Optimal control of a system governed by nonlinear Volterra integral equations with delay

摘要

In this paper we consider an optimal control problem whose states are governed by a type of nonlinear Volterra integral equation with delay. The problem includes control constraints as well as equality/inequality constraints on the terminal states. First, using Pontryagin-type control variations, a maximum principle is established under a rather general set of assumptions. We show that these results immediately yield the classical Pontryagin maximum principle for a control process governed by an ordinary differential equation (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.