Discontinuous feedback laws for infinite dimensional systems

Abstract

The application of discontinuous feedback laws to infinite-dimensional control systems, with particular reference to sliding motions, is discussed for both linear systems with distributed control and parabolic differential equations with Neumann boundary control. In the first case it is shown how, using differential inclusions and viability theory, it is possible to interpret the constrained motion on the sliding surface as a generalised solution of the discontinuous control problem. For the second class of systems a variational approach is considered. Under some growth assumptions it is shown that Faedo-Galerkin approximations of the evolution, satisfying the sliding constraint in the limit, do converge to an ideal sliding state.