Adaptive dynamic programming for nonaffine nonlinear optimal control problem with state constraints

TL;DR

This paper introduces a novel constrained adaptive dynamic programming algorithm for nonlinear optimal control with state constraints, utilizing neural networks and a trust region approach for effective policy updates.

Contribution

It develops a constrained generalized policy iteration framework and an actor-critic method that directly handle state constraints in nonlinear control problems.

Findings

Successfully applied to vehicle path-tracking control.

Outperforms traditional methods in handling state constraints.

Ensures stable policy updates with trust region constraints.

Abstract

This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state constraints. Firstly, a constrained generalized policy iteration (CGPI) framework is developed to handle state constraints by transforming the traditional policy improvement process into a constrained policy optimization problem. Next, we propose an actor-critic variant of CGPI, called CADP, in which both policy and value functions are approximated by multi-layer neural networks to directly map the system states to control inputs and value function, respectively. CADP linearizes the constrained optimization problem locally into a quadratically constrained linear programming problem, and then obtains the optimal update of the policy network by solving its dual problem. A trust region constraint is added to prevent excessive policy update, thus ensuring linearization accuracy. We determine the feasibility of the policy optimization problem by calculating the minimum trust region boundary and update the policy using two recovery rules when infeasible. The vehicle control problem in the path-tracking task is used to demonstrate the effectiveness of this proposed method.