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

^** Email: bayon{at}uniovi.es In this paper we have developed a much simpler theory than previousones that resolves the problem of the optimization of hydrothermalsystems. The problem involves non-holonomic inequality constraints.In particular, we have established a necessary condition forthe stationary functions of the functional. We shall use Pontryagin'sMinimum Principle as the basis for proving this theorem, settingout our problem in terms of optimal control in continuous time,with the Lagrange-type functional. This theorem allows us toelaborate the optimization algorithm that leads to the determinationof the optimal solution of the hydrothermal system. We generalizethe problem, taking into account a cost associated with thewater, to then set out and solve the corresponding Bolza's problem.Finally, we present an example employing the algorithm developedfor this purpose with the ‘Mathematica’ package.