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 , submitted to Systems and Control Letters , 1995.
E. Altman and V. A. Gaitsgory , A hybrid (differential-stochastic) zero-sum game with fast stochastic part , Annals of the International Society of Dynamic Games , Vol. 3, pp. 47-59, 1995.
E. Altman, T. Basar and Z. Pan , Admission and flow control in telecommunication networks as a hybrid control problem , 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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