Hybrid Control

We analyze systems having two types of dynamics: one, determined by differential equations that corresponds to some process having a smooth behavior, and another discrete part that is directly controlled. Assuming that the discrete process changes much quicker that the continuous part, we are able to obtain some policies which are asymptotically optimal.

Papers:

E. Altman and V. A. Gaitsgory , Control of a hybrid stochastic system , Systems and Control Letters , Vol. 20, pp. 307-314, 1993.
E. Altman and V. A. Gaitsgory , Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process , SIAM Journal on Control and Optimization , 1997, Vol. 35, No. 6, pp. 2070-2085
E. Altman and V. A. Gaitsgory , A hybrid (differential-stochastic) zero-sum game with fast stochastic part [ps,pdf] , Annals of the International Society of Dynamic Games , Vol. 3, pp. 47-59, 1995.
Peng Shi, Eitan Altman and Vladimir A. Gaitsgory , On Asymptotic Optimization of a Class of Nonlinear Stochastic Hybrid Systems , Mathematical Methods of Operations Research , 47:289-315, 1998.
Minh-Tuan Nguyen, Eitan Altman, Vladimir Gaitsgory, On Stochastic Hybrid Zero-Sum Games with Nonlinear Slow Dynamics Annals of the International Society of Dynamic Games Volume 6, 2001, pp 129-145
E. Altman, T. Basar and Z. Pan , Admission and flow control in telecommunication networks as a hybrid control problem [ ps, pdf], Proceedings of the Princeton conference , March 1995.
E. Altman, T. Basar, Z. Pan, , Piecewise-deterministic differential games and dynamic teams with hybrid controls , Annals of the International Society of Dynamic Games , vol. 5, Birkhauser, V. Gaitsgory, J. Filar and K. Mizukami, editors, pp. 223-256, 2000.
R. El. Azouzi, M. Abbad and E. Altman, A Taylor series expansion for H-infinitely control of perturbed Markov jump linear systems, Advances in Dynamic Games, Vol. 7, Birkhauser, Boston, Basel, Berlin, pp. 499-514, 2005.

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