Stochastic control

Participant : Frédéric Bonnans.

With J. Gianatti (U. Rosario) and F. Silva (U. Limoges) we obtained an extension of the Sakawa-Shindo algorithm (for computing a solution of the optimality system of a deterministic optimal control problem) to stochastic control problems. The paper is in progress.

Stochastic programming

Participants : Frédéric Bonnans, Nicolas Grebille, Faisal Wahid.

In the framework of the thesis of Nicolas Grébille, we continued our study of decomposition algorithms for a stochastic model of optimal electricity energy production.The energy production is divided in a number of zones. The idea is to constrain the energy flows between these zones, by linear feedback to the demand (wich is a random variable). The coefficients of the feedback are to be optimized. Then the problem is decomposed for each zone (and can then be solved easily by a SDDP type algorithm). We obtained encouraging preliminary numerical results in a three zones problem.

Faisal Wahid developed a mixed integer program model for hydro-power producers participating in the future intra-day French Electricity Balancing Market. He has also formulated the mixed integer stochastic dynamic program model for the more general hydro- bidding under uncertainty. The objective of this model is to produce optimal offer policies in the form of supply curves under a time inhomogeneous Markov process of electricity market clearing prices.

Dynamic programming and error estimates for stochastic control problems with maximum cost

Participants : Athena Picarelli, Hasnaa Zidani.