MIMO自校正控制器的全局稳定算法

本文为确定性多变量线性系统建立了全局稳定的MIMO自校正控制器算法。使用这种适应控制算法,无论系统的和算法的初始条件如何,都能保证系统稳定,而且能使自校正控制器的输出渐近地跟踪最优控制器的输出。该算法不用在线解方程组,避免了麻烦的矩阵求逆运算。文献[1]中的主要结果以及文献[2]中的确定性结果,大体上可视为本文结果的特殊情况。     

回溯自校正调节器研究之路

首先介绍了著名自校正调节器的定义,在自适应控制发展中所起的作用,以及对其进行理论研究的困难.其次,简单回顾了自1973年瑞典(A)str(o)m与Wittenmark教授发表著名论文起,国际控制界在自校正调节器理论研究中所走过的一段艰难曲折历程.接着,作者回顾了自己的相关研究经历,并简单介绍了最终如何建立自校正调节器的全局收敛性理论等.最后,给出了若干研究感悟和启示.     

浅谈H_∞控制理论的发展与应用

H_∞范数是鲁棒控制理论的重要性能指标之一.当系统中存在不确定外界干扰时,H_∞控制理论可以用来分析系统鲁棒性和设计控制器.本文从确定性系统、随机系统和离散时间系统等角度,分别介绍了H_∞控制理论的发展,并通过具体例子介绍H_∞理论的应用.     

“控制室科研工作介绍”专辑

<正>前言2012年是中国科学院系统控制重点实验室的前身中国科学院数学所控制理论研究室成立50周年.大约在一年以前,系统控制室的一些科研团队成员建议在系统科学研究所30周年所庆材料中系统控制重点实验室科研工作简介的基础上,由《系统科学与数学》出一个专辑比较系统地介绍系统控制室的研究工作,以便于进行学术交流.本专辑所收集的文章对系统控制室的研究人员在系统控制相关领域的部分代表性研究工作做了总结,其中包括自校正调节器、变界截尾随机逼近算法、矩阵半张量积的理论与应     

动力学系统参数辨识问题最优控制解的理论与方法(Ⅰ)--基本概念及确定性系统参数辨识

本文基于动力学系统参数辨识问题最优控制解的概念和确定性动力学系统的最优控制理论,建立了参数辨识研究与最优控制理论的对应关系.将最优控制的数学理论和算法应用于参数辨识问题的研究.依据Hamilton-Jacobi-Bellman (HJB)方程解的理论阐述了动力学系统参数辨识最优控制解的存在唯一性问题,并据此得到了解决确定性系统参数辨识问题的具体算法步骤.     

动力学方程的积分型直接积分法

提出了一个求解动力学问题的新方法(DIM-IM).将动力学方程化成积分方程的形式,借助于该方程构造出了具有显式预测-校正的单步、自起动和四阶精度的积分型直接积分算法.理论分析和算例指出,这一方法较中心差分法、Houbolt法、Newmark法和Wilson-θ法都有较高的精度.本方法适用于强非线性,非保守系统.     

线性多变量调节器的设计

调节器问题是自动控制理论研究的重要问题之一。调节器的设计要求是:求一个反馈控制器使闭环系统稳定并且使输出趋向于零(控制理论中称为输出调节)。很多实际系统的控制问题归结为线性多变量调节器的设计问题。例如经典控制理论中的调节问题和跟踪问题都可化为调节器问题,在经济系统中也提出了一些线性多变量调节器的设计问题。     

动力学系统参数辨识问题最优控制解的理论与方法（I）—基本概 …

本文基于动力学系统参数辨识问题最优控制解的概念和确定性动力学系统的最优控制理论,建立了参数辨识研究与最优控制理论的对应关系。将最优控制的数学理论和算法应用于参数辨识问题的研究。依据Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ－Ｂｅｌｌｍａｎ（ＨＪＢ）方程解的理论阐述了动力学参数辨识最优控制解的存在唯一性问题,并据此得到了解决确定性系统参数辨识问题的具体算法步骤。     

基于自适应极大后验估计的空间目标运动状态确定

提出一种新的基于自适应极大后验(AMAP)估计的空间目标运动状态确定方法,致力于削弱未知干扰对状态估计的不利影响.针对带有干扰的离散时间非线性随机系统设计了AMAP估计算法,采用高斯-牛顿优化方法实现极大后验(MAP)估计,通过模式切换和加权融合强化算法的自适应能力.基于理论分析导出了状态估计均方误差(MSE)的表达式,说明所提算法能够达到优于传统扩展卡尔曼滤波(EKF)和MAP估计算法的精度.以空间目标运动状态确定系统为例,通过蒙特卡洛仿真验证了AMAP估计算法的性能优势,不同条件下的对比研究表明,所提算法具备应对未知干扰的自适应能力,能够有效提升空间目标运动状态估计精度.     

P_*(κ)线性互补问题基于新核函数的大步校正算法（英文）

本文研究了P*(κ)线性互补问题的大步校正原始-对偶内点算法.基于一个强凸且不同于通常的对数函数和自正则函数的新核函数,对具有严格可行初始点的该问题,算法获得的迭代复杂性√为O(1+2κ)n(log n)2lognε,该结果缩小了大步校正内点算法的实际计算与理论复杂性界之间的差距.     

Optimal persistent disturbance attenuation control for linear hybrid systems

In this paper, the disturbance attenuation properties for a class of linear hybrid systems are investigated, and a hybrid optimal persistent disturbance attenuation control problem is studied. First, a procedure is developed to determine the minimal l^∞$l^{\infty }$ induced gain of linear hybrid systems. However, for general hybrid systems, the termination of the procedure is not guaranteed. Then, the decidability issues are discussed. The termination of the procedure in a finite number of steps is shown for a subclass of hybrid systems with simplified discrete event dynamics, called switched linear systems. Finally, the optimal persistent disturbance attenuation controller synthesis problem is studied. It is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law, and a systematic approach is proposed to design such feedback control.     

离散系统Lyapunov第二方法的一些问题

本文讨论线性时不变离散系统Lyapunov方程解集的几何性质以及分段线性离散系统的稳定性,得出每个子系统都是稳定的分段线性离散系统渐近稳定的一些充分条件,并把这些结果应用于二阶分段线性系统.     

Disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator

This paper is concerned with the problems of disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator. Using the switched Lyapunov function approach, a sufficient condition for the existence of a state feedback controller is proposed such that the disturbance tolerance capability of the closed-loop system is ensured. By solving a convex optimization problem with linear matrix inequality (LMI) constraints, the maximal disturbance tolerance is estimated. In addition, the problem of disturbance rejection of the closed-loop system is solved. Two examples are given to illustrate the effectiveness of the proposed method.     

Multivariable state-feedback self-tuning controllers ∗

This paper describes a state-space approach for self-tuning control of a class of multivariable stochastic systems having the same number of inputs as outputs. A multivariable state-feedback self-tuning controller, based on pole-assignment concepts, is derived. The developed multivariable self-tuner can be applied to stable/unstable and minimum/non-minimum phase linear time-invariant multivariable systems. A multivariable reduced-order self-tuner and a state-feedback minimum-variance self-tuner are also derived. The simplicity and flexibility of the proposed state-space approach facilitate the practical applications of self-tuning control concepts to real systems     

Internal ellipsoidal estimates of attainability sets for linear systems under conditions of uncertainty

The problem of constructing internal ellipsoidal estimates of the geometric difference between two ellipsoids and applying the estimated results for the attainability sets of linear systems with a disturbance is considered. An addition to the existing method of constructing the difference between two ellipsoids is presented, and the previous constraints are removed. In the process of validating the addition, some relationships between certain properties of constructed ellipsoidal estimations and set convexity are given, being the data for the problem. A method for estimating the attainability sets for linear systems with a disturbance, equivalent to the existing approach to systems without disturbances, are given. The disturbances are considered using the obtained results.     

Disturbance decoupling and model matching problems for discrete-time systems with time-varying delays

In this paper, the disturbance decoupling problem and the model matching problem for discrete-time linear systems with time-varying delays are considered. Solvability of the above problems is characterized by means of structural necessary and sufficient conditions that can be checked by algorithmic procedures. The basic method used to analyze the considered problems consists in representing the discrete-time linear systems with time-varying delays as switching linear systems, whose properties can be studied by a powerful structural approach. In this way, the considered control problems can be reduced to the corresponding problems for switched linear systems, whose solvability has been recently characterized.     

Galerkin finite element method for nonlinear fractional Schrödinger equations

In this paper, a class of nonlinear Riesz space-fractional Schrödinger equations are considered. Based on the standard Galerkin finite element method in space and Crank-Nicolson difference method in time, the semi-discrete and fully discrete systems are constructed. By Brouwer fixed point theorem and fractional Gagliardo-Nirenberg inequality, we prove the fully discrete system is uniquely solvable. Moreover, we focus on a rigorous analysis and consideration of the conservation and convergence properties for the semi-discrete and fully discrete systems. Finally, a linearized iterative finite element algorithm is introduced and some numerical examples are given to confirm the theoretical results.     

离散型线性定常系统的摄动矩阵李亚普诺夫方程的若干问题

本文讨论了离散型线性定常系统在系统参数发生扰动时的李亚普诺夫稳定性与波波夫超稳定性.给出了容许的摄动界,使得离散型线性系统的李亚普诺夫稳定性与波波夫超稳定性的维持得到了保证.该结果在MRAC(模型参考自适应控制)中是具有意义的.     

The algebraic regulator problem from the state-space point of view

We study the algebraic aspects of the regulator problem, using some new ideas in the state-space (“geometric”) approach to feedback design problems for linear multi- variable systems. Necessary and sufficient conditions are given for the solvability of a general version of this problem, requiring output stability, internal stability, and disturbance decoupling as well. An algorithm is given by which these conditions can be verified from the system parameters.     

一般目标信号和干扰信号下多采样率系统的最优预见控制器设计

针对目标信号和干扰信号为多项式的情形,研究了多采样率离散时间控制系统的最优预见控制问题.首先利用离散时间系统提升技术,把所研究的系统转化成单采样率的扩大系统.然后构造扩大误差系统,把问题转化为包含预见信号的最优调节问题.最后利用最优预见控制理论的结果得到系统的最优预见控制输入,其中包含积分器和预见前馈补偿.本文还对扩大误差系统的能控性和能观测性和相应的代数Riccati方程的可解性进行了讨论.