Output Regulation for a Class of MIMO Uncertain Stochastic Nonlinear Systems by Active Disturbance Rejection Control Approach

Chunwan Lv,Guoshun Huang,Jian Chen,Lingxin Bao,Zhengyong Ouyang

doi:10.1155/2019/5674212

Abstract

In this paper, the active disturbance rejection control (ADRC) approach is applied to a class of multi-input multioutput (MIMO) uncertain stochastic nonlinear systems. An extended state observer (ESO) is first designed for estimation of both unmeasured states and stochastic total disturbance of each subsystem which represents the total effects of internal unmodeled stochastic dynamics and external stochastic disturbance with unknown statistical property. The ADRC controller based on the states of ESO is further designed to achieve the closed-loop system’s output regulation performance including practical mean square reference signals tracking, disturbance attenuation, and practical mean square stability when the reference signals are zero avoiding solving any partial differential equations in the conventional output regulation theory. Some numerical simulations are presented to demonstrate the effectiveness of the proposed ADRC approach.

Highlights

During the past couple of years, there have been existing representative control approaches to cope with uncertainties in controlled plants such as the internal model principle [1,2,3], the robust control [4], and the adaptive control [5]
The active disturbance rejection control (ADRC) approach is applied to the output regulation problem for a class of multi-input multioutput (MIMO) uncertain stochastic nonlinear systems subject to vast stochastic uncertainties
The stochastic uncertainties of each subsystem including unknown nonlinear system functions, external stochastic disturbance with unknown statistical property, unknown stochastic inverse dynamics, uncertain nonlinear coupling effects between subsystems, and uncertainties caused by the partially unknown input gains are first regarded as the stochastic total disturbance of each subsystem

Summary

Introduction

During the past couple of years, there have been existing representative control approaches to cope with uncertainties in controlled plants such as the internal model principle [1,2,3], the robust control [4], and the adaptive control [5]. The disturbance coped with by ADRC is much more general which can be the total coupling effects of internal unmodeled system dynamics and external disturbance. The most noteworthy feature of ADRC is that an extended state observer (ESO), as its key part, is designed to estimate the disturbance in real time so that the disturbance can be cancelled in the ESO-based feedback loop. This estimation/cancellation strategy leads to less control energy consumption in the control engineering practice [7]

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Conclusion