A General Dynamic Programming Approach to the Optimal Water Storage
Management for Irrigation
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 examine
in our formulation, which deals with the control of water storage in
tanks, incorporates assumptions that are milder compared to those
previously discussed in the literature concerning 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 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.