Robust Adaptive Fuzzy Control via State-Dependent Function for Nonlinear Stochastic Large-Scale Systems Subject to Dead Zones

Chang-Qi Zhu,Lei Liu,Kalyana C Veluvolu

doi:10.1155/2021/1491995

Abstract

This paper concentrates on the adaptive fuzzy control problem for stochastic nonlinear large-scale systems with constraints and unknown dead zones. By introducing the state-dependent function, the constrained closed-loop system is transformed into a brand-new system without constraints, which can realize the same control objective. Then, fuzzy logic systems (FLSs) are used to identify the unknown nonlinear functions, the dead zone inverse technique is utilized to compensate for the dead zone effect, and a robust adaptive fuzzy control scheme is developed under the backstepping frame. Based on the Lyapunov stability theory, it is proved ultimately that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. Finally, an example based on an actual system is given to verify the effectiveness of the proposed control scheme.

Highlights

It is worth mentioning that most of the results mentioned are for the strict-feedback nonlinear systems instead of nonstrict-feedback nonlinear systems
Different from the strict-feedback nonlinear systems, the unknown nonlinear functions in the nonstrict-feedback nonlinear systems are composed of the whole states
Motivated by all the mentioned works, an adaptive fuzzy robust control scheme is developed for stochastic state-constrained nonlinear large-scale systems with unknown dead zones

Summary

Preliminaries

Consider a class of stochastic nonlinear large-scale systems with unknown dead zones which are composed of N subsystems connected by outputs. e i th subsystem can be expressed as. Xi,j]T, 1 ≤ i ≤ N and 1 ≤ j ≤ ni, ui ∈ R and yi ∈ R denote the actuator input and sensor output of the system, respectively, Di(ui) ∈ R denotes the output of the dead zone, fi,j(xi) and gi,j(xi) are the unknown nonlinear functions, Δi,j(y) is the interconnected term which connects each subsystem, and w is an independent r- dimensional Wiener process, and we assume that the states of the system can be measured directly. E algebraic loop problem means that if the control design method in strict feedback systems is adopted, the virtual control signal αi in nonstrict-feedback nonlinear systems for the i th subsystem will be a function which contains the entire states x [x1, x2, . Where λi,j,1 and λi,j,2 are time-varying bounded functions and χi,j is the state which is constrained. Υ∈Λ where φi(υ) are always φ(υ) [φ1(υ), φ2(υ), . . basis function vectors chosen as . , φN(υ)]T/ and satisfy the Gaussian functions. 􏽐0N1

Robust Constrained Control Design

Simulation Example

Conclusion