Adaptive Fuzzy Decentralized Control for Fractional-Order Nonlinear Large-Scale Systems With Unmodeled Dynamics

Shuai Sui,C L Philip Chen,Yongliang Zhan,Shaocheng Tong,Junwei Jin

doi:10.1109/access.2021.3119611

Abstract

This paper addresses the decentralized control issue for the fractional-order (FO) nonlinear large-scale strict-feedback systems with unmodeled dynamics. The unknown nonlinear functions are identified by fuzzy logic systems (FLSs) and the FO dynamic signals are introduced to dominate the unmodeled dynamics. Additionally, the fractional-order dynamic surface control (FODSC) design technique is introduced into the adaptive backstepping control algorithm to avoid the issue of “explosion of complexity”. Then, an adaptive fuzzy decentralized control scheme is developed via the FO Lyapunov stability criterion. It is proved that the controlled FO systems are stable and the tracking errors can converge to a small neighborhood of zero. The simulation example is provided to confirm the validity of the put forward control scheme.

Highlights

F RACTIONAL-ORDER nonlinear systems (FONSs) can be treated as the extension of integer-order nonlinear systems (IONSs), which is a research hotspot developed on the basis of fractional-order calculus theory
Some real systems can be modeled by utilizing FONSs, for example, micro-electro-mechanical resonators [1], hyperchaotic economic systems [2] and lithiumion batteries [3]
Control objectives: On the basis of FO Lyapunov stability criterion, an adaptive fuzzy decentralized controller is designed for systems (1), which makes all signals in the controlled systems are bounded as well as the tracking errors as small as possible

Summary

INTRODUCTION

F RACTIONAL-ORDER nonlinear systems (FONSs) can be treated as the extension of integer-order nonlinear systems (IONSs), which is a research hotspot developed on the basis of fractional-order calculus theory. In references [7]-[16], they are utilized to identify unknown nonlinear functions in FONSs. The authors in [7][11] put forward several adaptive intelligent (fuzzy and NN) control strategies for FONSs with measurable or unmeasured states, respectively. The conventional backstepping control design technique adopted in the abovementioned intelligent adaptive control strategies, which may lead to the issue of “explosion of complexity” since the repeated derivation of the virtual control functions. The authors in [25]-[27] put forward intelligent adaptive backstepping decentralized control schemes for the uncertain non witched or switched FO nonlinear large-scale systems. This paper considers the fuzzy adaptive decentralized control design issue for the FO nonlinear large-scale systems with unmodeled dynamics. The main features of this study are as below: i) For the issue of unmodeled dynamics, firstly, the systems are required to have Mittag-Leffler ISpS Lyapunov functions, and some FO dynamic signals are introduced to solve this problem. ii) By applying FODSC technique, the put forward control strategy avoids the issue of “explosion of complexity” in the previous methods [7]-[11] and [24]-[25]

SYSTEM DESCRIPTIONS The FO nonlinear large-scale systems are as follows:

PRELIMINARIES

SIMULATION STUDY

CONCLUSIONS