Gregory P. Matthews

Decentralized tracking for a class of interconnected nonlinear systems using variable structure control

Abstract This paper presents a solution to the decentralized tracking or servomechanism problem for a class of nonlinear, multivariable systems. Decentralized variable structure control is used to decompose the solution into two parts: (1) the design of a set of decentralized, nonlinear controls that force each subsystems state trajectory onto an interconnected manifold in the composite system state space; and (2) the construction of the manifold such that asymptotic tracking occurs when the subsystem state trajectories are restricted to the manifold. While numerical methods are not explicitly considered, manifold design is relatively straightforward, requiring only the use of known decentralized eigenvalue assignment techniques and the solution of linear algebraic equations. The structure of a simple, decentralized, nonlinear control law is proposed which requires little design effort beyond the construction of the manifold.

Decentralized variable structure control of interconnected multi-input/ multi-output nonlinear systems

For a broad class of interconnected nonlinear systems, this paper develops a complete design methodology for decentralized variable structure control. Specifically, the paper sets forth design schemes for local switching surfaces and the related local switched feedback gains which together force the original nonlinear interconnected system to behave as a reduced order interconnected equivalent system having a desired response such as stability, tracking, or prespecified eigenvalues. Also developed is a numerical algorithm for constructing the switched local feedback gains. A simple nonlinear example illustrates the control strategy.