Daily generation scheduling: decomposition methods to solve the hydraulic problems

International audienceShort-term hydro-generation management poses a non-convex or even non-continuous optimization problem. For this reason, the problem of systematically obtaining feasible and economically satisfying solutions has not yet been completely solved. Two decomposition methods, which, as far as we know, have not been applied in this field, are proposed here. The first is based on a decomposition by prediction method and the co-ordination is a primal-dual relaxation algorithm. Handling the dynamic constraints by duality, the second achieves a price decomposition by an Augmented Lagrangian technique. Numerical tests show the efficiency of these algorithms. They will enable the process in use at Electricité de France to be improved. © 1994

Daily generation scheduling: decomposition methods to solve the hydraulic problems

International audienceShort-term hydro-generation management poses a non-convex or even non-continuous optimization problem. For this reason, the problem of systematically obtaining feasible and economically satisfying solutions has not yet been completely solved. Two decomposition methods, which, as far as we know, have not been applied in this field, are proposed here. The first is based on a decomposition by prediction method and the co-ordination is a primal-dual relaxation algorithm. Handling the dynamic constraints by duality, the second achieves a price decomposition by an Augmented Lagrangian technique. Numerical tests show the efficiency of these algorithms. They will enable the process in use at Electricité de France to be improved. © 1994

Dual effect free stochastic controls

In stochastic optimal control, a key issue is the fact that "solutions" are searched for in terms of "feedback" over available information and, as a consequence, a major potential difficulty is the fact that present control may affect future available information. This is known as the "dual effect" of control.Given a minimal framework (that is, an observation mapping from the product of a control set and of a random set towards an observation set), we define open-loop lack of dual effect as the property that the information provided by observations under open-loop control laws is fixed, whatever the open-loop control. Our main result consists in characterizing the maximal set of closed-loop control laws for which the information provided by observations closed with such a feedback remains also fixed.We then address the multi-agent case. To obtain a comparable result, we are led to generalize the precedence and memory-communication binary relations introduced by Ho and Chu for the LQG problem, and to assume that the precedence relation is compatible with the memory-communication relation.When the precedence relation induces an acyclic graph, we prove that, when open-loop lack of dual effect holds, the maximal set of closed-loop control laws for which the information provided by observations closed with such a feedback remains fixed is the set of feedbacks measurable with respect to this fixed information. We end by studying the dual effect for discrete time stochastic input-output systems with dynamic information structure, for which the same result holds