A reduction method for optimal control of Volterra integral equations

摘要

We present and analyze a novel method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential equations. The resulting approximating problems can then be solved by dynamic programming methods for ODE controlled systems. We also derive the connection between our version of dynamic programming and the Hamiltonian equations for Volterra controlled systems.