2014/06/13 by Wei Zhang, Zhang, Wei, Juan C. Latorre +5
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1406.3458
arxiv created 2014/06/13 · openalex publication_date 2014/06/13 · arxiv updated 2014/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy "first reduce, then optimize"--rather than "first optimize, then reduce"--is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state sufficient and necessary conditions, under which the "first reduce, then control" strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the "first reduce, then optmize" approach and discuss possible pitfalls.