The connection between discrete and continuous state constraints optimal control systems: the deterministic case

TL;DR

This paper investigates the relationship between discrete and continuous state constraints in optimal control systems, proving convergence of solutions and validating findings through a linear quadratic example.

Contribution

It introduces a discrete state constraints optimal control problem as a near-optimal approximation and proves convergence to the continuous problem's solution.

Findings

Discrete control problem is near-optimal for the continuous one.

Optimal solutions of the discrete problem converge to the continuous solution.

Linear quadratic example verifies the theoretical results.

Abstract

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and prove that this 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 one. Finally, we use a linear quadratic optimal problem to verify the main results of this study.