On the value of differential game with asymmetric control constraints

Vladimir Turetsky; Shmuel Y. Hayoun; Tal Shima; Alexander Tarasyev

doi:https://doi.org/10.1016/j.ifacol.2018.11.463

On the value of differential game with asymmetric control constraints

Vladimir Turetsky, Shmuel Y. Hayoun, Tal Shima, Alexander Tarasyev

Aerospace Engineering

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

A differential game with asymmetric constraints on the players’ controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented.

Original language	English
Pages (from-to)	799-804
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	51
Issue number	32
DOIs	https://doi.org/10.1016/j.ifacol.2018.11.463
State	Published - 2018

Keywords

Isaacs equation
differential game
game value
program maximin

All Science Journal Classification (ASJC) codes

Control and Systems Engineering

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https://doi.org/10.1016/j.ifacol.2018.11.463

Cite this

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title = "On the value of differential game with asymmetric control constraints",

abstract = "A differential game with asymmetric constraints on the players{\textquoteright} controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented.",

keywords = "Isaacs equation, differential game, game value, program maximin",

author = "Vladimir Turetsky and Hayoun, {Shmuel Y.} and Tal Shima and Alexander Tarasyev",

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AU - Shima, Tal

AU - Tarasyev, Alexander

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N2 - A differential game with asymmetric constraints on the players’ controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented.

AB - A differential game with asymmetric constraints on the players’ controls and an asymmetric cost functional is considered. In this game hard geometric constraints are imposed on the maximizer, whereas the minimizer is soft-constrained by including the control effort term into the cost functional. The sufficient condition is derived, subject to which the program maximin is the game value. In the proof, it is shown that the program maximin is the generalized solution of the Hamilton-Jacobi-Bellman partial differential equation. Examples are presented.

KW - Isaacs equation

KW - differential game

KW - game value

KW - program maximin

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EP - 804

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 32

ER -

On the value of differential game with asymmetric control constraints

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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