Optimal management of pumped hydroelectric production with state constrained optimal control

Abstract We present a novel technique to solve the problem of managing optimally pumped hydroelectric storage system. This relies on representing system as stochastic optimal control with state constraints, these latter corresponding finite volume reservoirs. Following recent level-set approach presented in O. Bokanowski, A. Picarelli, H. Zidani, State-constrained problems via reachability approach, SIAM J. Control and Optim. 54 (5) (2016), we transform original constrained an auxiliary unconstrained one augmented spaces, obtained by introducing exact penalization constraints. The is fully treatable classical dynamic programming arguments.