Randomized algorithms for probabilistic robustness with real and complex structured uncertainty

作     者：Calafiore, GC Dabbene, F Tempo, R 

作者机构：Politecn Torino IRITI CNR Dipartimento Automat & Informat I-10129 Turin Italy 

出 版 物：《IEEE TRANSACTIONS ON AUTOMATIC CONTROL》 (IEEE Trans Autom Control)

年 卷 期：2000年第45卷第12期

页      面：2218-2235页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 

基　　金：IRITI-CNR  (CNR 99.01960) 

主　　题：random matrices randomized algorithms robust control uncertainty 

摘      要：In recent Sears, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems, Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance, if a certain design specification is met with a given probability. One of the advantages of this approach is that the robustness margins can be often increased by a considerable amount, at the expense of a small risk. In this sense, randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information, The applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres, Sampling in more general uncertainty sets is generally performed through overbounding, at the expense of an exponential rejection rate. In this paper, randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general M-Delta configuration are studied, In particular, efficient polynomial-time algorithms for uncertainty structures Delta consisting of an arbitrary number of full complex blocks and uncertain parameters are developed.