Realization of closed-loop specific optimal control

Designing nonlinear control systems warrants considerable effort under most circumstances. This fact is accentuated when one considers the optimal control problem. In this paper we address synthesis of specific optimal control for general nonlinear, fixed structure systems. By considering the stability relative to optimal open-loop solutions, we arrive at conditions sufficient for a given policy to produce optimal or suboptimal performance in a closed-loop configuration. The approach is applicable to any system and performance index whose open-loop solution may be obtained. A bound for the departure of the propagated closed-loop state from optimum is given as a function of time, control policy, and initial condition. An example problem is also given.