Synthesis of Robust Controllers with Structured Real Uncertain Parameters

提出这一建议的动机来自于结构实不确定参数存在时的鲁棒控制问题。更具体地说，它专门处理由传递函数或状态空间模型描述的线性系统，该模型包括进入各种对象系数的不确定参数。研究的起点是以哈里托诺夫定理为动力的文学本体。鉴于这方面的文献几乎完全涉及到鲁棒稳定性分析，研究的第一个焦点是鲁棒镇定控制器的综合。最近关于区间对象(区间多项式之比)具有一阶控制器的鲁棒镇定的一些极点结果(涉及PI)为这项工作提供了火花。所谓的价值集方法也提供了额外的动力。鉴于值集在分析上下文中的广泛使用，一个悬而未决的问题是：值集在综合上下文中的用处有多大？这项提议的第二个重点是稳健的业绩。也就是说，目标是在稳定性之上处理健壮的性能规范。类似于鲁棒镇定的研究，目的是从研究低阶控制器的鲁棒性能问题开始，然后跟进高阶情况。在这个框架下，提出了一些重要的研究问题。第三个也是最后一个焦点是由词语生成机制描述的。也就是说，为了扩大可容纳的不确定性类别，建议对分析中出现的“不确定”多项式和有理函数施加更多的结构。

The motivation for this proposal is derived from the problem of robust control in the presence of structured real uncertain parameters. More specifically, it deals exclusively with linear systems described by a transfer function or state space model which includes uncertain parameters entering into various plant coefficients. The takeoff point for research is the body of literature motivated by Kharitonov's Theorem. Given the fact that this body of literature deals almost exclusively with robust stability analysis, the first focal point of the research is synthesis of robust stabilizing controllers. A spark for this line of work is provided by some recent extreme point results (involving the PI) on robust stabilization of an interval plant (ratio of interval polynomials) with a first order controller. Additional motivation is also provided by the so-called value set approach. Given the widespread use of value sets in an analysis context, the open question is: To what extent are value sets useful in a synthesis context? The second focal point of this proposal is robust performance. That is, the objective is to deal with robust performance specifications over and above stability. Analogous to the investigation of robust stabilization, the intention is to begin the work by looking at robust performance problems with low order controllers and then to follow up with the higher order case. In this framework, a number of important research problems are proposed. The third and final focal point is described by the words generating mechanism. That is, to enlarge the class of uncertainties which can be accommodated, it is proposed to impose more structure on the "uncertain" polynomials and rational functions which arise in the analysis.