离散时间不定号随机线性二次型最优控制:无限时区情形

应用渐近分析方法讨论了无限时区离散时间不定号随机线性二次型最优控制问题. 所进行的研究是建立在这一问题有限时区情形结果和系统均方能镇定假设基础之上的. 广义代数Riccati方程(GARE)解的一些性质也得到了考虑. 最后提供了两个例子来说明所推出的结果是有效的.     

时变系统的模型匹配与跟踪问题

仿照时不变系统的次优模型匹配解的存在性证明方法,可以得到J–谱分解条件下时变系统的Nehari型模型匹配问题的次优解存在性.如何针对双边模型匹配的次优问题证明解的存在性还没有有效的方法.本文在套代数框架下研究了时变线性系统的次优模型匹配和跟踪问题.首先,应用Douglas值域定理证明了耦合J–谱分解条件下次优模型匹配解的存在性,然后指出应用双参数控制器同时镇定n个系统,并且要求跟踪指标小于r的次优跟踪问题等价于同时强r镇定n-1个相关四块问题,最后给出了次优解的参数化.     

广义代数Riccati方程和最优调节器的研究

利用能稳性和精确能观性, 对广义代数Riccati方程和相关的随机最优调节器问题进行了深入的研究. 对广义代数Riccati方程得到了下列结果: 如果随机系统既是能稳定的又是精确能观的, 则广义代数Riccati方程有一个最大解, 同时也是一个反馈镇定解. 在精确能观性的假设下, 广义代数Riccati方程的所有非负定解(如果存在的话)必是正的反馈镇定解. 作为应用, 最优调节器问题, 广义代数Riccati方程的最大解, 反馈镇定解三者之间的关系获得了澄清. 所有这些结果在随机控制和随机稳定性理论中是有     

时滞依赖型中立系统的观测器设计与镇定

研究了一类时滞依赖型线性中立系统的观测器的设计与镇定问题,首先建立了一个时滞依赖型稳定性准则,基于LMI正定解的存在性,给出确保误差动力系统渐近稳定的充分条件及经状态反馈而达到镇定的设计方案.最后通过数值仿真来说明本文所得结论的正确性和有效性.     

球形对象族的最优鲁棒镇定

本文对球形对象族系统最优鲁棒镇定问题进行了研究.利用最小范数解方法求解球形对象族的可镇定性半径.可镇定性半径是系统稳定性半径的上界,最优控制器的稳定性半径等于镇定性半径.文中给出球形对象族最优鲁棒控制器的形式,并通过示例具体说明球形对象族最优鲁棒控制器的设计方法.     

一类不确定性时滞关联大系统的分散鲁棒稳定控制器设计

对一类满足匹配条件的不确定性关联大系统，设计了基于一组线性矩阵不等式（LMI）有解的系统状态反馈镇定的充分条件。本文采用了实对称矩阵集合的最小上界定理，并对设计参数进行优化处理，从而使得所设计的控制器具有较小反馈增益。同时系统的不确定性采用区间矩阵表示，因此该设计方法具有很好的普遍性。最后给出的仿真实例说明了该方法的有效性。     

一类关联时滞系统的分散稳定化控制器设计

应用Lyapunov稳定性理论,提出一类关联时滞系统能用分散线性状态反馈镇定的充分条件,进而证明了该条件等价于子系统级上N个带参数的代数Riccati矩阵方程的正定解的存在性,并利用这些正定解矩阵给出了相应的稳定化分散控制器。应用所提出的方法,可望得到具有更小反馈增益参数的分散稳定化控制律。     

一类随机分布参数系统反馈控制的镇定

研究一类随机分布参数系统的镇定.主要方法是将所考虑的系统的解随机场关于空间变量的积分形式上视为相应的随机常微分方程的解过程,通过构造一个关于空间变量平均的Lyapunov函数来达到运用It^o微分公式研究该系统的镇定性的目的.并获得了若干构造性的代数判据.     

双曲极小相位系统的必要条件及一类非线性对称大系统的反馈镇定

给出仿射非线性系统为双曲极小相位的一个必要条件,并讨论了一类非线性对称大系统的镇定问题,将该大系统的镇定归结为两个你阶系统的镇定。     

Infinite horizon indefinite stochastic linear quadratic control for discrete-time systems

This paper discusses discrete-time stochastic linear quadratic (LQ) problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation (GARE) that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality (LMI). Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.     

Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon

This paper is concerned with a stochastic linear-quadratic (LQ) problem in an infinite time horizon with multiplicative noises both in the state and the control. A distinctive feature of the problem under consideration is that the cost weighting matrices for the state and the control are allowed to be indefinite. A new type of algebraic Riccati equation – called a generalized algebraic Riccati equation (GARE) – is introduced which involves a matrix pseudo-inverse and two additional algebraic equality/inequality constraints. It is then shown that the well-posedness of the indefinite LQ problem is equivalent to a linear matrix inequality (LMI) condition, whereas the attainability of the LQ problem is equivalent to the existence of a “stabilizing solution” to the GARE. Moreover, all possible optimal controls are identified via the solution to the GARE. Finally, it is proved that the solution to the GARE can be obtained via solving a convex optimization problem called semidefinite programming.     

On the existence of solutions of the general algebraic Riccati equation

This paper addresses the problem of real symmetric solutions of the general algebraic Riccati equation (GARE) with an indefinite quadratic term. The GARE arises in linear quadratic differential games, in the stabilization of uncertain systems, robust optimal control and disturbance attenuation problems. Using the properties of the solutions of the differential equation corresponding to the GARE and the related conclusions of differential games, we have established the main results of this paper. Theorems 1 and 2     

Critical stability and stabilization of discrete-time stochastic systems and its applications

In this paper, critical stability and critical stabilization for discrete stochastic systems with both state and control dependent noise are discussed via the spectrum technique. The Popov-Belevitch-Hautus (PBH) criterion for exact observability in a discrete version is presented. As applications, some interesting results on a class of generalized Lyapunov equations (GLE), unremovable spectra and discrete generalized algebraic Riccati equation (GARE) are obtained. Finally, the problem of assigning the spectra of discrete stochastic systems in a specified disk is considered and some numerical examples are given to demonstrate our results.     

On the well-posedness of a spectral fractional forward–backward pseudo-parabolic equation

We prove existence, uniqueness and stability of solution of a forward–backward pseudo-parabolic equation with spectral fractional Laplacian. Then we define and prove existence of Young measure valued solution for fractional forward–backward problem by the vanishing viscosity method.     

正倒向随机微分方程与一类线性二次随机最优控制问题

讨论一类正倒向随机微分方程解的存在唯一性及其对应的一类线性二次随机最优控制 问题,利用单调性方法证明了一类特殊的正倒向随机微分方程解的存在唯一性定理,利用该结果 研究一类耦合了一个倒向随机微分方程的线性随机控制系统广义最优指标随机控制问题,得到 由正倒向随机微分方程的解所表示的唯一最优控制的显式表达式,并得到精确的线性反馈及其 对应的Riccati方程.     

Existence conditions and properties for the maximal periodic solution of periodic Riccati difference equations

The existence and properties of the maximal symmetric periodic solution of the periodic Riccati difference equation, is analysed for the optimal filtering problem of linear periodic discrete-time systems. Special emphasis is given to systems not necessarily reversible and subject only to a detectability assumption. Necessary and sufficient conditions for the existence and uniqueness of periodic non-negative definite solutions of the periodic Riccati difference equation which gives rise to a stable filter are also established. Furthermore, the convergence of non-negative definite solutions of the Riccati equation is investigated.