Decentralized Control of Nonlinear Systems I

Abstract

In this chapter, we examine decentralized control techniques for classes of nonlinear interconnected systems. We identify classes for the system structure along with the underlying assumptions and emphasize the information and design constraints. The subsequent sections focus on a class of large-scale interconnected minimum-phase nonlinear systems with parameter uncertainty and nonlinear interconnections. The uncertain parameters are allowed to be time-varying and enter the systems nonlinearly. The interconnections are bounded by nonlinear functions of states. The problem we address is to design a decentralized robust controller such that the closedloop large-scale interconnected nonlinear system is globally asymptotically stable for all admissible uncertain parameters and interconnections. It is shown that decentralized global robust stabilization of the system can be achieved using a control law obtained by a recursive design method together with an appropriate Lyapunov function.The problem of decentralized output-feedback tracking with disturbance attenuation is addressed for a new class of large-scale and minimum-phase nonlinear systems. Common assumptions like matching and growth conditions are not required for the underlying decentralized system with a diagonal structure. An observer-based decentralized controller design is presented. The proposed decentralized output-feedback laws achieve asymptotic tracking and internal Lagrange stability when the disturbance inputs disappear, and, guarantee external stability in the presence of disturbance inputs. These external stability properties include Sontag's ISS and iISS conditions and standard L 2 -gain property. Classes of Nonlinear Interconnected SystemsIn what follows, we summarize the classes of nonlinear interconnected systems (NIS) that will be treated in the subsequent sections. We focus on the features of each class before addressing the topics of stability analysis and decentralized outputfeedback control design.M.S. Mahmoud, Decentralized Systems with Design Constraints,