Static duality and a stationary-action application

Abstract

Conservative dynamical systems propagate as stationary points of the action functional. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via solution of an associated dynamic program. Further, such a fundamental solution may be represented as a set of solutions of differential Riccati equations (DREs), where the solutions may need to be propagated past escape times. Notions of “static duality” and “stat-quad duality” are developed, where the relationship between the two is loosely analogous to that between convex and semiconvex duality. Static duality is usef..