Optimal control of finite dams: continuous output procedure

The problem discussed is that of controlling optimally the release of water from a finite dam, when the release rate may vary continuously and the optimality is defined in terms of a cost structure imposed on the operation of the dam. A diffusion model is suggested and by considering a family of plausible output policies, the control problem is reduced to the solution of a free boundary problem associated with a certain partial differential equation. A set of necessary conditions for the optimal choice of these boundaries is established and a method of solution is suggested. By using this method, together with well-established computational techniques, numerical solutions are obtained. These numerical solutions indicate that this optimal policy does not result in very much improvement over a much simpler policy where the output rate is constrained to take only two values.