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This piece is a follow-up of the research started by the authors on the constrained optimal control problem applied to pollution accumulation. We consider a dynamic system governed by a diffusion process with multiple modes that depends on an unknown parameter. We will study the components of the model and their restrictions and propose a scheme to solve the problem in which it is possible to determine (adaptive) policies that maximize a suitable discounted reward criterion using standard dynamic programming techniques in combination with discrete estimation methods for the unknown parameter. Finally, we develop a numerical example to illustrate our results with a particular case of the method of minimum least square error approximation.

This paper deals with two-person nonzero-sum stochastic differential games (SDGs) with an additive structure, subject to constraints that are additive also. Our main objective is to give conditions for the existence of constrained Nash equilibria for the case of infinite-horizon discounted payoff. This is done by means of the Lagrange multipliers approach combined with dynamic programming arguments. Then, following the vanishing discount approach, the results in the discounted case are used to obtain constrained Nash equilibria in the case of long-run average payoff.

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The purpose of this research is the calculation of the exergy destruction of the single-flash and double-flash cycles of a geothermal power plant located on the ladder of the 233 m Cerro Prieto volcano, on the alluvial plain of the Mexicali Valley, Mexico. The methodology developed in this research presents thermodynamic models for energy and exergy flows, which allows determining the contribution of each component to the total exergy destruction of the system. For the case-base, the results indicate that for the single-flash configuration the efficiency of the first and second law of thermodynamics are 0.1888 and 0.3072, as well as the highest contribution to the total exergy destruction is provided by the condenser. For the double-flash configuration, the efficiency of the first and second law of thermodynamics are 0.3643 and 0.4983. The highest contribution to the total exergy destruction is provided by the condenser and followed by the low-pressure turbine.