Adaptive Event-Triggered Near-Optimal Tracking Control for Unknown Continuous-Time Nonlinear Systems

Kunfu Wang,Qinglai Wei,Baiqiao Huang,Qijia Gu,Tianmin Zhou

doi:10.1109/access.2021.3140076

Abstract

This paper studies the event-triggered optimal tracking control (ETOTC) problem of continuous-time (CT) unknown nonlinear systems. In order to solve the ETOTC problem, an augmented system composed of the error system dynamics and the reference dynamics is used to introduce a new discounted performance index function (DPIF). A novel event-triggered (ET) adaptive dynamic programming (ADP) method is developed to solve the ET Hamilton-Jacobi-Bellman equation (HJBE). The presented method is implemented via an identifier-critic architecture, which consists of two neural networks (NNs): an identifier NN is applied to estimate the unknown system dynamics, and a critic NN is constructed to obtain the approximate solution of the ET HJBE. The augmented closed-loop system and the critic estimation error are proved to be ultimately uniformly bounded (UUB) by the Lyapunov direct method. Finally, two simulations illustrate the effectiveness of the developed method.

Highlights

Adaptive dynamic programming (ADP), a branch of the reinforcement learning, is widely concerned in solving optimal control problems in recent years [1]
ADP techniques can be classified into several categories, such as heuristic dynamic programming (HDP), dual HDP (DHP), globalized DHP (GDHP) and their action dependent form [18]–[22]
An augmented system composed of the error system dynamics and the reference dynamics is used to introduce a new discounted performance index function (DPIF) for event-triggered optimal tracking control (ETOTC)

Summary

INTRODUCTION

Adaptive dynamic programming (ADP), a branch of the reinforcement learning, is widely concerned in solving optimal control problems in recent years [1]. For the identified augmented system, a particular ET adaptive implement method is developed without initial stable control law, and the closed loop identified augmented system and the critic weight estimation error are proved to be uniformly bounded (UUB). 1) We extend the ADP-based ETC method to address the optimal tracking control problem. It makes the actual trajectory of the unknown system track its desired one. 3) Under the ET mechanism, we propose a novel NN weights update law for optimal tracking of unknown systems without requiring an initial stable control law, which is an extension time-triggered optimal control methods. C1( a : R+) is the set of once differentiable functions with respect with its argument on a. diag(·) is a diagonal matrix operator

PROBLEM FORMULATION

THEORETICAL ANALYSIS

SIMULATION STUDY

EXAMPLE 2

CONCLUSION