ANNIHILATOR STRUCTURE OF A PRINCIPAL IDEAL - RELATION TO OPTIMAL COMPENSATORS

作     者：MEYER, DG 

作者机构：Robotics and Control Laboratory Department of Electrical Engineering University of Virginia Charlottesville VA 22901 United States 

出 版 物：《AUTOMATICA》 (自动学)

年 卷 期：1988年第24卷第6期

页      面：829-833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：(duality) convex programming discrete time systems functional analysis Optimal control optimization 

摘      要：Given a linear, time-invariant, discrete-time plant, we consider the optimal control problem of minimizing, by choice of a stabilizing compensator, the seminorm of a selected closed-loop map in a basic feedback system. The seminorm can be selected to reflect any chosen performance feature and must satisfy only a mild condition concerning finite impulse responses. We show that if the plant has no poles or zeros on the unit circle, then the calculation of the minimum achievable seminorm is equivalent to the maximization of a linear objective over a convex set in a low-dimensional Euclidean space. Hence, for a wide variety of optimal control problems, one can compute the answer to an infinite-dimensional optimization by a finite-dimensional procedure. This allows the use of effective numerical methods for computation.