Locally optimal controllers and globally inverse optimal controllers

TL;DR

This paper explores the design of controllers that ensure global stability while matching local behavior, linking control Lyapunov functions with optimal control approaches, and illustrating applications to specific system classes and orbital transfer problems.

Contribution

It establishes a connection between local LQ-based control laws and global inverse optimal controllers using control Lyapunov functions, with applications to backstepping, feedforward systems, and orbital transfers.

Findings

Control Lyapunov functions can represent value functions of local optimal problems.

LQ-based local control laws can be extended to globally stabilizing controllers.

Framework applicability demonstrated on backstepping, feedforward systems, and orbital transfer problems.

Abstract

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem.