NDLI: The averaging principle for perturbations of continuous time control problems with fast controlled jump parameters

Content Provider	IEEE Xplore Digital Library
Author	El Azouzi, R. Altman, E. Gaitsgory, V.
Copyright Year	2000
Abstract	We consider a class of singularly perturbed zero-sum differential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a finite-state Markov process. Player 1 controls the continuous dynamics, whereas Player 2 controls the rate of transition for the finite-state Markov process; both have access to the states of both processes. Player 1 wishes to minimize a given quantity. For player 2, we consider two possible scenarios: one in which it wishes to minimize the same quantity (team framework), and one in which it wishes to maximize it (zero sum game). The transition rates of the Markov process are fast, of the order of 1//spl epsiv/. To solve the above problem, we use the dynamic programming approach. In particular, we study the asymptotic properties of the underlying system for sufficiently small /spl epsiv/. The viscosity solution method is employed to verify the convergence of the value function, which allows us to obtain the convergence in a general setting and helps us to characterize the structure of the limit system. We apply this to the special case of linear quadratic games with jump parameters, which allows us to obtain an explicit solution for the limiting problem.
Starting Page	730
Ending Page	735
File Size	606523
Page Count	6
File Format	PDF
ISBN	0780366387
ISSN	01912216
DOI	10.1109/CDC.2000.912855
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2000-12-12
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Control systems Markov processes Viscosity Dynamic programming Equations Australia Mathematics Process control Aging Costs
Content Type	Text
Resource Type	Article

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