A two-player game representation for a class of infinite horizon control problems under state constraints

TL;DR

This paper introduces a two-player game framework for solving a class of infinite horizon control problems with state constraints, extending viability results to nonlinear dynamics and deriving feedback laws.

Contribution

It presents a novel two-player game representation for infinite horizon control problems with nonlinear dynamics and state constraints, expanding existing linear-quadratic regulator results.

Findings

Extended viability results to nonlinear dynamics

Derived feedback laws under controllability assumptions

Applicable to a broader class of control problems

Abstract

In this paper we give feedback laws for a class of parametrized infinite horizon control problems under state constraints. We provide a two-player representation assuming time dependent dynamics and Lagrangian and the set constraints merely compact. Using viability results recently investigated for infinite horizon settings in presence of state constraints, we extend some known results for the linear-quadratic regulator problem to control problems with nonlinear dynamics in the state and affine in the control. Feedback laws are obtained under suitable controllability assumptions.