A General Dynamic Programming Approach to the Optimal Water Storage Management for Irrigation

ABSTRACT This paper proposes a dynamic programming approach targeted to solve a natural resource problem of water storage management for irrigation in an environmentally and socially sustainable way. The problem we address in our formulation, focusing on the control of water storage in tanks, is based on assumptions that are less restrictive than those commonly adopted in the literature for similar approaches. Specifically, we consider a time periodic optimal control problem whose performance functional to be maximized merely satisfies a contraction assumption (in the sense of Boyd and Wong) weaker than the one usually considered in the pertinent literature. By using an appropriate fixed point theorem, a time periodic value function can be constructed to enable the definition of optimal feedback control strategies. After showing the insufficiency of the Banach contraction frameworks and proving the underlying auxiliary mathematical results, we show our main result under conditions that are weaker than the previous related ones. Simulation results illustrate the performance of our approach.