A New Approach to Solving Stochastic Optimal Control Problems

Pablo T. Rodriguez-Gonzalez, Vicente Rico-Ramirez, Ramiro Rico-Martinez and Urmila M. Diwekar
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Pablo T. Rodriguez-Gonzalez: Tecnologico Nacional de Mexico en Celaya, Departamento de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas S/N, Celaya 38010, Guanajuato, Mexico
Vicente Rico-Ramirez: Tecnologico Nacional de Mexico en Celaya, Departamento de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas S/N, Celaya 38010, Guanajuato, Mexico
Ramiro Rico-Martinez: Tecnologico Nacional de Mexico en Celaya, Departamento de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas S/N, Celaya 38010, Guanajuato, Mexico
Urmila M. Diwekar: Center for Uncertain Systems: Tools for Optimization and Management, Vishwamitra Research Institute, Crystal Lake, IL 60012, USA

Mathematics, 2019, vol. 7, issue 12, 1-13

Abstract: 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.

Keywords: stochastic differential equations; stochastic optimal control; BONUS algorithm; biodiesel production (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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