Long term aging : an adaptative weights dynamic programming algorithm

Benjamin Heymann (1, 2) , Pierre Martinon (2, 1) , Frédéric Bonnans (2, 1)

1 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We introduce a class of optimal control problems with periodic data. A state variable that we call the age of the system represents the negative impact of the operations on the system qualities over time: other things being equal, older systems have higher operating costs. Many industrial problems relate to this class. If we envision to perform an optimization over a large number of periods, there is a tradeoff between minimizing repeatedly the one-period criterion in a short sighted way and taking into account the impact of the decision on the aging speed (which modifies the minimal one period criterion). In general, because the aging process is slow, short term optimization strategies-such as one period sliding horizon strategies-either neglect it or use rule-of-thumb penalization terms in the criterion, which leads to suboptimal solutions. On the other hand, for most applications it is unrealistic to envision a brute-force numerical resolution by dynamic programming of the long term problem because of the computation burden. We introduce a two-scale method to reduce this computation burden. The method relies on Lagrangian duality and some monotony properties. We expose the theoretical foundations of the method and discuss some practical aspects: approximation errors, asymptotic estimation, computation burden, possible extensions, etc. Since our initial motivation was the difficulty to take long term battery aging in Energy Management Systems into account, we implement the method on a toy long term microgrid energy management problem.

Domaines: Mathématiques [math]

Benjamin Heymann, Pierre Martinon, Frédéric Bonnans. Long term aging : an adaptative weights dynamic programming algorithm. 2016. ⟨hal-01349932v1⟩