Toward reliable designs of data-driven reinforcement learning tracking control for Euler–Lagrange systems

Abstract

This paper addresses reinforcement learning based, direct signal tracking control with an objective of developing mathematically suitable and practically useful design approaches. Specifically, we aim to provide reliable and easy to implement designs in order to reach reproducible neural network-based solutions. Our proposed new design takes advantage of two control design frameworks: a reinforcement learning based, data-driven approach to provide the needed adaptation and (sub)optimality, and a backstepping based approach to provide closed-loop system stability framework. We develop this work based on an established direct heuristic dynamic programming (dHDP) learning paradigm to perform online learning and adaptation and a backstepping design for a class of important nonlinear dynamics described as Euler–Lagrange systems. We provide a theoretical guarantee for the stability of the overall dynamic system, weight convergence of the approximating nonlinear neural networks, and the Bellman (sub)optimality of the resulted control policy. We use simulations to demonstrate significantly improved design performance of the proposed approach over the original dHDP.