Model Order Reduction for Stochastic Optimal Control
Author(s)
Nguyen, Ngoc-Hien
Willcox, Karen
Khoo, Boo Cheong
Date Issued
May 2, 2018
Journal
Volume 1: Advanced Computational Mechanics; Advanced Simulation-Based Engineering Sciences; Virtual and Augmented Reality; Applied Solid Mechanics and Material Processing; Dynamical Systems and Control
Publisher
ASME International
Citation
Nguyen, Ngoc-Hien, et al. "Model Order Reduction for Stochastic Optimal Control." ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis, 2-4 July, 2012, Nantes, France, ASME, 2012, p. 599.
Version
Final published version
Abstract
This work presents an approach to solve stochastic optimal control problems in the application of flow quality management in reservoir systems. These applications are challenging because they require real-time decision-making in the presence of uncertainties such as wind velocity. These uncertainties must be accounted for as stochastic variables in the mathematical model. In addition, computational costs and storage requirements increase rapidly due to the stochastic nature of the simulations and optimisation formulations. To overcome these challenges, an approach is developed that uses the combination of a reduced-order model and an adjoint-based method to compute the optimal solution rapidly. The system is modelled by a system of stochastic partial differential equations. The finite element method together with collocation in the stochastic space provide an approximate numerical solution-the "full model", which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order model that approximates the full model. The conjugate-gradient method with Armijo line-search is then employed to find the solution of the optimal control problem under the uncertainty of input parameters. Numerical results show that the stochastic control yields solutions that are above the bound of the set solutions of the deterministic control. Applying the reduced model to the stochastic optimal control problem yields a speed-up in computational time by a factor of about 80 with acceptable accuracy in comparison with the full model. Application of the optimal control strategy shows the potential effectiveness of this computational modeling approach for managing flow quality. Copyright © 2012 by ASME.
MIT Department
Singapore-MIT Alliance in Research and Technology (SMART)
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1115/ESDA2012-82061
