一类非线性控制系统可生存性的判别

讨论了一类微分包含可生存性的判别问题. 基于非光滑分析理论，通过判别一个线性不等式组的相容性,或等价地求解一个辅助的线性规划问题,来判别此微分包含在一点处是否满足可生存性条件.     

一类非线性控制系统关于非光滑区域生存性的判别

讨论微分包含关于非光滑区域生存性的判别问题．当右端集值映射为多面体，边界为次可微函数，且次微分为有限点集凸包时，基于非光滑分析理论，给出了在一点处检验生存性条件是否成立的方法．该方法将生存性判别转化为判别线性不等式组的相客性或等价地转化为求解一个线性规划问题．最后讨论了次可微函数上图的生存性问题。     

线性控制系统多面体区域的生存性判别

利用非光滑分析, 讨论线性控制系统多面体区域的生存性判别. 对于有界多面体(利用有限点集的凸包来表示), 其生存性判别只需检验其在极点处是否满足生存性条件, 去掉了以往对输入集合为多面体的要求, 这种生存性判别方法简便易行. 最后利用所给出的生存性条件讨论了生存性设计.

     

非线性切换系统的近似生存性判别

研究了由有限个动态子系统组成的非线性切换系统的生存性判别问题．首先通过构造一个分段常数反馈控制器证明了系统在任意切换准则下都是近似生存的,并给出系统关于一个任意集合近似生存的充分判别条件,最后基于非光滑分析理论给出系统关于不等式区域近似生存的一个充分判别条件.     

切换系统多面体区域的生存性判别

本文研究了切换系统关于多面体区域的生存性判别问题.考虑多面体由有限点集凸包来表示,利用非光滑分析理论,得到一个切换系统生存性的充分条件.该条件只需检验在极点处是否满足特定条件,而不需要对每个边界点进行验证.其优点在于将生存性的判别转化为向量内积与切锥的计算.这种生存性判别方法简便易行.最后通过实例阐述了算法的有效性.     

线性系统近似生存域的计算

研究了构造控制系统近似生存域的方法和线性系统的近似生存性条件. 基于集合的逼近法锥, 给出了凸紧集的过剩近似生存域表达式．在凸紧集边界上采样足够多个点的情况下, 此近似生存域可以逼近真实的生存域. 并研究了连续线性控制系统和离散线性控制系统在此近似生存域上的生存性, 将求生存控制器的问题转化为线性不等式组问题. 最后, 以悬挂点可以移动的钟摆模型和两类细菌数量变化模型为例说明了算法的有效性.     

一类具有凸多面体不确定性的非线性变参数系统鲁棒H_(∞)控制EI北大核心CSCD

针对具凸多面体不确定性的非线性变参数(NPV)系统,本文研究了其非线性鲁棒H_(∞)控制问题.基于Lya-punov稳定性理论和多项式平方和(SOS)方法,对该系统设计了非线性鲁棒状态反馈镇定控制器.在此基础上,进一步考虑存在外部扰动情形,给出相应的非线性鲁棒H_(∞)控制可解性条件.该条件以状态和时变参数依赖的线性矩阵不等式形式(LMIs)给出,可借助凸优化工具进行有效检验.最后,通过数值仿真验证了所得方法的有效性和优势.     

一类时滞组合系统的优化保成本容错控制

对一类时滞组合系统，研究了依赖时滞的分散状态反馈可靠保成本控制器的设计问题．采用线性矩阵不等式方法，导出了时滞依赖可靠保成本控制器的存在条件和参数化表示．进而，通过建立和求解一个线性矩阵不等式组约束的凸优化问题，给出了优化保成本容错控制器的设计方法．仿真实例验证了这个设计法的有效性．     

线性不等式组的一个解法和简约

线性不等式组的讨论,在理论上和实践中都是很重要的。本文给出了初等矩阵方法用于解线性不等式组的计算方案,并指出线性不等式组可约性、相容性的条件。最后,对初等矩阵方法的计算量做出估计,还对节约存储、减少计算量等问题做了考虑。     

考虑参数不确定性的主动悬架鲁棒H2/H∞混合控制

基于线性矩阵不等式方法,提出了一种新的考虑参数不确定性的鲁棒H2／H∞控制器设计方法,并用于车辆主动悬架设计．假定系统不确定参数是范数有界的,通过引入同一个Lyapunov矩阵来同时满足闭环系统的也和H∞性能条件,把鲁棒H2／H∞控制器设计转化为具有线性矩阵不等式约束的凸优化问题,进而应用内点法等凸优化技术进行求解．以四分之一车辆模型主动悬架设计为例,进行了数值仿真．结果表明,无论车辆簧上质量是否存在变异,鲁棒H2／H∞控制器均能给出很好的控制效果．     

Determining the Viable Unbounded Polyhedron Under Linear Control Systems

This paper proposes a new method to determine the viability of linear differential inclusions on an unbounded polyhedron. Based on nonsmooth analysis and viability theory, a sufficient and necessary condition of viability for a convex cone is presented. We then apply the result to an autonomous continuous‐time positive linear system and a continuous‐time positive linear system with scalar inputs, respectively. We give a sufficient condition that guarantees the viability of linear differential inclusions on an unbounded polyhedron. The advantage of the proposed methods is that determining the viability is transformed into solving a finite number of linear programmings. Finally, the effectiveness of our approach is demonstrated through an example.     

Stability analysis and synthesis for an affine fuzzy control systemvia LMI and ILMI: a continuous case

A new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper. The method suggested is based on the numerical convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities (LMIs). The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In the synthesis, the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner. Fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains. Continuous iterative LMI (ILMI) approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system     

不确定性关联时滞大系统的分散鲁棒控制——LMI方法

对一类满足匹配条件的不确定性关联时滞大系统,Lyapunov稳定性原理,给出了其可分散状态反镇定的充分条件,即一组线性矩阵不等式（LMI）有解,在此基础上,通过求解一凸优化问题,提出了具有较小的反馈增益的分散稳定化状态反馈控制律的设计方法,文中最后用示例说明了该方法的应用与优越性。     

Adaptive vector control of an induction motor on the basis of the method of recurrent objective inequalities

The problem is considered for control of an electromagnetic moment of the induction motor with a squirrel-cage rotor without the measurement of its rotational speed. By means of the principle of vector control, this problem reduces to developing an adaptive observer of values of the vector of the rotor magnetic-flux linkage. The method of recurrent objective inequalities (ROIs) is used, which enables one to reduce adaptation problems to counting systems of inequalities relative to the vector of the parameters estimated. For the control problem under consideration, these inequalities prove to be nonconvex, which makes it impossible to use directly the projection algorithms developed in the framework of the method of ROIs. In this connection, the common method for the stepwise reduction of the dimension of the nonlinear portion of inequalities is suggested in this work. On condition that the processes of a closed system display a certain natural property of nondegeneracy, this method permits reducing nonconvex inequalities to convex ones and ensures the achievement of the control aim on completion of the transient processes.     

一类不确定切换奇异系统的动态输出反馈鲁棒H∞控制

研究一类由任意有限多个不确定子系统组成的切换奇异系统的动态输出反馈鲁棒H∞控制问题. 利用共同 Lyapunov 函数方法和凸组合技术, 给出由矩阵不等式表示的控制器存在的充分条件, 并设计了相应的子控制器和切换策略. 采用消元法, 将该矩阵不等式转化为一组线性矩阵不等式 (LMIs). 最后, 数值实例验证了所提方法的有效性.     

Robust stabilization of linear discrete-time systems with time-varying input delay

This paper presents a sufficient condition to stabilize linear discrete-time systems with time-varying input delay and model uncertainties. The key idea consists of applying Artstein’s reduction method and the scaled bounded real lemma; the robust stabilization problem is cast as a set of linear matrix inequalities on a transformed delay-free system. Hence, a novel convex characterization of the problem, an alternative to bilinear matrix inequalities in prior literature, is provided. Predictor-based controllers and robust state-feedback stabilization are particular cases of the proposal. Furthermore, numerical examples show that this proposal may improve tolerance against delay variations when compared to other methods available in literature.     

时滞大系统分散鲁棒跟踪控制器设计: LMI 方法

针对一类满足匹配条件的不确定性关联时滞系统,导出了分散鲁棒输出跟踪控制器存在的充分条件。基于不确定项的表达形式,给出了存在分散鲁棒跟踪控制器的线性矩阵不等式（LMI）条件。通过建立求解受LMIs约束的凸优化问题,提出了具有较小反馈增益LMI设计方法,使受控系统渐近跟踪给定的参考输入。仿真示例说明了该方法的应用。