Nonlinear optimal control synthesis via occupation measures

TL;DR

This paper presents a method using occupation measures and LMI relaxations to approximate solutions for nonlinear polynomial optimal control problems, enabling the derivation of nearly optimal control laws.

Contribution

It extends occupation measure techniques to approximate the value function on specific sets and construct near-optimal controls for polynomial nonlinear systems.

Findings

Effective approximation of the value function demonstrated

Constructed near-optimal control laws from approximations

Numerical examples confirm the approach's efficiency

Abstract

We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given OCP, using a hierarchy of linear matrix inequality (LMI) relaxations. In the second part, we extend the methodology to approximate the optimal value function on a given set and we use such a function to constructively and computationally derive an almost optimal control law. Numerical examples show the effectiveness of the approach.