2006/11/15 by S. A. Belbas, Belbas, S. A.
Mathematics · #49K20 #49K22 #49K99 #49L20 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC #msc:49K20 #msc:49K22 #msc:49K99 #msc:49L20
paper · pdf · doi:10.48550/arxiv.math/0611485
22 pages
arxiv created 2006/11/15 · arxiv updated 2009/12/01
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.