Stability of a class of discrete-time nonlinear recursive observers

This work provides a framework for nominal and robust stability analysis for a class of discrete-time nonlinear recursive observers (DNRO). Given that the system has linear output mapping, local observability and Jacobian matrices satisfying certain conditions, the nominal and robust stability of the DNRO is defined by the property of estimation error dynamics and is analyzed using Lyapunov theory. Moreover, a simultaneous state and parameter estimation scheme is shown to be Input-to-State Stable (ISS), and adaptively reduce plant-model mismatch on-line. Three design strategies of the DNRO that satisfy the stability results are given as examples, including the widely used extended Kalman filter, extended Luenberger observer, and the fixed gain observer.     

An enhanced exact procedure for the absolute robust shortest path problem

The aim of this paper is to investigate the use of heuristic information to efficiently solve to optimality the robust shortest path problem. Starting from the exact algorithm proposed by Murty and Her, we describe how this algorithm can be enhanced by using heuristic rules and evaluation functions to guide the search. The efficiency of the proposed enhanced approach is tested over a range of random generated instances. Our computational results indicate that the use of heuristic criteria is able to speed up considerably the search and that the enhanced exact solution method outperforms the state‐of‐the‐art algorithm proposed by Murty and Her in most of the instances.     

Robust exponential stability conditions for retarded systems with Lipschitz nonlinear stochastic perturbations

This paper investigates robust mean‐square exponential stability of a class of uncertain stochastic state‐delayed systems with Lipschitz nonlinear stochastic perturbation. Based on Lyapunov–Krasovskii functional (LKF) method and free‐weighting matrix technique, some new delay‐dependent stability conditions are established in terms of linear matrix inequalities (LMIs). In order to reduce the conservatism, (1) the delay is divided into several segments, i.e. the delay decomposition method is applied; (2) cross terms estimation is avoided; (3) some information of the cross terms relationships which has not been involved in Reference (IET Control Theory Appl. 2008; 2(11):966–973) is considered. Moreover, from the mathematical point of view, the results obtained by free‐weighting matrix technique can be equivalently re‐formulated by simpler ones without involving any additional free matrix variables. The effectiveness of the method is demonstrated by numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved delay‐dependent absolute stability and robust stability for a class of nonlinear systems with a time‐varying delay

This paper investigates the problem of the absolute stability of Lur'e systems with a time‐varying delay. By considering the relationships among the time‐varying delay, its upper bound, and the difference between them, less conservative delay‐dependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov–Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust MIMO disturbance observer analysis and design with application to active car steering

A multi‐input–multi‐output extension of the well‐known two control degrees‐of‐freedom disturbance observer architecture that decouples the problem into single‐input–single‐output disturbance observer loops is presented in this paper. Robust design based on mapping D‐stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Multiple robust H∞ controller design using the nonsmooth optimization method

This paper proposes a systematic technique to design multiple robust H_∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd.     

直升机鲁棒保性能控制律设计

考虑直升机在飞行包线内模型参数的变化及不确定性影响,设计了鲁棒保性能控制律;根据直升机一个标称状态点构造出了参数不确定性矩阵,利用Lyapunov稳定性定理和线性矩阵不等式方法给出了控制器存在的充分条件及参数化设计方法,进行直升机三轴姿态稳定保性能控制律的设计;仿真结果表明,所设计的控制器满足三轴姿态稳定要求且具有很好的鲁棒性。     

基于信息势能的鲁棒估计器及其在同时定位与地图构建问题中的应用

提出了一种基于信息势能鲁棒估计器来解决机器人室内的同时定位与地图构建（SLAM）问题．结构化的室内环境可以用线段近似表示．然而动态环境中,测距传感器测得的数据通常湮没在大量的噪声信号中．本文采用“分割与合并”（split—and．merge）方法进行线段的分类,根据信息势能的性能指标衡量每个采样数据对该线段的信息贡献量．按照信息优化理论设计估计器,选择信息量贡献大的样本点作为信息内点提取线段参数,构建局部地图．采用粒子滤波器进行地图及机器人路径的更新．采用递推的方法估计信息势能,降低了对样本点的信息量贡献做估计时的复杂度．仿真和实验结果证明,本文所提出的方法具有较强的鲁棒性,提高了SLAM策略的准确性和实时性．     

线性自抗扰控制系统的鲁棒稳定性

针对线性自抗扰控制系统,研究了模型参数不确定情况下的鲁棒稳定性问题.首先给出对象为非自治模型时该系统的H∞判据.然后针对线性误差模型的状态矩阵只在某一行存在不确定参数的情况,基于奇异值理论,得到H∞判据的一种新的等价描述,把H∞范数约束转化为对奈奎斯特图的约束.之后为了降低新判据在实际应用中的保守性,对不确定性矩阵的分解方式进行优化.在此基础之上提出了一种新的方法,用于计算时变参数不确定性的最大边界,为线性自抗扰控制器设计提供理论依据.数值实例表明该方法不仅保守性小,而且计算简单.     

参数不确定统一混沌系统鲁棒最优控制

针对含有参数不确定性的统一混沌系统,基于鲁棒最优控制理论,提出了一种简单的线性状态反馈控制策略.该策略给出了系统渐进稳定的充分条件,并可以通过求解线性矩阵不等式(LMI),快速有效地求得系统反馈的控制增益,利用Lyapunov方法证明了闭环系统的稳定性.仿真结果验证了所提出的控制策略的有效性.