利用LQ逆问题参数化解研究鲁棒控制系统稳定界

研究了具有非线性扰动控制系统鲁棒稳定界的定义、优化等问题,而且分析了鲁棒控 制稳定界与Riccati矩阵方程解的关系,给出了基于LQ最优控制逆问题参数化解的极大化鲁棒 控制稳定界的优化算法.通过对上述问题的研究,使得约束条件下鲁棒控制系统稳定界与IQ 最优控制逆问题的解法相联系.     

具有时滞的不确定鲁里叶控制系统的绝对鲁棒稳定性

讨论了具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定性问题,应用Bellman-Gronwell不等式和Lyapunov泛函方法研究了不确定鲁里叶控制系统的鲁棒绝对稳定性并给出了系统的滞相关稳定和时滞无关稳定的充分判据,运用这些条件可以直接估计具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定界和时滞界。     

不确定系统鲁棒LQ设计的稳定裕度分析和工程应用研究

针对不确定线性系统, 研究鲁棒LQ设计的稳定裕度分析问题. 首先提出不确定系统α_0裕度稳定鲁棒界, 针对结构和非结构不确定系统, 分别给出了鲁棒LQ控制系统的鲁棒稳定裕度性分析方法, 进一步给出对结构不确定系统优化鲁棒界的算法. 最后是造纸打浆过程实例的鲁棒稳定裕度性分析以及相应仿真结果.     

参数不确定性系统二次保性能控制的鲁棒性

讨论参数不确定性系统二次保性能控制的鲁棒性问题,给出了一种参数依赖的二次保性能控制鲁棒界,以及通过优化该鲁棒界来增加二次保性能闭环控制系统鲁棒性的算法和优化步骤。     

一类不确定参数系统鲁棒稳定界的解析分析与应用

研究一类具有不确定参数系统鲁棒性稳定界的解析分析方法.在定义了鲁棒稳定界的基础上,证明了鲁棒稳定界只与标称系统的最小特征值有关.利用这一结论不仅可以方便地分析多项式的稳定性,而且可以根据系统的不确定性设计闭环控制系统的期望极点,并进行极点配置.     

一类不确定参数系统鲁棒稳定界的解析分析与应用

研究一类具有不确定参数系统鲁棒性稳定界的解析分析方法，在定义了鲁棒稳定界的基础上，证明了鲁棒稳定只与标称系统的最小特征值有关，利用这一结论不仅可以方便地分析多项式的稳定性，而且可以根据系统的不确定性设计闭环控制系统的期望极点，并进行极点配置。     

广义不确定系统稳定鲁棒控制

利用李雅普诺夫稳定理论和矩阵范数性质研究了广义不确定系统的稳定鲁棒控 制问题.在不同情况下,分别给出了保证闭环不确定系统渐进稳定的两类稳定鲁棒控制:状态 反馈、正常动态补偿器的设计方法,得到了鲁棒稳定控制的不确定量的范数界,而且提出了在 多个稳定鲁棒控制器中寻找具有最大的不确定量范数界的控制器的方案.     

具有结构不确定性的线性反馈控制系统的鲁棒稳定性

本文研究了具有结构不确定性(Structured Uncertainty)因素的反馈控制系统的鲁棒稳 定性问题,对于一个普通的补偿器,给出了闭环系统鲁棒稳定的充要条件,当补偿器满足某些 假设条件时,得出了闭环系统鲁棒稳定的有限检验的充分必要条件.     

具有滞后型执行机构的Lurie控制系统的鲁棒绝对稳定性

本文对于具有滞后型执行机构的不确定性Lurie控制系统，构造了一个关于Lyapunov泛函中自由参数的LMI。通过这个LMI的解来构造Lyapunov泛函保证系统的鲁棒绝对稳定性。在此基础上，获得了保证系统绝对稳定的鲁棒扰动界的LMI，并给出了利用迭代法获得鲁棒扰动界的方法。最后给出一个实例说明本文方法的有效性。     

具动态不确定性系统的观测器-控制器设计的鲁棒性

研究存在动态不确定性的线性化系统的龙伯格观测器-控制器设计的鲁棒稳定性问题,并 给出了易于通过系统参数摄动界来验证鲁棒稳定的充分条件.     

不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

Robust H_2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared to the existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

Robust H2 estimation and control

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with normbounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linear matrix inequalities ( LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2 control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.     

离散不确定控制系统的鲁棒性分析与设计

本文在文献［4］的基础上研究了一类离散不确定系统的状态反馈控制问题．文中通过将系统的鲁棒控制器解存在的充分条件转化为一类极小极大的优化命题，然后再通过确定系统的最优解，给出了一种简便而有效的确定极大鲁棒稳定界的方法．从而克服了设计鲁棒控制器所存在的保守性．利用文中的结果还可以将系统的状态反馈系数矩阵的增益设计到最小的程度．     

Event‐triggered probabilistic robust control of linear systems with input constrains: By scenario optimization approach

This paper addresses the problem of probabilistic robust stabilization for uncertain systems subject to input saturation. A new probabilistic solution framework for robust control analysis and synthesis problems is addressed by a scenario optimization approach, in which the uncertainties are not assumed to be norm bounded. Furthermore, by expressing the saturated linear feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is probabilistic stable. Based on these conditions, the problem of designing the state feedback gains for achieving the largest size of the domain of attraction is formulated and solved as a constrained optimization problem with linear matrix inequality constraints. The results are then illustrated by a numerical example.     

基于T-S模型的非线性系统非脆弱极小极大控制

研究一类非线性离散系统的鲁棒非脆弱极小极大控制问题.针对含有不确定项的非线性离散系统,构造T-S模型,引入参数不确定项,使得模糊模型能够更精确逼近原系统.考虑系统和控制器同时含有不确定性,利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,设计鲁棒且非脆弱的控制器.考虑不确定性使得性能指标最大的情形,得到极小极大鲁棒非脆弱控制器存在的充分条件.引入凸优化算法,求解使闭环系统渐近稳定且性能指标上界最小的最优极小极大鲁棒控制器的参数.最后以著名的truck-trailer模型为例的仿真结果表明所设计的控制器具有良好的鲁棒性和非脆弱性.     

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min–max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min–max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min–max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.     

Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

This paper focuses on a class of uncertain nonlinear systems which are subject to norm-bounded parameter uncertainty in the forward path and a vector-valued periodic nonlinearity in the feedback path, and addresses robust analysis and synthesis problems for such systems. Sufficient conditions for global asymptotic stability are derived in terms of linear matrix inequalities (LMIs) and a technique for the estimation of the uncertainty bound is proposed by solving a generalized eigenvalue minimization problem. The problem of robust synthesis is concerned with designing a feedback controller such that the resulting closed-loop system is globally asymptotically stable for all admissible uncertainties. It is shown that a solution to the robust synthesis problem for the uncertain system can be obtained by solving a synthesis problem for an uncertainty free system. A concrete example is presented to demonstrate the applicability and validity of the proposed approach.     

Decentralized robust control of uncertain Markov jump parameter systems via output feedback

This paper addresses the problem of decentralized robust stabilization and control for a class of uncertain Markov jump parameter systems. Control is via output feedback and knowledge of the discrete Markov state. It is shown that the existence of a solution to a collection of mode-dependent coupled algebraic Riccati equations and inequalities, which depend on certain additional parameters, is both necessary and sufficient for the existence of a robust decentralized switching controller. A guaranteed upper bound on robust performance is also given. To obtain a controller which satisfies this bound, an optimization problem involving rank constrained linear matrix inequalities is introduced, and a numerical approach for solving this problem is presented. To demonstrate the efficacy of the proposed approach, an example stabilization problem for a power system comprising three generators and one on-load tap changing transformer is considered.