Q-Learning for Linear Quadratic Optimal Control with Terminal State Constraint

TL;DR

This paper develops a Q-learning algorithm for discrete-time linear quadratic optimal control problems with terminal state constraints, addressing unknown system matrices and extending existing methods to constrained scenarios.

Contribution

It introduces a novel Q-learning approach capable of handling terminal state constraints in linear quadratic control with unknown system dynamics.

Findings

Algorithm effectively handles terminal constraints

Numerical example verifies the approach's effectiveness

Extends Q-learning to constrained optimal control

Abstract

This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the time-varying system matrices and input matrices are both unknown. Different from the existing Q-learning algorithms in the literature which are mainly for the unconstrained optimal control problem, the novelty of the proposed algorithm is available to deal with the case with terminal state constraints. A numerical example is illustrated to verify the effectiveness of the proposed algorithm.