稳定降阶控制器设计的新方法(英文)

New methods for stable and reduced-order controller design

中文关键词  稳定控制器  同时镇定  H无穷控制  严格正实  范数约束  NP难问题

英文关键词  stable controllers  simultaneous stabilization  $H_{\infty}$ control  SPR  norm constraint  NP-hard problems

中文摘要

      这篇文章首先提出了稳定降阶控制器的一个特殊结构, 然后给出了两种控制器设计方法. 一种是基于新的松弛变量的特殊构造, 另一种是基于分离李雅普诺夫矩阵和控制器矩阵的两步法. 新的方法可以处理具有不同阶数和不同数目不稳定极点的几个系统的同时镇定问题, 而这个问题是很难用一般的鲁棒控制方法处理的. 本文提出的新方法还可以拓展到处理H无穷, 严格正实以及分散控制问题. 最后, 我们讨论了控制器的范数约束问题. 在该方法中, 甚至每一个控制器参数都可以被施加绝对值约束. 本文还讨论了相关的NP难问题, 给出了相应的控制器设计算法. 最后, 给出了几个例子验证了所提出的设计方法的有效性, 并且对这两种设计方法进行了对比.

英文摘要

      In this paper, a special structure is first proposed for stable and reduced-order controllers. Then, two controller design methods are presented, where one is based on a special construction on the new introduced slack matrix variables, the other is based on the separation of Lyapunov matrix and control matrix from the two stage algorithms. The new methods can deal with the simultaneous stabilization problems for several plants with different orders and different numbers of unstable poles which can not be solved by general robust control methods. The new methods are also generalized to solve $H_{\infty}$, strict positive real (SPR) and decentralized control problems. Finally, norm constraint problems of controllers are discussed, even an absolute value constraint can be added to each controller parameter in the proposed methods. Related NP hard problems have been discussed in this paper, and related controller design algorithms are proposed. Two new methods are compared with each other in several examples, and the effectiveness of the new methods are illustrated.