Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

基于模糊模型的不确定非线性系统鲁棒D 镇定

针对 T- S模糊模型描述的不确定非线性系统 ,应用二次 D-稳定概念 ,对给定复平面上的某一D域提出模糊系统全局鲁棒 D-稳定的充分条件 ,基于并行分布补偿 (PDC)技术 ,各局部状态反馈镇定控制器设计归结于解一组耦合线性矩阵不等式 (L MI) ,全局控制器通过隶属度函数由各局部控制器混合而成 ,并以此保证整个系统的鲁棒 D-稳定性。最后用质量弹簧阻尼系统给出了仿真示例。     

计及随机传感器时滞的不确定半Markov跳变系统鲁棒滑模控制

在实际系统中,系统参数与结构随机变化、未知外界干扰、传感器时滞等现象时有发生并严重影响了系统的稳定运行.为了解决这一问题,本文提出计及随机传感器时滞的一类不确定半Markov跳变系统鲁棒滑模控制方法,其中系统的传感器时滞通过使用Bernoulli随机分布进行描述.考虑系统状态信息不可测量条件下,文章设计模态依赖Luenberger观测器去估计半Markov跳变系统的运行状态.然后,本文构造一个积分滑模面并借助随机Lyapunov理论,提出两种半Markov跳变系统的随机稳定性分析方法.进而,文章提出基于观测器的滑模控制方法使得系统状态能够在有限时间内到达滑模面上以及滑模动态在H_∞性能指标γ下是随机稳定的.最后,通过一种基于他励直流电动机模型的数值仿真例子验证所设计的滑模控制方法的有效性与正确性.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

时延不确定离散时间系统的鲁棒跟踪控制

研究一类时延不确定离散时间系统的鲁棒跟踪控制问题．基于线性矩阵不等式(LMI)的控制方法，设计无记忆反馈控制器，构造了适用于时延不确定离散时间系统的Lyapunov函数．通过求解一个LMI便可得到控制器的增益矩阵，从而使系统的状态变量渐近跟踪预先设定的轨迹．仿真示例说明所提出的鲁棒跟踪控制算法是有效的．     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.     

Stability of uncertain piecewise affine systems with time delay: delay-dependent Lyapunov approach

This article addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMIs) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the article are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time delay systems. Numerical examples are presented to show the effectiveness of the approach.     

Robust H2 guaranteed cost fuzzy control for uncertain discrete‐time fuzzy systems via poly‐quadratic Lyapunov functions

In this paper, new approaches regarding H₂ guaranteed cost stability analysis and controller synthesis problems for a class of discrete‐time fuzzy systems with uncertainties are investigated. The state‐space Takagi‐Sugeno fuzzy model with norm‐bounded parameter uncertainties is adopted. Based on poly‐quadratic Lyapunov functions, sufficient conditions for the existence of the robust H₂ fuzzy controller can be obtained in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design a suboptimal fuzzy controller which minimizes the upper bound on the quadratic cost function. The effectiveness of the proposed design approach is illustrated by two examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralized tracking control for linear uncertain interconnected systems with time delays

This paper investigates the robust output tracking problem for a class of large‐scale linear uncertain systems with interactions and time delays. Time delays exist in both states and controls. Using the Riccati equation, a procedure for determining decentralized linear control laws is presented such that the closed‐loop system asymptotically tracks the reference output and rejects any constant but unknown disturbances. The main feature of this approach is that the uncertain systems may contain time delays in both states and controls as well as in interactions between subsystems. A numerical example is included to show the results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Simultaneous fault estimation and fault-tolerant tracking control for uncertain nonlinear discrete-time systems

This paper deals with simultaneous fault estimation and control for a class of nonlinear systems with parameter uncertainty, which is described by Takagi–Sugeno (T–S) fuzzy model with parameter uncertainties and unknown disturbance. In this paper, a fuzzy reference model is used to generate error dynamic for tracking control. By considering actuator fault as an auxiliary state vector, we construct an augmented error system and propose a fault estimator/controller to achieve simultaneous fault estimation and fault-tolerant tracking control. H_∞ approach is used in the design of estimator/controller to attenuate the effect of the unknown disturbance and parameter uncertainties. The design conditions are formulated into a set of linear matrix inequalities (LMIs), which can be efficiently solved. Finally, a pitch-axis nonlinear missile model is used to illustrate the effectiveness of the proposed method.     

Robust L1 output tracking control for uncertain networked control systems described by T-S fuzzy model with distributed delays

This paper concentrates on investigating the robust L₁ output tracking control problem for the networked control systems described by Takagi–Sugeno fuzzy model with distributed delays and uncertainties. First, according to the parallel distributed compensation and Lyapunov theory, a fuzzy delay-dependent and basis-dependent Lyapunov–Krasovskii function that contributes to reducing the conservatism is constructed. Second, the L₁ performance criterion guaranteeing the asymptotic stability of the corresponding tracking control system and satisfying the prescribed tracking performance is derived. Furthermore, the output tracking control problem is converted into a convex optimisation problem. Finally, the results from simulation certify the effectiveness of the designed controller.     

Robust nonlinear variable selective control for networked systems

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi–Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H₂ performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.     

Exponential stability and stabilisation of fuzzy time-varying delay systems

This article presents new exponential stability and stabilisation conditions for Takagi–Sugeno fuzzy time-varying delay systems. Based on an improved Lyapunov–Krasovskii functional, the exponential stability and stabilisation conditions are derived in terms of linear matrix inequalities, which allows one to compute simultaneously the two bounds that characterise the exponential stability rate of the solution. Finally, some numerical examples are given to illustrate the effectiveness of the proposed conditions.     

不确定时滞混沌系统的鲁棒控制

针对不确定时滞混沌系统中不稳定不动点的控制需要，应用线性矩阵不等式（LMI）方法，得到了系统存在时滞反馈控制器的充分条件，并利用该控制器对系统中存在的不稳定周期轨道的跟踪问题进行研究。数值仿真结果表明了该方法的有效性。     

Robust tracking control for a class of flexible-joint time-delay robots using only position measurements

In this paper, robust tracking control is investigated for a class of uncertain flexible-joint robots with time delays and time-varying perturbations. By employing the Lyapunov--Krasovskii functional technique and backstepping design technique, a novel robust tracking control scheme using only position measurements is developed such that all the states and signals of the closed-loop flexible-joint time-delay robot system remain bounded and the tracking error can asymptotically converge to a small neighbourhood around the origin. By appropriately choosing the weighting gains in the Lyapunov–Krasovskii functionals, the circular phenomenon in the controller design is overcome. Due to suitably designing the velocity observer and the virtual control input, the link-side dynamics does not need to be incorporated into the actuator-side tracking error dynamics, and so the complexity in the backstepping design is avoided. Consequently, we can easily construct the Lyapunov–Krasovskii functionals, and, in turn, the robust tracking control scheme developed here is a linear time-varying controller and can be simply implemented. Simulation examples are provided to verify the effectiveness of the proposed control algorithm.     

Robust stabilization for uncertain discrete singular systems with state delay

The robust stabilization problem for uncertain discrete singular time‐delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay‐dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay‐independent and delay‐dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust H-infinity reliable control for a class of nonlinear uncertain neutral delay systems

This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI) such that the plant satisfies robust H-infinity performance for all adnfissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.     

双入双出延迟系统模型辅助自抗扰控制研究

本文针对一类双入双出时延系统进行了模型辅助自抗扰控制设计.通过静态解耦矩阵矩阵可以将双入双出系统解耦,同时两回路间的干扰作为"总扰动"的一部分,可以由模型辅助的扩张状态观测器进行估计补偿.将可以获得的模型信息加入到控制器中,可以减少状态观测器的估计负担和相应的带宽需求,从而提高系统抗干扰以及时延的能力.本文通过对3种典...