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Open AccessFeature PaperArticle

A New Approach to Solving Stochastic Optimal Control Problems

1
Tecnologico Nacional de Mexico en Celaya, Departamento de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas S/N, Celaya 38010, Guanajuato, Mexico
2
Center for Uncertain Systems: Tools for Optimization and Management, Vishwamitra Research Institute, Crystal Lake, IL 60012, USA
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1207; https://doi.org/10.3390/math7121207
Received: 6 September 2019 / Revised: 18 November 2019 / Accepted: 4 December 2019 / Published: 9 December 2019
(This article belongs to the Special Issue Stochastic Differential Equations and Their Applications)
A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle. View Full-Text
Keywords: stochastic differential equations; stochastic optimal control; BONUS algorithm; biodiesel production stochastic differential equations; stochastic optimal control; BONUS algorithm; biodiesel production
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MDPI and ACS Style

Rodriguez-Gonzalez, P.T.; Rico-Ramirez, V.; Rico-Martinez, R.; Diwekar, U.M. A New Approach to Solving Stochastic Optimal Control Problems. Mathematics 2019, 7, 1207. https://doi.org/10.3390/math7121207

AMA Style

Rodriguez-Gonzalez PT, Rico-Ramirez V, Rico-Martinez R, Diwekar UM. A New Approach to Solving Stochastic Optimal Control Problems. Mathematics. 2019; 7(12):1207. https://doi.org/10.3390/math7121207

Chicago/Turabian Style

Rodriguez-Gonzalez, Pablo T.; Rico-Ramirez, Vicente; Rico-Martinez, Ramiro; Diwekar, Urmila M. 2019. "A New Approach to Solving Stochastic Optimal Control Problems" Mathematics 7, no. 12: 1207. https://doi.org/10.3390/math7121207

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