Adaptive Robust Control for Uncertain Systems via Data-Driven Learning

Jun Zhao,Qingliang Zeng,Chun-Xi Yang

doi:10.1155/2022/9686060

Abstract

Although solving the robust control problem with offline manner has been studied, it is not easy to solve it using the online method, especially for uncertain systems. In this paper, a novel approach based on an online data-driven learning is suggested to address the robust control problem for uncertain systems. To this end, the robust control problem of uncertain systems is first transformed into an optimal problem of the nominal systems via selecting an appropriate value function that denotes the uncertainties, regulation, and control. Then, a data-driven learning framework is constructed, where Kronecker’s products and vectorization operations are used to reformulate the derived algebraic Riccati equation (ARE). To obtain the solution of this ARE, an adaptive learning law is designed; this helps to retain the convergence of the estimated solutions. The closed-loop system stability and convergence have been proved. Finally, simulations are given to illustrate the effectiveness of the method.

Highlights

Existing achievements of control techniques are mostly acquired under the assumption that there are no dynamical uncertainties in the controlled plants
The closed-loop system generally satisfies the uniformly bounded (UUB). These results fully show that the approximate dynamic programming (ADP) method is suitable for the robust control design of complex systems in uncertain environment
The robust control problem of uncertain systems is first transformed into an optimal control problem of the nominal systems with an appropriate cost function

Summary

Introduction

Existing achievements of control techniques are mostly acquired under the assumption that there are no dynamical uncertainties in the controlled plants. Based on the above facts, we develop a robust control design for uncertain systems via using an online datadriven learning method For this purpose, the robust control problem of uncertain systems is first transformed into an optimal control problem of the nominal systems with an appropriate cost function. A data-driven technique is developed, where Kronecker’s products and vectorization operations are used to reformulate the derived ARE To solve this ARE, a novel adaptive law is designed, where the online solution of ARE can be approximated.

Preliminaries and Problem Formulation

Online Solution to Robust Control via DataDriven Learning

Example 1

Example 2

Conclusion