Optimal Control and Identification Problems

The present chapter addresses the optimal control and the parameter inden-tification problem of systems governed by hemivariational inequalities. This is a nonclassical mathematical problem, because the state of the problem is connected with the control function through a hemi variational inequality. We recall here that optimal control problems governed by state variational inequalities have been already studied (cf. e.g. [Yvon], [Lio71], [Panag77], [Mign76, 84], [Shi], [Hasli86a,b] [Barb]). However the present problem is more complicated, because we have state hemivariational inequalities. Here due to the lack of convexity of the superpotentials involved, compactness arguments will be applied. The mathematical framework is quite general to cover most of the usual engineering structures, as e.g. beams, plates in stretching and bending etc. The chapter is based mainly on [Panag92] and [Hasli93]. We refer also to [Panag84,89,90,91], [Hasli89]. Some application of the theory to engineering problems close the present chapter and illustrate the prospects for applications of the developed theory.