A computational method for a general class of optimal control problems involving integrodifferential equations

In this paper we consider a general class of optimal control problems involving integrodifferential equations. The integral equation component is a Volterra integral equation with convolution kernel. A method is proposed to approximate the kernel which gives rise to a system of ordinary differential equations approximating the Volterra integral equation. Thus the optimal control problem is approximated by a sequence of standard optimal control problems involving only differential equations. Each of the approximate problems is solvable by any of the existing methods for standard optimal control problems, such as the gradient restoration algorithm and the control parametrization algorithm. Convergence analysis is also carried out to justify the proposed approximation. As an application we consider an optimal control problem involving production and marketing systems with distributed time lags. This problem is then solved numerically using the proposed method