Optimal control of deterministic systems described by integro-differential equations

The paper is concerned with design of optimal control for deterministic systems described by integro-differential equations. The dynamic programming method lead to the equation for a «generating functional» which generalizes the Bellman function. For a linear process and a quadratic objective functional an analytical solution is obtained. The optimal control is shown to be a functional for the process phase path that precedes the current time. A solution is given in the framework of the minimum generalized work principle.