Imperial College London
Alternate

Emeritus ProfessorRichardVinter

Faculty of Engineering, Department of Electrical and Electronic Engineering

Emeritus Professor in Electrical and Electronic Engineering
 
 
 
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Contact

 

+44 (0)20 7594 6287r.vinter Website

 
 
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Assistant

 

Mrs Raluca Reynolds +44 (0)20 7594 6281

 
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Location

 

618Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Bettiol:2019:10.1007/s00245-019-09608-8,
author = {Bettiol, P and Quincampoix, M and Vinter, RB},
doi = {10.1007/s00245-019-09608-8},
journal = {Applied Mathematics and Optimization},
pages = {765--799},
title = {Existence and characterization of the values of two player differential games with state constraints},
url = {http://dx.doi.org/10.1007/s00245-019-09608-8},
volume = {80},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider a two player, zero sum differential game with a cost of Bolza type, subject to a state constraint. It is shown that, under a suitable hypothesis concerning existence of inward pointing velocity vectors for the minimizing player at the boundary of the constraint set, the lower value of the game is Lipschitz continuous and is the unique viscosity solution (appropriately defined) of the lower Hamilton-Jacobi-Isaacs equation. If the inward pointing hypothesis is satisfied by the maximizing player’s velocity set, then the upper game is Lipschitz continuous and is the unique solution of the upper Hamilton-Jacobi-Isaacs equation. Under the classical Isaacs condition, the upper and lower Hamilton-Jacobi-Isaacs equation coincide. In this case, even if the inward pointing hypothesis is satisfied w.r.t. both players, the value of the game might fail to exist; however imposing stronger constraint qualifications (involving the existence of inward pointing vectors associated with saddle points for the Hamiltonian) the game value does exist and is the unique solution to this Hamilton-Jacobi-Isaacs equation. The novelty of our work resides in the fact that we permit the two players’ controls to be completely coupled within the dynamic constraint, state constraint and the cost functional, in contrast to earlier work, in which the players’ controls are decoupled w.r.t. the dynamics and state constraint, and interaction between them only occurs through the cost function. Furthermore, the inward pointing hypotheses that we impose are of a verifiable nature and less restrictive than those earlier employed.
AU  - Bettiol,P
AU  - Quincampoix,M
AU  - Vinter,RB
DO  - 10.1007/s00245-019-09608-8
EP  - 799
PY  - 2019///
SN  - 0095-4616
SP  - 765
TI  - Existence and characterization of the values of two player differential games with state constraints
T2  - Applied Mathematics and Optimization
UR  - http://dx.doi.org/10.1007/s00245-019-09608-8
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000493654500008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/94029
VL  - 80
ER  -
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