Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

Xiao Yu

doi:10.1155/2020/5381215

Abstract

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

Highlights

In the past few years, the output tracking control for interconnected systems that are composed of interconnected lower-dimensional individual subsystems has attracted a great deal of interests from researchers
If we find a suitable controller to ensure that the closedloop system of system (26) is asymptotically stable, the expected output tracking is achieved, since the tracking error is a component of the state vector x(k). erefore, the output tracking problem under consideration is reduced to a stabilization problem of system (26)
By means of the difference approach, the augmentation technique, and the partition method, we construct a novel augmented error system where the known future knowledge of the desired trajectory is fully taken into account. ereby, the output tracking problem is

Summary

Introduction

In the past few years, the output tracking control for interconnected systems that are composed of interconnected lower-dimensional individual subsystems has attracted a great deal of interests from researchers. The state reconstruction in a decentralized framework, which depends only on the local control input and output of the subsystem, provides an efficient and low-cost observer design to replace the usual state feedback for interconnected systems [10, 11]. The observer-based decentralized tracking controller design with preview action for interconnected nonlinear systems is studied for the first time. A novel observer-based decentralized tracking control scheme with preview action is proposed for a class of Lipschitz nonlinear interconnected systems that are widely employed in practical applications. The symbol “∗” replaces terms that are induced by symmetry

Problem Formulation

Observer-Based Decentralized Preview Tracking Controller Design

Numerical Simulations

Conclusions