One-and-Two Target Distributed Optimal Control of a Parabolic System

In this paper models for two-target optimal controls of a linear diffusion equation are considered. That is, we seek to control the solution of the given PDE in order to guide it to a specified target within a given error at some fixed finite time. At the same time it is desired to keep the variation of the solution from a second target as small as possible. Thus the problem is essentially a multi-objective optimization problem but with a clearly defined primary goal. Two different models for this problem are studied and the primal and dual problems associated with these models are formulated with a goal of finding algorithmic approaches to solving the two-target problem. An analysis of two versions of the one-target model is provided as a basis for the study of the two-target model.