Integral Reinforcement Learning Control for a Class of High-Order Multivariable Nonlinear Dynamics With Unknown Control Coefficients

Qingling Wang

doi:10.1109/access.2020.2993265

Qingling Wang

Open Access

https://doi.org/10.1109/access.2020.2993265

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Abstract

This paper develops an integral reinforcement learning (IRL) controller for a class of high-order multivariable nonlinear systems with unknown control coefficients (UCCs). A new long-term performance index is first presented, and then the critic neural network (NN) and the action NN are presented to estimate the unobtainable long-term performance index and the unknown drift of systems, respectively. By combining the critic and action NNs with Nussbaum-type functions, the IRL controllers for high-order, nonsquare multivariable systems are proposed to cope with the problem of UCCs. The analysis are given to illustrate that the stability of the closed-loop system can be obtained, and the signals of the closed-loop systems are semiglobally uniformly ultimately bounded (UUB). Finally, one simulation example is provided to show the effectiveness of the proposed IRL controllers.

Highlights

Adaptive control of multivariable systems has attracted significant attention in the last several decades, where the design of control laws is much more challenging than the single-input systems due to the dynamic couplings of the high-frequency gain matrix [1], [2]
One of fundamental problems of multivariable systems is how to deal with the unknown high-frequency gain matrix known as unknown control coefficients (UCCs), which makes the extension from single-input systems to multivariable systems far from trivial
In this paper, we have developed an integral reinforcement learning (IRL) controller for a class of high-order multivariable nonlinear systems with UCCs

Summary

Introduction

Adaptive control of multivariable systems has attracted significant attention in the last several decades, where the design of control laws is much more challenging than the single-input systems due to the dynamic couplings of the high-frequency gain matrix [1], [2]. The high-frequency gain matrix of these works are known in advance to design controllers. Some practical systems can not possess the knowledge of the high-frequency gain matrix in priori, see for example, in [3]–[5]. One of fundamental problems of multivariable systems is how to deal with the unknown high-frequency gain matrix known as UCCs, which makes the extension from single-input systems to multivariable systems far from trivial.

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