Adaptive Robust Control for Networked Strict-Feedback Nonlinear Systems with State and Input Quantization

Yanbin Liu,Luis Gomes,Weichao Sun,Jue Wang

doi:10.3390/electronics10222783

Abstract

Backstepping method is a successful approach to deal with the systems in strict-feedback form. However, for networked control systems, the discontinuous virtual law caused by state quantization introduces huge challenges for its applicability. In this article, a quantized adaptive robust control approach in backsetpping framework is developed in this article for networked strict-feedback nonlinear systems with both state and input quantization. In order to prove the efficiency of the designed control scheme, a novel form of Lyapunov candidate function was constructed in the process of analyzing the stability, which is applicable for the systems with nondifferentiable virtual control law. In particular, the state and input quantizers can be in any form as long as they meet the sector-bound condition. The theoretic result shows that the tracking error is determined by the pregiven constants and quantization errors, which are also verified by the simulation results.

Highlights

Nonlinear systems in parametric strict-feedback form with uncertainties have been investigated a lot due to their widespread applications in modeling real systems, such as chaotic systems, robot/manipulator systems, vehicle systems and so on [1,2,3,4]
These two control laws have their own advantages and disadvantages: under the AC method, the closed-loop system is asymptotically stable in the existence of uncertain parameters only, but it may lead to instability when there is disturbance; under the DRC method, uniform ultimate boundedness (UUB) is guaranteed in the case of both uncertain parameters and disturbance
Treating the quantized errors of state signal as unmodeled dynamics, we propose an adaptive robust controller based on backstepping method for the plant (1) with state quantization only

Summary

Introduction

Nonlinear systems in parametric strict-feedback form with uncertainties have been investigated a lot due to their widespread applications in modeling real systems, such as chaotic systems, robot/manipulator systems, vehicle systems and so on [1,2,3,4]. Kokotovic in [5] in 1992, is a successful way to deal with the systems in strict-feedback form Under this method, the plant can be divided into a variety of subsystems by introducing virtual control inputs, and a step-by-step controller is designed for the plant. Jing Zhou et al designed an adaptive backstepping controller for a class of strict feedback system with quantized input signals in [26]. It is quite necessary to propose a universal method to deal with state and input quantization problems of strict-feedback systems.

Problem Statement

Results

Conclusions