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Mixing Dynamic Programming and Spatial Decomposition Methods

Banff International Research Station for Mathematical Innovation and Discovery

We consider a stochastic optimization problem in which different units are connected together via a network. Each unit is a (small) control system, located at a node. Each unit state evolution is affected by uncertainties and controls of the neighboring nodes transmitted through edges. Static constraints couple all units at each time. We formulate the associated global stochastic optimization problem. We propose two decomposition methods, whether we decouple the constraints by prices or by resources. We show that the optimal value of the global problem can be bounded above by a sum of resource-decomposed nodal value, and below by a sum of price-decomposed nodal value. We provide conditions under which these nodal values can be computed by dynamic programming. We illustrate these results with numerical studies that tackle the optimization of urban micro-grids of large size. Finally, we introduce two different information structures for these microgrids, namely the centralized and the decentralized ones, and we analyse the lower and upper bounds when considering these information structures.

Mathematics; Probability theory and stochastic processes; Operations research, mathematical programming; Control/Optimization/Operation Research

video/mp4

Author affiliation: ENSTA ParisTech

2020-03-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73783

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/