Relaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems

TL;DR

This paper introduces RCTAC, a novel algorithm for continuous-time nonlinear control that guarantees convergence to nearly optimal policies without requiring initial policy admissibility, demonstrated through theoretical proofs and practical simulations.

Contribution

The paper proposes RCTAC, a new continuous-time actor-critic algorithm that relaxes previous restrictions and guarantees convergence for nonlinear systems with known dynamics.

Findings

Proven convergence and near-optimality via Lyapunov analysis.

Effective in path-tracking control of vehicles.

Faster convergence through relaxed update conditions.

Abstract

This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as the path-tracking control of vehicles. RCTAC has several advantages over existing adaptive dynamic programming algorithms for CT systems. It does not require the ``admissibility" of the initialized policy or the input-affine nature of controlled systems for convergence. Instead, given any initial policy, RCTAC can converge to an admissible, and subsequently nearly optimal policy for a general nonlinear system with a saturated controller. RCTAC consists of two phases: a warm-up phase and a generalized policy iteration phase. The warm-up phase minimizes the square of the Hamiltonian to achieve admissibility, while the generalized policy iteration phase relaxes the update termination conditions for faster convergence. The convergence and optimality of the algorithm are proven through Lyapunov analysis, and its effectiveness is demonstrated through simulations and real-world path-tracking tasks.