NONLINEAR BOUNDARY CONTROL OF SEMILINEAR PARABOLIC-SYSTEMS

Nonlinear boundary control problems for a class of semilinear paraboli c systems are considered, from the point of view of semigroup theory. The method is based on some recent general results on parabolic evolut ion equations with nonlinear boundary conditions. Existence of optimal (boundary) controls is proved using the theory of measurable selectio ns and the Cesari property for multifunctions. Three results are prese nted covering relaxed controls and controls with state constraints. Th is generalises, in a substantial way, existing results on linear bound ary control problems [M.C. Delfour and M. Sorine, Control of Distribut ed Parameter Systems, Pergamon Press, Oxford, 1983, pp. 87-90], [I. La siecka, Appl. Math. Optim., 6 (1980), pp. 287-383], [P. Acquistapace, et al., SIAM J. Control Optim., 29 (1998), pp. 89-118]. The result pre sented can be further extended to differential inclusions. Two example s are presented for illustration.