Staticization, its dynamic program and solution propagation

doi:10.1016/j.automatica.2017.03.004

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Staticization, its dynamic program and solution propagation

2017-07-01

William M. McEneaney *

Peter M. Dower

DOI：10.1016/j.automatica.2017.03.004

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Abstract

En 中文

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 to exist, and one must be able to use the DPP and/or HJ PDE to solve forward to such time horizons. In linear/quadratic models, this leads to a requirement for propagation of solutions of differential Riccati equations past finite escape times. Such propagation is also required in (nonlinear) n-body problem formulations where the potential is represented via semiconvex duality. The dynamic programming tools developed here are applicable. (C) 2017 Elsevier Ltd. All rights reserved.

Keywords:

Dynamic programming

Stationary action

Two-point boundary value problem

Hamilton-Jacobi

Optimal control

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