An approximation scheme for optimal control of Volterra integral equations

Details An approximation scheme for optimal control of Volterra integral equations An approximation scheme for optimal control of Volterra integral equations

2006-11-15

arxiv.org/abs/math/0611485v1

Mathematics

Optimization and Control

22 pages

Scientific paper

We present and analyze a new 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. Other, straightforward versions of dynamic programming, are not applicable to Volterra integral equations. We also derive the connection between our version of dynamic programming and the Hamiltonian equations for Volterra controlled systems.

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