Static duality and a stationary-action application

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

McEneaney, William M.¹  Dower, Peter M.² 

[1] Univ Calif San Diego, Dept Mech & Aero Engn, La Jolla, CA 92093 USA

[2] Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic, Australia

关键词: Dynamic programming;    Stationary action;    Convex duality;    Semiconvexity;    Staticization;    Two-point boundary value problem;   

DOI  :  10.1016/j.jde.2017.08.054

来源: Elsevier

【 摘 要 】

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 useful for smooth functionals where one may not be guaranteed of convexity or concavity. Some simple properties of this duality are examined, particularly commutativity. Application to stationary action is considered, which leads to propagation of DREs past escape times via propagation of stat-quad dual DREs. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free