离散时间系统的滑模控制器设计与仿真研究

针对不确定性离散时间系统,分析和设计了一类变结构控制器。当存在外界干扰和不确定性时,系统状态也是全局有界稳定的。一个新的切换面作为系统的输出信号被提出,特别用来设计滑模控制器。系统状态一旦进入到准滑动模态,就对设备参数变化和外界干扰显示出强的鲁棒性,因为控制器的设计完全考虑了边界层的影响。外推法被用来估计不确定离散时间系统的不确定值。两种方法均有效地消除了系统的抖振,确保了系统的稳定性,且保证了变结构控制系统良好的品质。最后,仿真结果证实了所提出方法的有效性。     

线性离散不确定系统区域极点配置的状态反馈实现方法

研究利用状态反馈对线性离散不确定系统进行区域极点配置的问题。导出了一个由离散代数Ｒｉｃａｔｉ方程表示的对线性离散不确定系统进行区域极点配置的充分条件,并给出了一个通过求解该方程来确定状态反馈增益矩阵的算法。     

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

The research on discrete‐time higher‐order sliding mode has received a considerable attention recently. Systems with unmatched uncertainties are common in practice; however, the existing discrete‐time higher‐order sliding mode control algorithms are designed considering only matched uncertainty. This paper proposes a technique to design discrete‐time higher‐order sliding mode control for an uncertain LTI system in the presence of unmatched uncertainty. The proposed technique is numerically simulated and experimentally validated on an electromechanical rectilinear plant. Various experiments are conducted considering the several operational conditions of electromechanical systems in industries to verify the performance of the proposed controller.     

噪声强度不确定的连续系统的鲁棒采样估计

基于内采产特性讨论噪声强度不确定的连续系统的鲁棒采样估计问题,主要目的是为这类不确定系统设计离散滤波器,使每个状态的估计误差方差不大于预先指定值,从而获得满意的稳态滤波特性,文中首先研究了仅有模型噪声强度不确定时的情形,随后说明当测量噪声强度不确定时可用同样方法进行研究,最后用数值例子说明了本文设计方法的有用性和有效性。     

Disk pole location for uncertain systems through convex optimization

In this paper, a necessary and sufficient condition for disk pole location for uncertain continuous or discrete time systems subject to norm-bounded uncertainty is derived. This condition being convex, the control law design is made through convex optimization. The approach adopted follows the quadratic stabilizability philosophy in the problem of pole placement.     

Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

In this paper, we consider discrete time systems with polytopic time varying uncertainty. We look for a class of parameter dependent Lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter. We show that extending the new discrete time stability condition proposed by de Oliveira et al. (Systems Control Lett. 36 (1999) 135.) to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a Lyapunov function. This allows to check asymptotic stability of the system under study. The obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem.     

一类非线性离散系统模糊控制器的分析和设计

针对一类非线性离散不确定系统,在系统状态不可测的情况下,以T-S模型描述不同状态空间的局部动态区域,并通过中心平均反模糊化、乘积推理、单点模糊化方法得到全局模糊系统模型.基于李亚普诺夫理论和线性矩阵不等式,设计了一种基于观测器的鲁棒控制器,并对离散状态下的此类系统进行了稳定分析.最后通过M ATLAB仿真,证明了该方法的有效性.     

Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.     

线性离散时滞系统鲁棒严格耗散控制

提出线性离散时滞系统的耗散控制问题,研究无记忆状态反馈控制律存在的条件及 相应的控制器设计方法,以使相应的闭环系统渐近稳定,同时具有严格(Q,S,R)-耗散性.进 一步考虑耗散的不确定性,研究不确定系统鲁棒严格耗散控制的分析与综合问题.结果表明, 鲁棒耗散控制器存在的条件和综合问题等价于线性矩阵不等式(LMI)的可解性问题.     

BIBO stability and stabilization of networked control systems with short time‐varying delays

This paper presents a robust control approach to solve the stability and stabilization problems for networked control systems (NCSs) with short time‐varying delays. A new discrete‐time linear uncertain system model is proposed to describe the NCS, and the uncertainty of the network‐induced delay is transformed into the uncertainty of the system matrix. Based on the obtained uncertain system model, a sufficient BIBO stability condition for the closed‐loop NCS is derived by applying the small gain theorem. The obtained stability condition establishes a quantitative relation between the BIBO stability of the closed‐loop NCS and two delay parameters, namely, the delay upper bound and the delay variation range bound. Moreover, design procedures for the state feedback stabilizing controllers are also presented. An illustrative example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

Criteria of robust stability for time-varying 2D Wang–Mitchel differential systems: integral funnel method

Two-dimensional nonlinear systems with parametrical interval uncertainty are studied. Differential geometric extremal deviations method is developed. Its basic elements are integral funnels (IFs) and their boundaries. Extreme matrix-valued functions determining the branches of the boundaries of IFs are synthesised. Typical phase portraits of considered uncertain systems with different oscillatory properties are presented. Analytical criteria of robust stability for different oscillatory classes of uncertain systems are formulated.     

Pole assignment for uncertain systems in a specified disk by statefeedback

This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the “quadratic d stabilizability” concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation     

非匹配的不确定时滞离散系统的滑模控制

针对一类不确定离散时滞系统,研究了其滑模控制问题。所考虑的系统是变时滞的,并且含有非匹配的时变参数不确定项。通过非奇异矩阵变换将其转化为两部分,一部分满足传统的匹配争件;另一部分是非匹配,但是满足范数有界的条件。利用变结构控制方法,设计了满足到达条件的滑模控制器,使系统状态在有限时间内到达滑模面。并且在控制器的作用下保持在滑模面上,从而使系统具有稳定的滑动模态,克服了传统滑模控制方法中不确定项需满足匹配条件的保守性。     

基于LMI方法的网络闭环控制系统离散鲁棒模糊控制

针对网络闭环控制系统中时延和不同步等不确定因素,将时延的不确定性转换为系统状态方程系数矩阵的不确定性,提出了一种新的网络闭环控制系统建模方法———具有时滞的不确定离散模糊T-S模型;并在此模型的基础上,利用并行分布补偿原理和Lyapunov理论及LMI方法,证明了通过状态的静态反馈模糊控制,使闭环系统稳定的充分条件等价于求解一组LMI。仿真示例验证了该控制方法的有效性.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

A notion of possible controllability for uncertain linear systems with structured uncertainty

This paper introduces a notion of possible controllability for a class of uncertain linear systems with structured uncertainty described by averaged integral quadratic constraints. This notion relates to the question of when a state is controllable for some possible value of the uncertainty. The notion of possible controllability is motivated by a desire to extend the theory of minimal realization for linear time invariant systems to the case of uncertain systems with structured uncertainty.     

Robust adaptive control for uncertain systems with discrete and distributed delays

In this paper, a robust adaptive control scheme is proposed for the stabilization of uncertain linear systems with discrete and distributed delays and bounded perturbations. The uncertainty is assumed to be an unknown continuous function with norm-bounded restriction. The perturbation is sector-bounded. Combining with the liner matrix inequality method, neural networks and adaptive control, the control scheme ensures the exponential stability of the closed-loop system for any admissible uncertainty.     

基于模糊专家规则的离散事件辨识及其在交通诱导中的应用

传统离散事件动态系统中的离散事件状态的转换具有不确定性,其不确定性主要来自状态转向发生时刻的不确定性,而所转向的状态一般具有确定性。本文对具有状态转向时刻和转向状态的二重不确定性的离散事件动态系统进行了讨论,用模糊专家系统来对未来状态和状态迁移时刻二重不确定性的离散事件动态系统进行评价,并以智能交通系统中车辆诱导技术为例,说明了此类模糊专家规则的应用价值。本文提出了一种模拟淬火算法,通过模拟物质加温后急剧冷却的过程来求得目标函数的局部极值,以模拟淬火算法的转向概率作为模糊专家系统中的规则选择概率。该方法有效地保证了事件转换的实时性,提高了交通疏导的效率。