Maximum principle for a deterministic optimal control problem under state constraints: A limit approach

Shuzhen Yang

Published 2017-09-01Version 1

An optimal control problem driven by an ordinary differential equation under state constraints is considered in this study. Different from the classical maximum principle under state constraints, from an operational point of view, we first introduce a discrete state constraints optimal control problem and prove its maximum principle. Then, we prove that the discrete state constraints optimal control problem is a near-optimal control problem of the original problem. Furthermore, we show that the optimal solution of the near-optimal control problem converges to the optimal solution of the original problem. Finally, we use a linear quadratic optimal problem to verify the main results of this study.