Optimal initial data and control for a class of linear hereditary systems

In this paper a time-optimal problem for a class of systems described by linear integro-difference-differential equations is considered. Theorems for the existence, necessary conditions, and uniqueness of the optimal pair {u, φ} are derived. Emphasis is given to the optimization of the initial data. Choice of bounded measurable functions for the admissible classes of both the initial states and controls leads to the result that the optimal initial state function, the optimal initial control, and the optimal control are all of “bang-bang” type.