New developments in the application of Pontryagin's Principle for the hydrothermal optimization

In this paper we have developed a much simpler theory than previous ones that resolves the problem of the optimization of hydrothermal systems. The problem involves non-holonomic inequality constraints. In particular, we have established a necessary condition for the stationary functions of the functional. We shall use Pontryagin’s Minimum Principle as the basis for proving this theorem, setting out our problem in terms of optimal control in continuous time, with the Lagrange-type functional. This theorem allows us to elaborate the optimization algorithm that leads to the determination of the optimal solution of the hydrothermal system. We generalize the problem, taking into account a cost associated with the water, to then set out and solve the corresponding Bolza’s problem. Finally, we present an example employing the algorithm developed for this purpose with the ‘Mathematica’ package.