Control of infinite-dimensional plants

Abstract

In sliding mode control theory the major attention has been paid to finite dimensional systems described by ordinary differential equations. However, mathematical models of a wide range of processes in modern technology are partial differential equations, integro-differential equations and equations with delays. Attempts at theoretical generalisations and applications of sliding modes to control of infinite-dimensional plants show that control scientists and engineers are faced the challenge of increased complexity. Practically all the concepts of discontinuous control theory should be completely revised. Even the basic concepts discontinuity surface, sliding mode, component-wise design should be clarified or reintroduced. In the examples in this chapter we have touched upon infinite-dimensional systems mainly with distributed control.