A Continuous Feedback Optimal Control based on Second-Variations for Problems with Control Constraints

TL;DR

This paper introduces a continuous second-variation algorithm for solving optimal control problems with control constraints, enabling automatic detection of switching points and adaptive time mesh refinement.

Contribution

It presents a novel continuous second-variation method that efficiently handles control constraints and automatically identifies switching points in optimal control problems.

Findings

Successfully applied to bang-bang control problems

Automatically detects optimal switching points

Adapts time mesh during the solution process

Abstract

The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a locally feedback optimal control of the problem. Since the process involves a backward and a forward stage, which require storing trajectories, a method has been devised to accurately store continuous solutions of ordinary differential equations. Thanks to the continuous approach, the method adapts implicitly the numerical time mesh. The novel method is demonstrated on bang-bang optimal control problems, showing the suitability of the method to identify automatically optimal switching points in the control.