Robust Properties of Risk-Sensitive Control

The purpose of this paper is to characterize and prove robustness properties of risk-sensitive controllers precisely. In particular, we establish a stochastic version of the small gain theorem. This theorem is expressed in terms of an inequality which bounds the average output power in terms of the input power. Since this inequality is closely related to the risk-sensitive criterion, our stochastic small gain theorem can be expressed in terms of the risk-sensitive criterion. This provides a concrete motivation for the use of the risk-sensitive criterion stochastic robustness. Date received: September 10, 1998. Date revised: June 5, 2000.     

Small Parameter Limit for Ergodic, Discrete-Time, Partially Observed, Risk-Sensitive Control Problems

We show that discrete-time, partially observed, risk-sensitive control problems over an infinite time horizon converge, in the small noise limit, to deterministic dynamic games, in the sense of uniform convergence of the value function on compact subsets of its domain. We make use of new results concerning large deviations and existence of value functions. Date received: May 21, 1999. Date revised: April 7, 2000.     

Finite Horizon Minimax Optimal Control of Stochastic Partially Observed Time Varying Uncertain Systems

We consider a linear-quadratic problem of minimax optimal control for stochastic uncertain control systems with output measurement. The uncertainty in the system satisfies a stochastic integral quadratic constraint. To convert the constrained optimization problem into an unconstrained one, a special S-procedure is applied. The resulting unconstrained game-type optimization problem is then converted into a risk-sensitive stochastic control problem with an exponential-of-integral cost functional. This is achieved via a certain duality relation between stochastic dynamic games and risk-sensitive stochastic control. The solution of the risk-sensitive stochastic control problem in terms of a pair of differential matrix Riccati equations is then used to establish a minimax optimal control law for the original uncertain system with uncertainty subject to the stochastic integral quadratic constraint. Date received: May 13, 1997. Date revised: March 18, 1998.     

Robust control and differential games on a finite time horizon

It is well known that theH control problem has a state space formulation in terms of differential games. For a finite time horizon control problem, the analogous differential game is considered. The disturbance is the control for the maximizing player. In order to allow forL ² disturbances, the controls for at least one player must be allowed to be unbounded. It is shown that the value of the game is the viscosity solution of the corresponding Isaacs equation under rather general conditions.     

离散时间菱形不确定系统的鲁棒控制器设计

对一类MIMO的菱形不确定离散时间线性系统，利用有限端点检验结果，提出一种输出反馈控制器的设计方法，导出了输出反馈增益矩阵置所满足的一组特殊非线性方程，通过求解该方程组；使有限个线性系统输出反馈LQ问题同时达到最优，从而保证菱形闭环系统是鲁棒渐近稳定的。数值例子说明了该方法的正确性。     

Guaranteeing cost strategies for linear quadratic differential games under uncertain dynamics

This paper deals with the design of closed loop strategies for a class of two players zero-sum linear quadratic differential games, where each player does not know exactly the state equation and model it through a system subject to norm-bounded uncertainties. The finite horizon and the infinite horizon problems are both solved: it turns out that the optimal strategies, guaranteeing to each player a given level of performance, require, to be evaluated, the solution of two scaled differential (algebraic in the infinite horizon case) Riccati equations. A numerical example illustrates an application of the proposed technique.     

Asymptotic analysis of nonlinear stochastic risk-sensitive control and differential games

In this paper we consider a finite horizon, nonlinear, stochastic, risk-sensitive optimal control problem with complete state information, and show that it is equivalent to a stochastic differential game. Risk-sensitivity and small noise parameters are introduced, and the limits are analyzed as these parameters tend to zero. First-order expansions are obtained which show that the risk-sensitive controller consists of a standard deterministic controller, plus terms due to stochastic and game-theoretic methods of controller design. The results of this paper relate to the design of robust controllers for nonlinear systems.Research supported in part by the 1990 Summer Faculty Research Fellowship, University of Kentucky.     

Robust stability and performance of stochastic uncertain systems on an infinite time interval

In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.     

广义离散系统的状态反馈鲁棒H∞控制及仿真

针对一类范数有界参数不确定性的广义离散线性系统,研究了该系统的状态反馈鲁棒H∞控制问题.利用线性矩阵不等式(LMI)的方法,得到了问题可解的条件,并给出了相应的状态反馈控制律.在一定条件下,所得的状态反馈鲁棒H∞控制律使广义离散线性系统对所有容许的不确定性参数,能够保证闭环系统正则、具有因果关系并且渐进稳定,同时其传递函数矩阵能够满足给定的H∞性能指标.正常离散线性系统的相对应结果可作为论文结果的特殊形式.仿真例子验证了该方法的正确性.     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统,给出一种鲁棒渐近稳定控制器的设计方法,且对匹配与不匹配两类不确定系统进行了研究.与现有结果相比,按此方法设计的系统不但控制器增益较小,实现方便,而且可以容许较大的系统不确定性.     

移动机械手鲁棒自适应模糊控制

基于旋量理论建立了非完整移动机械手系统的动力学模型,通过反步控制技术,应用非线性参数化模糊逻辑系统设计了移动机械手的鲁棒自适应模糊控制器.该控制器放松了移动机械手控制器设计中斜对称性的要求,对移动机械手系统中存在的参数或外界扰动等不确定性具有较强的鲁棒性和自适应能力.理论证明和仿真结果表明,所设计的控制器是有效的.     

Web 服务器的鲁棒建模和过载控制

给出了一种Web 服务器的建模方法,说明了如何用控制理论管理不可预测的服务器负载。Web 服务器可以被仿真为一个多容器系统。该鲁棒Web 服务器模型适用于未知的负载干扰和不确定的匹配模型。过载控制技术基于自适应允许控制取得时间保证,用一个完整参数变化模型和大的过载来评估模型的性能。     

船舶鲁棒控制及仿真系统研究

采用ＶＢ和Ｍａｔｌａｂ混合编程技术,通过文件传送数据,通过仿人击键事件传达命令,开发了船舶鲁棒控制及仿真系统。该系统有“船舶模型”、“鲁棒控制算法”和“仿真”等五个模块,采用开放交互式设计结构,可随时更改设计及仿真参数,无需要改任何程序。研究了船舶鲁棒控制策略,并完成了回路成形、μ分析及鲁棒积分等五种鲁棒控制算法的标准Ｍａｔｌａｂ软件包实现,并针对每种算法,给出了实际的鲁棒控制算法设计及仿真示例。     

热工控制对象的不同控制方案的鲁棒性分析

针对热工控制对象模型的复杂性和参数不确定性,首先运用二步线性最小二乘法进行模型降阶,将对象模型降为二阶,然后对二阶模型设计定值控制器并进行控制器参数优化,包括:PID控制、鲁棒控制、内模控制和模糊控制的控制方法进行鲁棒稳定性分析、比较,得出分析结果.这一研究意义就在于,在理论分析及仿真试验的基础上找出最为适合热工控制对象参数时变这一特性的具有较强鲁棒性的控制器设计方案,对实际的工程应用进行指导.     

航向保持鲁棒最小二乘支持向量机控制

考虑到船舶航向控制中,存在的大量不确定因素及对控制系统的实时性要求,提出一种基于鲁棒最小二乘支持向量机(RLSSVM)的船舶航向保持控制方案.该控制策略充分利用最小二乘支持向量机良好的非线性映射能力、自学习适应能力和并行信息处理能力,并与H~2/H~∞鲁棒控制算法相结合,优势互补,形成闭环控制.仿真结果表明,该系统对海情的变化有良好的自适应能力,鲁棒性强,实现了航向保持精确控制.     

废水污泥焚烧过程的鲁棒自适应控制

This paper presents a robust model reference adaptive control scheme to deal with uncertain time delay in the dynamical model of a fluidized bed combustor for sewage sludge. The theoretical analysis and simulation results show that the proposed scheme can guarantee not only stability and robustness, but also the adaptive decoupling performance of the system.     

Coprime-factorized Model Predictive Control for Unstable Processes with Delay

This paper presents coprime-factorized model predictive control. The main idea of the proposed approach is in process-output prediction based on a coprime-factorized process model. The proposed approach provides a framework to design the control for a wide range of processes such as: higher order, phase non-minimal, unstable and also multivariable. In the paper the coprime-factorized predictive design methodology was studied and implemented on unstable processes with a time-delay which are very difficult to control. The proposed methodology leads to a simple analytical control law, which results in much better performance than previously known control methods.     

饱和约束系统的鲁棒模型预测控制

针对饱和约束系统提出了一种鲁棒模型预测控制算法,分别考虑了多面体不确定性和结构反馈不确定性.考虑无穷时域的最坏二次性能指标,通过采用带有饱和特性的反馈控制结构,将控制律的求解转化为一个在线的线性矩阵不等式优化问题.初始时刻优化问题的可行性保证了闭环控制系统的鲁棒稳定性.最后的仿真结果说明了算法的优越性.     

复杂工业过程控制结构的综合

介绍了复杂工业过程控制结构综合的研究进展，对所涉及的主要内容以及相关方法、策略进行了阐述，最后对研究复杂工业过程控制结构综合策略的发展方向作了展望。     

预报辨识、映照模型及自校正极点配置鲁棒控制系统

本文以反馈通道存在延时的实际系统为背景,提出了一种简单的参数预报辨识算法,分析证明了该算法的区域收敛性。此外,文中还引入了映照模型的概念,并以此为基础,设计了一种算法简单的自校正极点配置鲁棒控制器,证明了映照模型的跟踪性质和整个闭环系统的稳定性。理论分析及仿真的结果表明,本文给出的方法是可行的。