On the “bang-bang” principle for nonlinear evolution inclusions

Abstract

In this paper we establish the existence of extremal solutions for a class of nonlinear evolution inclusions defined on an evolution triple of Hilbert spaces. Then we show that these extremal solutions are in fact dense in the solutions of the original system. Subsequently we use this density result to derive nonlinear and infinite dimensional versions of the “bang-bang” principle for control systems. An example of a nonlinear parabolic distributed parameter system is also worked out in detail.