Nearly Optimal Patchy Feedbacks for Minimization Problems with Free Terminal Time

TL;DR

This paper proves the existence of nearly optimal patchy feedback controls for nonlinear minimization problems with free terminal time, ensuring trajectories are close to optimal solutions within a specified accuracy.

Contribution

It introduces a novel patchy feedback construction that guarantees nearly optimal trajectories for complex control problems with free terminal time.

Findings

Existence of patchy feedback controls for nonlinear systems.

Trajectories are nearly optimal with pre-assigned accuracy.

Applicable to problems with free terminal time.

Abstract

The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are all nearly optimal solutions, with pre-assigned accuracy.