The Study of Optimal Control for Some Parabolic Distributed Parameter Systems

This paper proves the existence of mixed linear optimal control in a quadratic criterion, by analysing the characteristics of linear differential operator A and using the properties of semigroups of compact operators and Picard theorem, for one-dimensional diffusion processes. And then, according to the reference3, the optimal control law has been given in detail. Besides, the results given in the references1-2are discussed as the special cases in the paper.