H<SUP>∞</SUP> optimization with plant uncertainty and semidefinite programming

作     者：Helton, JW Merino, O Walker, TE 

作者机构：Univ Calif San Diego Dept Math La Jolla CA 92093 USA Univ Rhode Isl Dept Math Kingston RI 02881 USA Univ Calif Berkeley Dept Math Berkeley CA 94720 USA 

出 版 物：《INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL》 (国际强度与非线性控制杂志)

年 卷 期：1998年第8卷第9期

页      面：763-802页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

主　　题：Optimal control systems 

摘      要：The fundamental H-infinity problem of control is that of finding the stable frequency response function that best fits worst case frequency domain specifications. This is a non-smooth optimization problem that underlies the frequency domain formulation of the H-infinity problem of control;it is the main optimization problem in qualitative feedback theory for example. It is shown in this article how the fundamental H-infinity optimization problem of control can be naturally treated with modern primal-dual interior point (PDIP) methods. The theory introduced here generalizes and unifies approaches to solving large classes of optimization problems involving matrix-valued functions, a subclass of which are commonly treated with linear matrix inequalities techniques, Also, in this article new optimality conditions for H-infinity optimization problems over matrix-valued functions are proved, and numerical experience on natural(PDIP) algorithms for these problems is reported. In experiments we find the algorithms exhibit (local) quadratic convergence rate in many instances. Finally, H-infinity optimization problems with an uncertainty parameter are considered. It is shown how to apply the theory developed here to obtain optimality conditions and derive algorithms. Numerical tests on simple examples are reported. (C) 1998 John Wiley & Sons, Ltd.