Control theory for stochastic distributed parameter systems,an engineering perspective |
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| Affiliation: | 1. Professor of Enterprise Information Systems at University of Lorraine, France;2. Professor of Product Innovation at Tecnologico de Monterrey, Mexico;3. Key Scientist, Robotic and Automation Systems, PROFACTOR GmbH, Austria;4. Professor of Industrial Technologies at Politecnico di Milano, Italy;1. Institute of Mathematics, UNAM, Mexico;2. Frankfurt Institute for Advanced Studies, Germany;3. University of Trento, Italy;4. Northeastern University, United States;5. University of Canterbury, New Zealand;6. Kookmin University, South Korea;7. Imperial College London, UK |
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| Abstract: | The main purpose of this paper is to survey some recent progresses on control theory for stochastic distributed parameter systems, i.e., systems governed by stochastic differential equations in infinite dimensions, typically by stochastic partial differential equations. We will explain the new phenomenon and difficulties in the study of controllability and optimal control problems for one dimensional stochastic parabolic equations and stochastic hyperbolic equations. In particular, we shall see that both the formulation of corresponding stochastic control problems and the tools to solve them may differ considerably from their deterministic/finite-dimensional counterparts. More importantly, one has to develop new tools, say, the stochastic transposition method introduced in our previous works, to solve some problems in this field. |
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| Keywords: | Stochastic distributed parameter system Controllability Optimal control Pontryagin-type maximum principle Stochastic linear quadratic problem |
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