Controlled diffusion processes with Markovian switchings for modeling dynamical engineering systems

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• 作者：Hé ; ctor Cañ ; ada ; ^{hector.canada.uc3m@gmail.com} ; Rosario Romera ^{rosario.romera@uc3m.es}
• 关键词：Controlled Markov chains ; Stochastic differential equations ; Uncertainty modeling ; Simulation
• 刊名：European Journal of Operational Research
• 出版年：2012
• 期刊代码：58_03772217
• 类别：et
• 出版时间：16 September, 2012
• 卷：221
• 期：3
• 页码：614-624
• 文件大小：505 K

摘要

In this paper the intrinsic complex nature of engineering systems under control is treated by introducing an approach based on Controlled Stochastic Differential Equations with Markovian Switchings (in short CSDEMS). Technical conditions for the existence and uniqueness of the solutions of the CSDEMS are provided. In this context it is not unusual to deal with non-linear CSDEMS that cannot be solved analytically. Therefore, we develop a new two-step, predictor-corrector method for finding numerical approximations to solutions of CSDEMS. This method utilizes the Euler-Maruyama method. An illustrative application to the biochemical engineering area is presented to highlight the usefulness of our approach as a simulation tool.