛定理及李雅普诺夫函数,研究了灰色随机线性时滞系统的渐近稳定性,得到了随机淅近稳定的几个充分性条件;最后,通过数值例子说明了所得结果在实际应用中的方便性和有效性.     

Output feedback stabilization of stochastic feedforward nonlinear systems with input and state delay

This paper considers the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with input and state delay. Under a set of coordinate transformations, we first design a linear output feedback controller for a nominal system. Then, with the aid of feedback domination technique and an appropriate Lyapunov–Krasovskii functional, it is proved that the proposed linear output feedback controller can drive the closed‐loop system globally asymptotically stable in probability. Copyright © 2015 John Wiley & Sons, Ltd.     

Sliding mode control for a class of nonlinear It ô stochastic systems with state and input delays

This paper deals with the problem of sliding mode control (SMC) for a class of nonlinear stochastic systems. The nonlinear uncertainties are unknown and unmatched. There exist state and input delays. A special switching function is designed such that the insensitivity of the system can be guaranteed throughout the entire response of the system from the initial time instance. Both the sliding surface and the sliding mode controller exist if a set of matrix inequalities is feasible. A simulation example is given to illustrate the proposed method. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il lee. The research was partially supported by NNSF under Grant (60674015, 60674089), the Technology Innovation Key Foundation of Shanghai Municipal Education Commission (09ZZ60), Shanghai Leading Academic Discipline Project (B504), China. Yugang Niu received the Ph.D. degree in Control Theory and Control Engineering Automation from Nanjing University of Science and Technology in 2001. His research interests include nonlinear control, stochastic control systems, sliding mode control and network congestion control. Bei Chen received the B.S. degree in Automation from East China University of Science & Technology in 2008. Her current research areas are sliding mode control, and networked control systems. Xingyu Wang received the Ph.D. degree in Industrial Automation from the East China Chemical Institute in 1984. His current research areas primarily cover control theory and applications, intelligent control, and brain control with its wide range of applications.     

Simultaneous compensation of input and state delays for nonlinear systems

The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.     

Output feedback stabilization for a class of stochastic non‐linear systems with delays in input

In this paper, constructive techniques are developed for a class of stochastic non‐linear systems with delays in input. Non‐linear terms considered in this paper are more general than those satisfying linear growth conditions. The purpose is to design an output feedback controller such that the resulting closed‐loop system is globally asymptotically stable in probability. The desired output feedback controller is explicitly constructed using the Lyapunov method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A delay decomposition approach to delay‐dependent stability for linear systems with time‐varying delays

This paper is concerned with delay‐dependent stability for linear systems with time‐varying delays. By decomposing the delay interval into multiple equidistant subintervals, on which different Lyapunov functionals are chosen, and new Lyapunov‐Krasvskii functionals are then constructed. Employing these new Lyapunov‐Krasvskii functionals, some new delay‐dependent stability criteria are established. The numerical examples show that the obtained results are less conservative than some existing ones in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust predictive extended state observer for a class of nonlinear systems with time-varying input delay

ABSTRACT

This paper deals with asymptotic stabilisation of a class of nonlinear input-delayed systems via dynamic output feedback in the presence of disturbances. The proposed strategy has the structure of an observer-based control law, in which the observer estimates and predicts both the plant state and the external disturbance. A nominal delay value is assumed to be known and stability conditions in terms of linear matrix inequalities are derived for fast-varying delay uncertainties. Asymptotic stability is achieved if the disturbance or the time delay is constant. The controller design problem is also addressed and a numerical example with an unstable system is provided to illustrate the usefulness of the proposed strategy.     

Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties

This paper presents a new robust sliding mode control （SMC） method with well-developed theoretical proof for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise （Wiener process）. The key features of the proposed method are to apply singular value decomposition （SVD） to all structural uncertainties and to introduce adjustable parameters for control design along with the SMC method. It leads to a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems via linear matrix inequality （LMI） forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1. Furthermore, it is theoretically proved that the proposed method with the SVD and adjustable parameters is less conservatism than the method without the SVD. The paper is mainly to provide all strict theoretical proofs for the method and results.     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

Guaranteed cost control of discrete-time uncertain systems with both state and input delays

The paper proposes a guaranteed cost feedback control for discrete-time uncertain systems with both state and input delays. The delays are assumed to be time-varying and bounded. In addition to norm-bounded parametric uncertainties, the class of admissible uncertainties and nonlinearities of the system comprehend several types of uncertainties frequently investigated in the literature. Using some recent developments, new sufficient conditions for the existence of the guaranteed cost control are given by bilinear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed method.     

具有多状态和控制时滞的控制系统的绝对稳定性分析

基于线性矩阵不等式方法, 对具有多个状态和控制的时变时滞的Lurie型控制系统的稳定性进行分析, 得到了系统绝对稳定的几个充分条件, 这些条件用线性矩阵不等式表示, 具有较低的保守性. 最后通过一个实例验证了所得条件的保守性较以往结果的保守性小.     

Robust stabilization of uncertain systems with unknown input delay

This paper is concerned with the robust controller design for uncertain input-delayed systems. The time delay is assumed to be an unknown constant. A controller with delay feedback for the robust stabilization of the system is proposed. The stability criterion of the closed-loop system is derived in terms of linear matrix inequalities (LMIs). Examples show that in many cases our method can give less conservative results than those by the existing methods. Moreover, for the same cases, our controllers have lower feedback gains than the existing ones.     

Unbalance compensation for AMB systems with input delay: An output regulation approach

Unbalance compensation is an important technique for reducing rotor vibration in high speed rotating machines caused by residual rotor unbalance. As rotating machines in remote applications aim for higher speeds to gain efficiency and to reduce footprint, there is a need to extend the unbalance compensation techniques to active magnetic bearing (AMB) systems with delays in the control loop. This paper investigates the unbalance compensation problem for AMB systems with input delays. An unbalance compensation method is developed based on a solution to the output regulator problem for systems with input delay. The proposed unbalance compensation method is verified through simulation, and experimentally validated on an AMB test rig.     

Finite-time stability theorem of stochastic nonlinear systems

A new concept of finite-time stability, called stochastically finite-time attractiveness, is defined for a class of stochastic nonlinear systems described by the Itô differential equation. The settling time function is a stochastic variable and its expectation is finite. A theorem and a corollary are given to verify the finite-time attractiveness of stochastic systems based on Lyapunov functions. Two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper.     

Reliable stabilization of stochastic time-delay systems with nonlinear disturbances

This paper is concerned with the stabilization problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures. Both the stability analysis and synthesis problems are considered. The purpose of the stability analysis problem is to derive easy-to-test conditions for the uncertain nonlinear time-delay systems to be stochastically, exponentially stable. The synthesis problem, on the other hand, aims to design state feedback controllers such that the closed-loop system is exponentially stable in the mean square for all admissible uncertainties, nonlinearities, time-delays and possible actuator failures. It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed design method.     

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, the stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities （LMIs）, which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.