Limit Hamilton–Jacobi–Isaacs Equations for Singularly Perturbed Zero-Sum Differential Games

A singularly perturbed zero-sum differential game with full information is considered. Upper and lower value functions of this game are shown to have limits as the singular perturbations parameter tends to zero. These limits are established to coincide with viscosity solutions of some Hamilton–Jacob...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 202; no. 3; pp. 862 - 899
Main Author Gaitsgory, Vladimir
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.09.1996
Elsevier
Subjects
Applied sciences
Calculus of variations and optimal control
Computer science; control theory; systems
Control theory. Systems
Differential games theory
Exact sciences and technology
Mathematical analysis
Mathematics
Sciences and techniques of general use
Differential equation
Hamilton Jacobi Isaacs equation
Singular perturbation
Viscosity solution
Control system
Zero sum game
Differential game
Equation system
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Summary:A singularly perturbed zero-sum differential game with full information is considered. Upper and lower value functions of this game are shown to have limits as the singular perturbations parameter tends to zero. These limits are established to coincide with viscosity solutions of some Hamilton–Jacobi type equations. A special case and two examples are considered to illustrate the general results.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1996.0352