Adaptive dynamic surface control of parametric uncertain and disturbed strict-feedback nonlinear systems

Chenhui Wang

doi:10.1186/s13662-019-1971-1

Abstract

The construction of backstepping control input needs the derivative of the virtual controller to be available. However, this requirement usually makes the implementation of the controller very difficult and complicated. To overcome this problem, in this paper, an adaptive dynamic surface control (ADSC) is proposed for a class of strict-feedback nonlinear systems with parametric uncertainty and external disturbance. In each step of the backstepping control design, the virtual control input is estimated by an auxiliary signal which is generated by a proposed dynamic surface. This signal’s derivative is easy to obtain, so it is not necessary to achieve the derivative of the virtual control input. By using the Lyapunov stability theorem, an ADSC has been established to guarantee the boundedness of all signals and the convergence of the tracking errors. Finally, a simulation example is given to indicate the effectiveness of our control approach.

Highlights

1 Introduction It is well known that tremendous success has been obtained in controlling nonlinear systems based on the development of adaptive backstepping control (ABC) and feedback linearization (FBL) methods [1, 2]
The main idea of FBL consists in transforming a strictfeedback nonlinear system (SFNS) that satisfies some matching conditions into a linear one
The ABC method establishes a systematic framework for controlling SFNSs, whose main idea is using some intermediate variables recursively as pseudo-control signals

Summary

Introduction

It is well known that tremendous success has been obtained in controlling nonlinear systems based on the development of adaptive backstepping control (ABC) and feedback linearization (FBL) methods [1, 2]. The adaptive dynamic surface control (ADSC) aims to enhance the drawback of ABC by driving the control input passing through a firstorder filter [23, 43,44,45,46]. This method solve the problem of “explosion of complexity”, and reduce the requirement of the system model as well as the referenced signal. Note that it is very difficult to obtain exact analytical expressions for the dynamic surface, the proposed ADSC method works well even in the presence of parametric uncertainty as well as of an external disturbance. Compared with the method proposed in [48, 49], our method combined with adaptation laws has a more concise construction and is easier to implement

Problem formulation

Simulation example

Conclusions