Improved Parameter-dependent H_∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads t...     

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

The H∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality （LMI） representation of H∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be effciently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.     

Delta算子不确定系统扩展参数依赖H_∞控制

研究了含有多面体参数摄动Delta算子系统的参数依赖H∞控制问题.基于Delta算子系统有界实引理,提出了扩展参数依赖H∞性能准则.利用该准则,以参数化的线性矩阵不等式形式给出了参数依赖H∞控制器存在的充分条件,并通过求解优化问题设计控制器.研究结果表明该方法保守性较低,且物理概念清晰.数值示例验证了所提方法的有效性.     

Delta算子系统具有圆形区域极点约束的非脆弱H∞滤波器设计: 一种LMI优化方法

研究了一类Delta算子线性系统具有圆形区域极点配置的非脆弱 H∞滤波器设计问题. 本文的目的是设计滤波器使得滤波误差系统不仅满足给定的圆点极点约束或D稳定约束, 而且从扰动输入到滤波误差的传递函数满足给定的 H∞范数约束. 所设计的滤波器具有乘性的滤波器增益变化, 基于Lyapunov稳定性理论和线性矩阵不等式方法, 给出具有区域极点配置的Delta算子离散系统非脆弱 H∞滤波器存在的充分条件. 数值仿真例子说明设计方法的有效性以及所提设计方法具有更小的保守性.     

Improved Results on Robust H∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.     

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

The H∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the exi...     

随机时延网络化不确定系统的鲁棒H∞滤波

研究了一类具有随机时延的网络化不确定系统的 H∞ 滤波器设计问题. 这类时延的产生是由于传感器和滤波器通过有限带宽的网络连接而引起的系统测量数据的滞后, 而且它是随机发生的. 本文采用满足 Bernoulli 分布随机变量来描述测量数据的这种随机时延. 利用线性矩阵不等式, 给出了全阶和降阶的滤波器存在的充分条件. 所设计的滤波器使得滤波误差系统是均方指数稳定且具有给定的H∞ 性能. 数值仿真表明设计方法的有效性.     

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.     

Delta算子描述系统的非脆弱H∞滤波器设计

研究了一类Delta算子描述的线性系统非脆弱H_∞滤波问题. 所设计的滤波器具有乘性的滤波器增益变化.采用线性矩阵不等式方法, 给出H_∞滤波器存在的充分条件, 所设计的滤波器在一定的乘性参数变化情况下, 仍能保证滤波误差系统渐近稳定, 且具有一定扰动抑制性能. 数值仿真例子说明了设计方法的有效性.     

基于多步控制策略的混合H2/H∞鲁棒预测控制器设计

针对具有外界扰动的线性定常(Linear time invariant, LTI)系统, 本文研究了其鲁棒预测控制器(Robust model predictive control, RMPC)的设计方法. 设计采用了混合的H2/H∞控制方法以有效地兼顾系统的抗干扰能力和闭环控制性能. 同时, 为了降低设计的保守性, 设计利用闭环多步控制策略以扩大控制器的可行范围, 改善系统控制性能. 进而, 为了便于实际实施, 提出该RMPC的简化设计, 通过将大部分在线计算量离线完成以降低鲁 棒预测控制器的在线计算量.     

考虑有限字长影响的离散时间非脆弱H∞滤波

本文研究了线性离散时间系统由有限字长影响的非脆弱滤波问题. 假定所设计的滤波器具有加性增益变量, 此增益变量反映了滤波器执行时的有限字长的影响. 为了解决该非脆弱滤波问题, 提出了一个结构的顶点分离器的概念, 并采用该分离器, 基于线性矩阵不等式给出了非脆弱滤波器设计的充分条件. 设计的结果使得误差系统渐进稳定且具有一定的性能水平. 数值例子验证了方法的有效性.     

不确定离散模糊时滞系统的时滞相关H∞控制

研究了不确定离散T-S模糊时滞系统的稳定性分析与H∞控制问题．通过构造适当的Lyapunov泛函,给出了系统的时滞相关稳定新判据．进而利用线性矩阵不等式方法,研究了H∞模糊状态反馈控制器存在的充分条件,并提出控制器优化设计的迭代算法．     

不确定离散模糊时滞系统的时滞相关H∞控制

研究了不确定离散T-S模糊时滞系统的稳定性分析与H∞控制问题．通过构造适当的Lyapunov泛函,给出了系统的时滞相关稳定新判据．进而利用线性矩阵不等式方法,研究了H∞模糊状态反馈控制器存在的充分条件,并提出控制器优化设计的迭代算法．     

容错控制系统鲁棒H∞和自适应补偿设计

通过设计动态输出反馈控制策略研究线性时不变系统执行器故障下的鲁棒自适应容错H∞控制问题. 结合自适应技术和线性矩阵不等式(Linear matrix inequalities, LMI)技术, 设计一个控制策略同时实现系统的故障补偿控制和性能优化控制. 在设计中, 提出由自适应律在线调节控制增益方程补偿未知执行器故障和摄动; 并设计一个基于模式依赖李亚普诺夫方程的LMI条件解出控制参数及次优H∞性能. 所设计的动态输出反馈控制器可以处理一般执行器卡死故障, 并得到更少保守性的H∞性能指标. 此外, 一个更具挑战性的问题, 即通过自适应机构补偿故障致使系统多少性能退化得到论证. 所提方法的有效性由一个解耦线性化动态飞行器系统仿真验证.     

不确定时滞线性离散切换系统的鲁棒H∞控制

研究一类具有不确定和时滞的线性离散切换系统的鲁棒H∞控制问题．利用多Lyapunov函数技术,在基于状态的切换规则下,给出了这类系统鲁棒镇定且具有H∞性能界的充分条件,以及切换规则和鲁棒H∞切换控制器的设计方案．并将结果应用到一类非切换系统,提出了切换状态反馈控制策略．最后的仿真例子进一步表明了本文结论的有效性．     

含有不确定性的2维离散线性系统的鲁棒 H2滤波设计

针对含有不确定参数的2维离散线性系统,本文给出了两种鲁棒H_2滤波设计方法. 第一种方法采用引入参数相关的矩阵函数的思想, 所设计的Lyapunov函数及引入的变量都是多项式参数相关的,随着矩阵函数次数的增加条件的保守性逐渐减小. 但是次数不能无限增加,当达到一定程度后,即使次数继续增加,条件的保守性不再改变.接着,为了进一步减小保守性, 通过详细分析现有条件的保守性来源,给出了第二种方法--循环迭代算法. 同现有文献相比,在此算法中引入的变量不需要满足特定的结构,因而具有更小的保守性. 最后,通过两个仿真算例证明了当第一种方法无法减小保守性时,第二种方法仍然可以进一步减小保守性.     

不确定模糊Delta算子系统的鲁棒H∞控制

研究了一类T-S模糊Delta算子系统的鲁棒H_∞控制问题.首先利用LMI形式给出了模糊Delta算子系统鲁棒镇定的充分条件,然后构造了可使闭环系统鲁棒稳定且对可允许的参数变化满足H_∞性能的状态反馈控制律.本文结果统一了连续与离散模糊系统的鲁棒H_∞镇定设计结论,数值算例说明了方法的可行性.     

不确定离散时间系统的变增益H2/H∞滤波

研究凸多面体不确定离散时间系统的变增益H2/H∞滤波器设计问题.通过引入附加松弛变量,提出一种新的Lyapunov矩阵与系统矩阵解耦的混合H2/H∞性能准则.基于该性能准则,推导了变增益H2/H∞滤波器存在的充分条件,并将滤波器设计问题转化为具有线性矩阵不等式约束的凸优化问题.仿真结果表明了所提出方法的有效性.     

Computation of Peak Output for Inputs Restricted in L2 and L∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.