Optimal Control of a Large Dam, Taking into Account the Water Costs

Consider a large dam model, which is characterized by an upper level L and lower level L , and if in time t the level of water Lt is between these bounds, then the dam is said to be in a normal state. The value L = L L is assumed to be large. The passage of lower or upper bounds leads to damage, the cost per time unit of which is J1 = j1L and J2 = j2L correspondingly, where j1 and j2 are given constants. Let cLt denote a water cost, depending on the level of water in time t, L < Lt ≤ L . Assuming that p1=limt→∞ P{Lt = L}, p2=limt→∞ P{Lt > L} and qi=limt→∞ P{Lt = i} (L lower < i ≤ L) exist, the aim of the paper is to choose the parameters of an output stream (specifically defined in the paper) minimizing the long-run expenses