具有次优保性能滑动模态的静态输出反馈滑模控制

针对一类不确定系统,提出了一种具有次优保性能滑模面的静态输出反馈滑模控制方法.首先将滑模面的设计问题等价为一个对称矩阵的求解问题,基于等效控制法,推导了保性能滑模面存在的充分条件.然后基于迭代线性矩阵不等式(iterative linear matrix inequality,ILMI)方法,给出了次优保性能线性滑模面的求解算法,最后基于线性矩阵不等式(linearmatrix inequality,LMI)方法,设计了输出反馈滑模控制器,使得闭环系统渐近稳定且切换函数能在有限时间内到达零.该方法首次实现了输出反馈滑模面的优化,且具有保守性小、无需对被控系统模型进行坐标变换的优点.仿真结果验证了本文方法的优越性.     

时滞系统的输出反馈滑模控制的一种奇异系统方法

利用一种奇异系统方法讨论了时滞系统的输出反馈滑模控制问题. 时滞系统的非线性项满足范数有界约束.首先,将滑动模态与线性切换面作为一个奇异时滞系统,基于奇异时滞系统的稳定性理论, 给出滑动模态稳定及切换面存在的线性矩阵不等式(Linear matrix inequality, LMI)充分条件.然后,给出使得系统闭环渐近稳定的静态输出反馈滑模控制器的设计方法,此控制器保证闭环 系统有限时间到达切换面.最后,用数值算例验证本文方法的有效性和正确性.     

时滞T-S模糊系统的无源控制器设计

针对时滞T-S模糊系统, 给出了使得系统无源的状态反馈控制器存在的充分条件, 与现有结果相比保守性更小. 在此基础上, 给出了基于观测器的无源控制器与动态输出反馈无源控制器存在的充分条件. 控制器的设计方法都归结为求解一组线性矩阵不等式(Linear matrix inequality, LMI). 最后通过仿真例子, 说明所给设计方法的有效性.     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

非线性扰动不确定时滞系统时滞相关鲁棒观测器设计

研究一类具有非线性扰动的不确定时滞系统的时滞相关鲁棒稳定性及其基于观测器 的时滞相关鲁棒控制问题.将线性矩阵不等式(LMI,1inear matrix inequality)与数值不等式 (AVI,algebraic value inequality)方法相结合给出了开环系统渐近稳定及其指数稳定的时滞相 关条件.并设计了系统的观测器,给出了该系统基于观测器的时滞相关可镇定条件.     

基于加权函数选择的伺服系统性能优化设计方法

为了尽可能提高伺服系统的性能, 提出一种基于加权函数选择的性能优化设计方法. 首先, 给出性能优化设计问题的描述; 其次, 给出了线性矩阵不等式(Linear matrix inequality, LMI)形式的优化指标; 再次, 提出一种基于加权函数选择的系统性能优化设计迭代算法; 最后, 利用Bode积分关系分析了算法的收敛性. 所提出的系统性能优化设计算法易于迭代计算, 仿真实例验证了算法的有效性.     

一类随机混杂系统的鲁棒方差控制

对一类结构参数不完全已知的Markov跳变参数系统, 研究使得闭环系统的稳态状态方差小于某个给定的上界, 同时满足一定H∞性能的状态反馈鲁棒方差控制器设计问题. 运用线性矩阵不等式(Linear matrix inequality, LMI)方法, 对系统进行了方差分析, 给出并证明了控制器存在的条件, 进而用一组线性矩阵不等式的可行解给出了控制器的一个参数化表示. 通过建立一个具有LMI约束的凸优化问题, 给出了最小方差鲁棒控制器的设计方法. 最后仿真结果表明了该方法的有效性.     

不确定离散线性系统的鲁棒单调反馈–前馈迭代学习控制

针对一类不确定离散线性系统,提出一种沿迭代方向鲁棒单调收敛和沿时间方向有界输入有界输出(bouned-input bounded-output,BIBO)稳定的反馈–前馈迭代学习控制策略.首先,将不确定反馈–前馈迭代学习系统表示为不确定二维Roesser模型系统;然后,把二维系统沿迭代方向的鲁棒单调收敛问题转化成一维系统的H∞干扰抑制控制问题,并给出系统的稳定性证明和用线性矩阵不等式(linear matrix inequality,LMI)表示的沿迭代方向鲁棒单调收敛的充分条件,该LMI充分条件不仅可以用于确定反馈–前馈控制器的增益矩阵,而且还可以保证系统沿时间轴方向是BIBO稳定的;最后,仿真结果证明了该反馈–前馈迭代学习控制策略的有效性.     

基于结构L yapunov 矩阵的静态输出反馈镇定

线性时不变系统的静态输出反馈控制可行性等价于两个耦合的线性矩阵不等式解的存在性问题，这导致了一个非线性最优化问题，是无法直接求解的．针对线性时不变系统(LTI)，深入研究这两个矩阵不等式的关系，通过构造一个结构Lyapunov矩阵，给出了一个问题有解的充分条件，并在此基础上提出一个静态输出反馈镇定算法．利用线性矩阵不等式(LMI)方法，可直接求解出相应的输出反馈增益．数值实例证明了该方法的有效性．     

Delta算子系统动态输出反馈D-稳定鲁棒协方差控制

研究Delta算子描述的线性不确定系统基于动态输出反馈的D-稳定鲁棒协方差控制问题.设计动态输出反馈控制器,使Delta算子不确定系统鲁棒D-稳定,且稳态输出协方差矩阵具有给定上界.利用线性矩阵不等式(LMI)方法,给出D-稳定鲁棒协方差控制器存在的充分条件.在此基础上,提出相应控制器的设计算法.数值算例表明了该设计方法的可行性.     

基于部分状态信息的模糊控制器设计

基于部分状态信息的控制器是一类特殊的静态输出反馈控制器,一般难以利用线性 矩阵不等式工具求解.该文研究了Takagi-Sugeno模糊模型的部分状态反馈控制问题,设计问 题可以归结为求解一组双线性矩阵不等式.通过使控制器增益由全状态反馈变化为部分状态 反馈,这类双线性矩阵不等式可以利用同伦算法求解.从而,镇定模糊部分状态反馈控制器可 以通过迭代方法得到.仿真例子验证了算法的有效性.     

Output feedback optimal guaranteed cost control of uncertain piecewise linear systems

This paper proposes the output feedback optimal guaranteed cost controller design method for uncertain piecewise linear systems based on the piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed‐loop augmented systems, the existence of the guaranteed cost controller for closed‐loop uncertain piecewise linear systems is cast as the feasibility of a set of bilinear matrix inequalities (BMIs). Some of the variables in BMIs are set to be searched by genetic algorithm (GA), then for a given chromosome corresponding to the variables in BMIs, the BMIs turn to be linear matrix inequalities (LMIs), and the corresponding non‐convex optimization problem, which minimizes the upper bound on cost function, reduces to a semidefinite programming (SDP) which is convex and can be solved numerically efficiently with the available software. Thus, the output feedback optimal guaranteed cost controller can be obtained by solving the non‐convex optimization problem using the mixed algorithm that combines GA and SDP. Numerical examples show the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

Fault-tolerant decentralized H-infinity control for multi-channel systems using homotopy method

This paper considers a fault-tolerant decentralized H-infinity control problem for multi-channel linear time-invariant systems. The purpose is to design a decentralized H-infinity output feedback controller to stabilize the given system and achieve a certain H-infinity performance requirement both in the normal situation and in the situation where any one of the local controllers fails. The designed problem is reduced to a feasibility problem of a set of bilinear matrix inequalities (BMIs). An algorithm is proposed to solve the BMIs. First, the normal situation is considered where all the local controllers are functioning. The local controllers are obtained from a standard centralized H-infinity controller by using a homotopy method imposing a structural constraint progressively. Secondly, the above case is extended to the one where any one of the local controllers fails. We again use a homotopy method where the coefficient matrices of the failed controller are decreased rogressively to zero. The efficiency of the proposed algorithm is demonstrated by an example.     

Fault-tolerant decentralized H-infinity control for multi-channel systems using homotopy method

This paper considers a fault-tolerant decentralized H-infinity control problem for multi-channel linear time-invariant systems. The purpose is to design a decentralized H-infinity output feedback controller to.stabilize the given system and achieve a certain H-infinity performance requirement both in the normal situation and in the situation where any one of the local controllers fails. The designed problem is reduced to a feasibility problem of a set of bilinear matrix inequalities （BMIs）. An algorithm is proposed to solve the BMIs. First, the normal situation is considered where all the local controllers are functioning. The local controllers are obtained from a standard centralized H-infinity controller by using a homotopy method imposing a structural constraint progressively. Secondly, the above case is extended to the one where any one of the local controllers fails. We again use a homotopy method where the coefficient matrices of the failed controller are decreased progressively to zero. The efficiency of the proposed algorithm is demonstrated by an example.     

Robust controller synthesis via non-linear matrix inequalities

Over thelastseveralyears fixed-structure multiplier versions of mixed structured singular value(MSSV) theory have been developed and have led to the development of linear matrix inequalities (LMIs) for the analysis of robust stability and performance. These LMIs have in turn led to the development of bilinear matrix inequalities BMIs for the synthesis of robust controllers. The BMI formulation in practice requires the multiplier to lie in the span of a stable basis, potentially introducing significant conservatism. This paper uses the LMI approach to MSSV analysis to develop an approach to robust controller synthesis that is based on the stable factors of the multipliers and does not require the multipliers to be restricted to a basis. It is shown that this approach requires the solution of non-linear matrix inequalities (NMIs). A continuation algorithm is presented for the solution of NMIs. This algorithm may be used to solve NMIs in general and its usefulness is not limited to the robust controller synthesis problem alone. The primary computational burden of the continuation algorithm is the solution of a series of LMIs. The use of this algorithm is demonstrated by designing a robust controller for a benchmark problem.     

BMI-based stability and performance design for fuzzy-model-based control systems subject to parameter uncertainties.

This paper presents the stability and performance design of a fuzzy-model-based control system subject to parameter uncertainties. A nonlinear controller with a favorable characteristic to relax the stability conditions is proposed to drive the system states of the nonlinear plant to follow those of a stable reference model. Stability and performance conditions in terms of bilinear matrix inequalities (BMIs) will be derived based on a Lyapunov-based approach. A combined genetic algorithm and convex programming technique process will be developed to solve the solution to the BMIs. An application example will be given to illustrate the merits of the proposed approach.     

不确定广义系统的保性能控制

针对一类具有范数有界不确定性的连续广义系统和一种具有时间乘积形式的二次性能指标,研究其状态反馈保性能控制器的设计问题.这种性能指标能够使系统状态响应随着时间的增加更快地趋于零,从而缩短系统达到稳定所需要的时间.文中给出了最优保性能控制器存在的充分必要条件并基于双线性矩阵不等式(BMI)、二次矩阵不等式(QMI)和LMI给出其设计方法,最后利用SDP软件和BMI软件举例说明所得结论的可行性.     

A tutorial on linear and bilinear matrix inequalities

This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applications including control structure selection, robust controller analysis and design, and optimal design of experiments. Software for solving LMI and BMI problems is reviewed.     

Lurie控制系统的关联绝对稳定性-双线性矩阵不等式方法

研究任意两个相互独立的Lurie控制系统能否通过关联或协调控制组成绝对稳定大系统的问题,给出两个Lurie控制系统可关联绝对稳定的充分条件,并给出了计算关联矩阵的双线性矩阵不等式方法.研究结果表明:两个非绝对稳定的系统可以通过关联或协调控制来实现关联大系统的绝对稳定性,取消了大系统稳定性分析中对关联的不合理限制.文末给出了本文结果的数值例子.     

奇异线性系统在执行器饱和受限下不变集条件的改进

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.