OPTIMAL-CONTROL PROBLEMS FOR DISTRIBUTED-PARAMETER SYSTEMS IN BANACH-SPACES

We consider the infinite-dimensional nonlinear programming problem of minimizing a real-valued function f0(u) defined in a metric space V subject to the constraint f(u) is-an-element-of Y, where f(u) is defined in V and takes values in a Banach space E and Y is a subset of E. We derive and use a theorem of Kuhn-Tucker type to obtain Pontryagin's maximum principle for certain semilinear parabolic distributed parameter systems. The results apply to systems described by nonlinear heat equations and reaction-diffusion equations in L1 and L(infinity) spaces.