具有饱和执行器的时滞广义系统的鲁棒控制

利用李亚普诺夫方法研究了时滞广义系统、不确定广义系统和不确定时滞广义系统的鲁棒镇定问题.首先设计了时滞广义系统的具有饱和执行器的控制律,并给出其闭环系统渐近稳定的充分条件.对不确定项是范数有界的不确定广义系统,给出其控制器的设计方法和闭环系统渐近稳定的充分条件.在此基础上,进一步给出了不确定时滞广义线性系统的镇定条件.最后,给出了一个数值算例来说明方法的有效性.     

线性广义时滞系统的状态反馈H∞控制

首先利用线性矩阵不等式(LMI)方法,给出线性广义时滞系统稳定的一个充分条件;然后讨论广义时滞系统的H_∞状态反馈控制,给出控制器存在的充分条件,同时给出控制器的设计.控制器可由矩阵不等式解得。     

时滞广义大系统的分散镇定

利用Lyapunov泛函数分析方法研究时滞广义分散控制系统,给出关联矩阵在某种解下的镇定条件及反馈控制器的设计方法,及具有相同时滞的广义分散系统,提供了镇定控制器的设计以保证闭环系统是渐近稳定的。     

一类不确定系统的最优极小极大鲁棒控制

讨论一类不确定系统的极小极大鲁棒动态输出反馈控制问题.给出不确定系统的极小极大鲁棒控制的定义.利用线性矩阵不等式(LMI)处理方法和Lyapunov稳定性理论,得到了在干扰和不确定性最大的情形下极小极大输出反馈控制器存在的充分条件.引入凸优化技术, 求得最优极小极大控制器.它不仅保证闭环系统渐近稳定, 且使得闭环系统性能指标的上界最小.仿真算例说明了所设计的控制器具有较强的干扰抑制功能.     

线性广义时滞系统的H∞状态反馈控制器

首先利用线性矩阵不等式(LMI)方法，给出线性广义时滞系统稳定的一个充分条件；然后讨论线性广义时滞系统的H∞状态反馈控制，给出控制器存在的充分条件，同时给出控制器的设计，控制器可由线性矩阵不等式解得；最后举例说明了所提出方法的可行性。     

广义系统的时滞相关非脆弱H_∞保成本控制

研究了时滞不确广义系统的时滞相关非脆弱H∞保成本控制器的设计问题。利用Lyapunov的稳定性理论和最近建立的积分不等式方法,得到了时滞不确定广义系统在非脆弱控制器作用下不仅内部渐近稳定,而且具有给定的H∞扰动抑制水平的时滞相关条件,以及相应的成本函数上界。假定其中的不确定项是范数有界的,但不需要满足严格的匹配条件.针对控制器增益具有加法式摄动和乘法式摄动两种情形,分别给出了非脆弱H∞保成本控制器的设计方法。这一方法不需要参数调节,利用Matlab的LMI工具箱求解方便。最后,数值仿真实例说明了所给方法的有效性。     

不确定离散时滞分段系统的广义H2弹性控制

针对一类不确定离散时滞分段系统,研究了广义H2稳定性分析和带有时滞的状态反馈弹性控制器设计问题.通过构造适当的离散分段二次李亚普诺夫函数,利用分段二次李亚普诺夫稳定性理论,给出了对于所有的容许参数不确定性,闭环系统是广义H2稳定的充分条件;在此基础上,基于线性矩阵不等式(LMI)处理方法,提出了带有时滞的状态反馈弹性控制器增益阵的设计方案.仿真实例验证了所提方法的有效性.     

不确定时滞广义双线性系统的鲁棒镇定

针对不确定参数是时变但满足匹配条件的时滞广义双线性系统的鲁棒控制问题进行了研究,设计状态反馈鲁棒控制器,使得所有满足条件的不确定时滞广义双线性系统鲁棒稳定.基于Lyapunov稳定性理论,采用线性矩阵不等式方法,提出了不确定时滞广义双线性系统鲁棒镇定的充分条件,并给出了使得闭环系统鲁棒镇定的状态反馈控制器设计方法.定理解决了介于非线性和线性之间的不确定时滞广义双线性系统的有关理论.仿真实例说明了定理的有效性和合理性.     

广义时滞系统的时滞相关型H∞控制

研究了广义时滞系统的时滞相关型H_∞控制问题.首先通过引入一个新的Lyapunov-Krasovskii泛函,以严格线性矩阵不等式的形式,得到了广义时滞系统的一个新的有界实引理.在此基础上,设计了使得闭环系统正则、无脉冲和稳定,且满足H_∞性能界的时滞相关型H_∞控制器,并给出了控制器增益的显式表示.最后的算例表明了本文方法具有更小的保守性.     

离散区间二型Tagaki-Sugeno模型时滞系统广义耗散控制设计

对带有时变时滞和外部扰动的一类离散区间二型Tagaki-Sugeno(T–S)模型非线性系统,研究了其广义耗散性能分析与状态反馈控制器的设计问题.与一型T–S模糊系统相比,区间二型模糊系统能更好地处理隶属函数中的不确定信息.首先,通过模型转换的方法,对系统的滞后状态进行变换,从而将时变时滞的不确定性从原系统中分离出.根据转换后的仅含定常时滞和具有有界误差范数的两个子系统,利用时滞依赖的李雅普诺夫-克拉索夫斯基泛函方法推导出了使系统渐近稳定并具有广义耗散性能的充分条件.接着,设计了保证闭环系统渐近稳定并具有广义耗散性能指标的状态反馈控制器.最后由数值仿真验证了设计方法的有效性.     

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.     

Robust tracking problem for continuous time stochastic uncertain systems

We propose a finite‐horizon robust minimax tracking controller design method for time‐varying continuous time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which stochastic noises, driving the system, are defined. A minimax optimal tracking controller is derived from the solution of a risk‐sensitive linear quadratic Gaussian control problem. Also a numerical example is presented to illustrate the characteristics of proposed tracking controller. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类不确定系统的鲁棒可靠跟踪控制及其在飞行控制中的应用

针对多面体不确定系统,基于参数相关Lyapunov函数的方法,研究了考虑执行器故障的可靠跟踪控制器的设计问题．利用描述系统方法,得到可靠跟踪控制器存在的充分条件．状态反馈可靠跟踪控制器设计方法可以归结为求解一族线性矩阵不等式(LMIs)．通过飞行控制系统的实例仿真验证了文中提出的设计方法的可行性．     

Uncertainty modeling and robust minimax LQR control of multivariable nonlinear systems with application to hypersonic flight

For a class of multi‐input and multi‐output nonlinear uncertainty systems, a novel approach to design a nonlinear controller using minimax linear quadratic regulator (LQR) control is proposed. The proposed method combines a feedback linearization method with the robust minimax LQR approach in the presence of time‐varying uncertain parameters. The uncertainties, which are assumed to satisfy a certain integral quadratic constraint condition, do not necessarily satisfy a generalized matching condition. The procedure consists of feedback linearization of the nominal model and linearization of the remaining nonlinear uncertain terms with respect to each individual uncertainty at a local operating point. This two‐stage linearization process, followed by a robust minimax LQR control design, provides a robustly stable closed loop system. To demonstrate the effectiveness of the proposed approach, an application study is provided for a flight control problem of an air‐breathing hypersonic flight vehicle (AHFV), where the outputs to be controlled are the longitudinal velocity and altitude, and the control variables are the throttle setting and elevator deflection. The proposed method is used to derive a linearized uncertainty model for the longitudinal motion dynamics of the AHFV first, and then a robust minimax LQR controller is designed, which is based on this uncertainty model. The controller is synthesized considering seven uncertain aerodynamic and inertial parameters. The stability and performance of the synthesized controller is evaluated numerically via single scenario simulations for particular cruise conditions as well as a Monte‐Carlo type simulation based on numerous cases. It is observed that the control scheme proposed in this paper performs better, especially from the aspect of robustness to large ranges of uncertainties, than some controller design schemes previously published in the literature. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nonlinear robust state feedback control system design for nonlinear uncertain systems

This paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.     

不确定广义系统的弹性H∞控制

研究了具有范数有界不确定性的广义系统的弹性H_∞控制问题. 首先证明了广义系统的有界实引理可以用一个严格的线性矩阵不等式来描述. 在此基础上, 针对控制器存在加性摄动的情形, 以严格线性矩阵不等式约束条件给出了弹性H_∞状态反馈控制器存在的充分必要条件, 并给出了控制器的显式表示. 算例验证了本文方法的可行性.     

Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty

This paper is concerned with the design of robust state feedback controllers for a class of uncertain time-delay systems. The uncertainty is assumed to satisfy a certain integral quadratic constraint. The controller proposed is a minimax optimal controller in the sense that it minimizes the maximum value of a corresponding linear quadratic cost function over all admissible uncertainties. The controller leads to an absolutely stable closed loop uncertain system and is constructed by solving a finite dimensional parameter-dependent algebraic Riccati equation.     

Design of minimax robust LQG controllers under parameter and noise uncertainties

The problem of design of minimax robust LQG controllers for linear systems with parameter and noise uncertainties is considered in this paper. Necessary and sufficient conditions for converting this problem to a two-person, zero-sum continuous game problem are presented. A simple procedure for design of a suboptimal minimax robust LQG controller, i.e., the LQG controller for least-favourable model, is proposed. Necessary and sufficient conditions for the existence of a saddle point are established. Under these conditions, the controller obtained is exactly the minimax LQG controller. When there does not exist a saddle point, the worst-case error between the controller obtained and the minimax robust LQG controllers under described uncertainties is bounded.