Staticization, its dynamic program and solution propagation

Abstract

Stationary-action formulations of dynamical systems are considered. Use of stationary-action formulations allows one to generate fundamental solutions for classes of two-point boundary-value problems (TPBVPs). One solves for stationary points of the payoff as a function of inputs rather than minimization/maximization, a task which is significantly different from that in optimal control problems. Both a dynamic programming principle (DPP) and a Hamilton–Jacobi partial differential equation (HJ PDE) are obtained for a class of problems subsuming the stationary-action formulation. Although convexity (or concavity) of the payoff may be lost as one propagates forward, stationary points continue t..