基于连续故障模型的Delta算子系统可靠鲁棒H_∞控制

研究具有执行器故障的Delta算子线性不确定系统的可靠鲁棒H_∞问题.设计控制器,确保在执行器发生故障时闭环系统仍能保持鲁棒稳定,且满足给定的H_∞指标.针对执行器连续故障模型,运用线性矩阵不等式方法,得到Delta算子系统α-次优可靠鲁棒H_∞状态反馈控制器的存在条件和设计方法,并进一步给出了Delta算子系统最优可靠鲁棒H_∞控制器的设计方法.数值算例表明,该设计方法是有效而可行的.

Abstract：

The reliable robust H_∞ control problem is studied for the Delta operator systems with actuator failure.The purpose is to design a controller which can tolerate actuator failures,such that the Delta operator closed-loop system is asymptotic stable for all admissible uncertainties,and the H_∞-performance index of the closed-loop system is less than a given upper bound.A more practical model of actuator failure,continuous failure model,is considered.A sufficient condition for the existence of the state feedback α-suboptimal reliable robust H_∞ controllers is derived by using the linear matrix inequality approach.Then the design procedures of such controllers and optimal reliable robust H_∞ controllers are proposed respectively.A numerical example demonstrates the effectiveness and feasibility of the design methods.     

Robust backstepping for the Euler approximate model of sampled-data strict-feedback systems

Stabilization of uncertain sampled-data strict-feedback systems is addressed. The stability study is carried out on the Euler approximation of the exact discretized model of the plant. Firstly, a class of state-feedback controllers is developed that guarantees an input-to-state stability property for the closed-loop system. Additionally, assuming some hypotheses on the uncertain terms hold, a practical asymptotic stability property is ensured by designing an appropriate class of controllers.     

Solvability of static output-feedback stabilization for LTI positive systems

This paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative. The synthesis of static output-feedback controllers that ensure the positivity and asymptotic stability of the closed-loop system is investigated. It is shown that this important problem is completely solved for single-input and single-output positive systems. The proposed approach can be applied to multi-input positive systems with controllers having one rank gains. All the provided conditions are necessary and sufficient and can be solved in terms of Linear Programming.     

使用多控制器结构的可靠镇定

采用因子化方法研究了具有强镇定被控对象的可靠镇定问题.证明了几种可靠镇定 问题定义之间的等价关系,并表征了可靠控制器的结构.给出了对于任意给定的控制器,存在 另一个控制器使其共同解决可靠镇定问题的充要条件,该条件提供了一种选择可靠控制器的 方法.     

基于LMI的大型互联线性系统的分散有限时间镇定

借助于有限时间稳定性的定义,针对大型互联线性系统,引入了分散有限时间镇定的概念.对一类大型互联线性系统进行分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式(LMI)的方法提出一个充分条件,当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.仿真算例说明了所得结论的可行性和有效性.     

基于线性矩阵不等式的参数不确定性关联模糊大系统的分散鲁棒镇定

讨论了参数不确定性关联模糊大系统的分散鲁棒镇定问题,所考虑的参数不确定性满足范数有界条件.基于李雅普诺夫稳定性理论及大系统分散控制理论,采用分散化PDC(parallel distributed compensation)控制器,给出了保证该关联模糊大系统闭环渐近稳定的LMI形式的充分条件,通过MATLAB软件中的LMI工具箱可求解出这些LMI中的控制器参数.仿真例子说明了所提方法的有效性.     

导数反馈下闭环广义系统的稳定性

针对导数反馈下闭环广义系统的稳定性问题,利用一种受限等价意义下的矩阵束分解[5],首先给出在不同动态阶(从最小到最大阶)下消除脉冲行为的充分条件.并根据各种动态阶,分别给出导数反馈控制器的设计方法.进而给出导数反馈下闭环广义系统稳定及局部导数反馈下闭环广义关联大系统的分散稳定的充分条件.最后用数值算例来验证所给结果的有效性.     

Reliable stabilization with integral action in decentralized control systems

Reliable stabilization with integral action is studied in a linear, time-invariant, multi-input, multi-output, two-channel decentralized control system, where the plant is stable. The objective is to achieve closed-loop stability when both controllers act together and when each controller acts alone. Necessary and sufficient conditions are obtained for existence of block-diagonal decentralized controllers that ensure reliable stabilization, and integral action and all such decentralized controllers are parametrized. Explicit controller design approaches are discussed for the case of square channels.     

传感器失效下不确定离散时滞系统的静态输出反馈鲁棒可靠保成本控制

针对一类参数不确定离散时滞系统,研究了当传感器发生增益故障情况下的静态输出反馈保成本可靠控制器设计问题.系统中的参数不确定性满足广义匹配条件,传感器元件具有部分输出增益故障.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了含有时滞记忆和无时滞静态输出反馈保成本鲁棒可靠控制律的存在条件.通过求解由一组线性矩阵不等式所表示的凸优化问题可以得到使得闭环保成本上界最小的鲁棒可靠控制器.最后通过仿真示例说明所提出方法的正确性.     

Reliable control using redundant controllers

This paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant. The resulting closed-loop control system is reliable in the sense that it provides guaranteed internal stability and H_∞ performance (in terms of disturbance attenuation), not only when all controllers are operational but also when some controller outages (sensor and/or actuator) occur. A numerical example is given to illustrate the proposed design procedures     

Handling communication disruptions in distributed model predictive control

In this work, we study distributed model predictive control (DMPC) of nonlinear systems subject to communication disruptions - communication channel noise and data losses - between distributed controllers. Specifically, we focus on a DMPC architecture in which one of the distributed controllers is responsible for ensuring closed-loop stability while the rest of the distributed controllers communicate and cooperate with the stabilizing controller to further improve the closed-loop performance. To handle communication disruptions, feasibility problems are incorporated in the DMPC architecture to determine if the data transmitted through the communication channel is reliable or not. Based on the results of the feasibility problems, the transmitted information is accepted or rejected by the stabilizing MPC. In order to ensure the stability of the closed-loop system under communication disruptions, each model predictive controller utilizes a stability constraint which is based on a suitable Lyapunov-based controller. The theoretical results are demonstrated through a nonlinear chemical process example.     

Reliable decentralized integral-action controller design

Reliable stabilizing controller design with integral-action is considered for linear time-invariant, multi-input-multi-output decentralized systems with stable plants. Design methods are proposed to achieve reliable closed-loop stability with integral-action in each output channel for asymptotic tracking of step-input references applied at each input. The design approaches guarantee stability and integral-action in the active channels when all controllers are operational and when any of the controllers is set equal to zero due to failure     

Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.     

Reliable nonlinear control system design using duplicated control elements

Reliable L₂ gain bounding (i.e., H_∞) controllers for nonlinear systems are designed by using redundant control elements. One sensor and one actuator are duplicated, and the resulting closed-loop system is reliable with respect to both the single contingency case and the primary contingency case. The design procedures for reliable controllers are developed by using the Hamilton–Jacobi inequalities from nonlinear H_∞ control theory. Linear reliable controller design methods are also obtained by restricting the proposed nonlinear methods to the linear case, and the linear methods are found to be less conservative than existing methods for linear reliable controller design. Examples are given to illustrate the design procedures for both linear and nonlinear reliable controllers and the advantages of the proposed linear method over existing ones. © 1997 by John Wiley & Sons, Ltd.     

一类不确定切换系统的鲁棒状态反馈镇定

研究了一类扰动项不满足匹配条件的不确定切换系统的鲁棒镇定问题.在每个子系统均不能镇定的情况下,利用完备性条件和多李雅普诺夫函数方法,分别得到了不确定切换系统可镇定的充分条件.状态矩阵和控制输入矩阵同时带有时变、未知且有界的不确定性,基于凸组合技术和LMI方法,设计出鲁棒状态反馈控制器及相应的切换策略,使得闭环系统在其平衡点处是渐近稳定的.最后仿真结果表明所设计的控制器及切换策略的正确有效性.     

Simultaneous stabilization with near-optimal model reference tracking

In this paper we consider the use of linear time-varying controllers for simultaneous stabilization and performance. We prove that for every finite set of plants, we can design a linear time-varying controller which provides not only closed-loop stability, but also near-optimal model reference tracking.     

Lur'e系统镇定问题的非线性控制器设计

本语文研究了用Ｌｕｒ‘ｅ多非线性系统描述的被控对象的镇定问题,把问题的可解笥归结到特殊的多线性矩阵不等式的的可解性,非线笥状态反馈和输出反馈控制器的设计分别依赖于一个双线性和三个三线性矩阵不等式的解,给出了基于线性矩阵不等式的交替寻优算法的设计步骤。     

Distributed optimal control of multiple systems

This article considers distributed optimal control of multiple linear systems. Distributed approximately optimal controllers are proposed for each system with the aid of communications between systems. The proposed controllers make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers if the communication digraph is strongly connected. If the communication digraph is switching and there are communication delays, the proposed controllers also make the states of the closed-loop systems exponentially converge to the states of the closed-loop systems with the centralised optimal controllers. Simulation results show effectiveness of the proposed controllers.     

Two-time scale sliding-mode control for a class of nonlinear systems

The paper deals with the robust asymptotic stabilization of a class of nonlinear singularly perturbed systems using sliding-mode control techniques. The approach consists of decomposing the original system into two reduced order systems, for which stabilizing sliding-mode controllers are applied and combined in a two-time scale sliding-mode control for the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. An example illustrates the design procedure and performance of the proposed control scheme. © 1997 by John Wiley & Sons, Ltd.