Abstract
Abstract This paper presents Optimal System Problem, that is what system is optimal when both control law and control criterion are given. Unlike optimal control and the inverse optimal control which have been well researched, Optimal System Problem has not been considered untill now. In this paper, only the case that the criterion is quadratic and the input is single is considered. A necessary and sufficient condition of existence of optimal system which makes closed-loop system stable by given control feedback control law is presented. Also a computation method to get an existing optimal system is discussed. At the last part of this paper, an example is presented to compare optimal control, inverse optimal control and optimal system problem.
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