A differential dynamic programming algorithm for differential games | Zendy

Trafalis Theodore B. | Zendy; Morin Thomas L. | Zendy

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A differential dynamic programming algorithm for differential games

Author(s) -

Trafalis Theodore B.,

Morin Thomas L.

Publication year - 2001

Publication title -

optimal control applications and methods

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.458

H-Index - 44

eISSN - 1099-1514

pISSN - 0143-2087

DOI - 10.1002/oca.680

Subject(s) - differential game , dynamic programming , differential dynamic programming , differential (mechanical device) , convergence (economics) , mathematics , hamiltonian (control theory) , optimal control , order (exchange) , first order , pontryagin's minimum principle , mathematical optimization , algorithm , computer science , finance , physics , economics , thermodynamics , economic growth

We develop and prove the convergence of a first‐order differential dynamic programming algorithm for the solution of a zero‐sum two‐person differential game with perfect information. The algorithm extends a first‐order strong variation algorithm for optimal control given by Mayne and Polak. Assuming separability of the Hamiltonian, we decompose the differential game problem into two control subproblems, C 1 and C 2 . The objective is to determine a point ( u * , v * ) in U × V , where U and V are the control spaces for C 1 and C 2 , respectively, that satisfies an integral form of Pontryagin's maximum principle for differential games. Copyright © 2001 John Wiley & Sons, Ltd.

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