时变系统的模型匹配与跟踪问题

Suboptimal model-matching and tracking problem of time-varying systems

中文关键词  次优控制  模型匹配  J–谱分解  同时镇定  时变系统

英文关键词  suboptimal control  model-matching  J–spectral factorization  simultaneous stabilization  time-varying system

中文摘要

      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.

英文摘要

      The existence of suboptimal solutions to the Nehari-type model-matching problem of time-varying system has been obtained by employed the same method used in the time-invariant case. Unfortunately there is no effective way to prove the existence of suboptimal solutions to the bilateral model-matching problem of time-varying case. This paper deals with the suboptimal model-matching problem and the suboptimal tracking problem using two-parameter controller for discrete time-varying linear systems in the frame work of nest algebra. According to Douglas’s range inclusion theorem, the existence of two coupled J-spectral factorizations determined by the models implies the existence of suboptimal solutions to the model matching problem. Furthermore, it is proved that the problem of simultaneously stabilizing n plants by two-parameter controller with the tracking performance less than a prescribed level r is equivalent to the problem of simultaneously strongly-r stabilizing n - 1 associated four block systems.