Robust Adaptive Control of MIMO Pure-Feedback Nonlinear Systems via Improved Dynamic Surface Control Technique

Yang Zhou,Renwei Zuo,Shuangyu Dong,Yong Chen,Zongcheng Liu,Wenhan Dong

doi:10.1109/access.2019.2929119

Yang Zhou, Renwei Zuo + Show 4 more

Open Access

https://doi.org/10.1109/access.2019.2929119

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Journal: IEEE Access	Publication Date: Jan 1, 2019
Citations: 13	License type: CC BY 4.0

Affiliation: Air Force Engineering University

Abstract

This paper presents a global dynamic surface control (DSC) method for a class of uncertain multi-input/multi-output (MIMO) pure-feedback nonlinear systems with non-affine functions possibly being in-differentiable. It is well known that the traditional DSC method is commonly used for reducing the design complexity of the backstepping control method; however, the regulation results of the DSC method are semi-global uniformly ultimately bounded (SGUUB). An improved DSC (IDSC) method is first designed in this paper so that the results are global uniformly ultimately bounded (GUUB). Comparing with the traditional DSC method, the parameters of first-order filters in IDSC are time varying rather than constants. The control design for MIMO pure-feedback nonlinear systems researched is much more complex than the SISO cases, and the presence of in-differentiable non-affine functions considered in this paper makes the control design even more difficult. Therefore, we proposed the IDSC method, which can significantly reduce the complexity of the control design for the MIMO pure-feedback nonlinear systems in cooperation with the backstepping method, and it is proved that IDSC can guarantee the GUUB of all the signals of the system. Finally, the simulation results are provided to demonstrate the effectiveness of the designed method.

Highlights

Over the past decades, adaptive-control schemes were extensively used to cope with the control problems of nonlinear systems with unknown nonlinearities
In the work of Chen et al [22], by using the backstepping design approaches, a novel adaptive neural control design approach was proposed for a class of nonlinear MIMO time-delay systems in block-triangular form
In the work of Tong et al [29], the filtered signals were introduced to circumvent algebraic loop problem existing in the controller design for the nonlinear pure-feedback systems, and an adaptive fuzzy output feedback control law was proposed for a class of uncertain MIMO pure-feedback nonlinear systems with immeasurable states

Summary

INTRODUCTION

Adaptive-control schemes were extensively used to cope with the control problems of nonlinear systems with unknown nonlinearities. In the work of Tong et al [29], the filtered signals were introduced to circumvent algebraic loop problem existing in the controller design for the nonlinear pure-feedback systems, and an adaptive fuzzy output feedback control law was proposed for a class of uncertain MIMO pure-feedback nonlinear systems with immeasurable states. In the work of Sui et al [30], an adaptive fuzzy output feedback tracking control approach was developed for a class of MIMO stochastic pure-feedback nonlinear systems with input saturation based on the backstepping recursive design technique. By combining the DSC method and mean value theorem, the robust stabilization problem was discussed for a class of non-affine pure-feedback systems with unknown time-delay functions and perturbed uncertainties [33]. Motivated by the above discussion, in this paper, a novel robust adaptive improved dynamic surface control (IDSC) approach is proposed for a class of MIMO pure-feedback nonlinear systems with in-differentiable non-affine functions. The simulation examples are given to demonstrate the effectiveness of the proposed method in Section V and followed by Section VI which concludes this paper

PROBLEM DESCRIPTION AND PRELIMINARIES

ADAPTIVE TRACKING CONTROLLER DESIGN

STABILITY ANALYSIS

SIMULATION RESULTS

CONCLUSION

PROOF OF LEMMA 4