Decentralized Control of Large-Scale Uncertain Nonlinear Systems by Linear Output Feedback

Abstract

This paper studies the problem of global decentralized control by output feedback for large-scale uncertain systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. We show that under a linear growth condition, there is a decentralized output feedback controller rendering the closed-loop system globally exponentially stable. This is accomplished by extending an output feedback domination design that requires only limited infor- mation about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. Furthermore, we need to only employ a linear observer in combination with a linear controller to stabilize the system. A time-varying output feedback con- troller is also constructed for use with large-scale systems that have unknown parameters. 1. Introduction. Decentralized control of interconnected systems has been an area of considerable research due to its obvious practical application to current prob- lems in the field of controls. Large-scale systems have very complex dynamic models due to the uncertain environment, the varying system parameters, and the intercon- nected structure of the system. Also it is inevitable that nonlinearities are prevalent throughout the dynamics of the interconnected systems. All these issues make the stabilization of such large-scale systems a difficult control problem. Though quite challenging, the research of large-scale systems are relevant to such areas as commu- nication networks, satellite constellations, and the formation control of autonomous vehicles. The research of large-scale nonlinear systems began in the late 1960's and early 1970's. One of the earliest investigations into the nonlinear issues of large-scale sys- tems centered around time-varying stabilization (2). The early research in (7) demon- strated a method of using high-gain state feedback to stabilize the nonlinearities of the large-scale systems. The research in the early 1980's focused on the use of state feedback to globally stabilize large-scale nonlinear systems. Adaptive control was ap- plied in (3) to stabilize a class of large-scale nonlinear systems with success. Output feedback had also been applied to linear large-scale system in such papers as (1), (15),