(204g) A New Approach to Solving Stochastic Optimal Control Problems

Authors: 
Rodríguez-González, P. T. Sr., Instituto Tecnológico de Celaya
Rico-Ramirez, V., Instituto Tecnologico de Celaya
Diwekar, U., Vishwamitra Research Institute, Center for Uncertain Systems: Tools for Optimization and Management

Dynamic systems like batch processes are difficult to design and control because of time dependent nature of the system.  Optimal control theory is used to establish efficient operating policies for batch unit operations.  However, the time dependent nature of the system makes it difficult to deal with uncertainties.  Recently, the problem of uncertainties in batch unit operation optimal control was handled by modeling the uncertainties in terms of Ito processes and Ito calculus with stochastic maximum principle methods were used to solve the resulting stochastic optimal control problem.  However, stochastic maximum principle could only be used for time dependent decisions.  In order to solve coupled design and control problems, a method is needed which can deal with time dependent uncertainties, static uncertainties, time dependent decisions and time independent decisions.  In this paper, we are presenting a new approach based on a novel algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS).  BONUS determines the search direction bypassing the need of excessive model evaluations through a reweighting scheme using Kernel Density Estimation. A simple batch reactor with uncertainties in reaction parameters is used as a study case to taste this novel approach looking obtain the optimal temperature profile that maximizes the product concentration.