On the "bang-bang" principle for nonlinear evolution inclusions

Abstract

We establish the existence of extreme solutions for a class of nonlinear evolution inclusions with non-convex right-hand side defined on an evolution triple of Banach spaces. Then we show that extreme solutions which belong to the solution set of the original system are in fact dense in the solutions of the system with convexified right-hand side. Subsequently we use this density result to derive nonlinear and infinite-dimensional version of the “bang-bang” principle for control systems. An example of a nonlinear parabolic distributed parameter system is also worked out in detail.