2023/05/15 by Gerhard Kirsten, Luca Saluzzi, Kirsten, Gerhard +1
Computer Science · Engineering · #49J15 #49J20 #49L20 #93B52 #Computational Physics and Python Applications #FOS: Mathematics #Microgrid Control and Optimization #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Power System Optimization and Stability
paper · pdf · doi:10.48550/arxiv.2305.08803
openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is via the Dynamic Programming principle. Nevertheless, despite many theoretical results, this method has been applied only to very special cases since it suffers from the curse of dimensionality. Our goalis to mitigate this crucial obstruction developing a new version of dynamic programming algorithms based on a tree structure and exploiting the compact representation of the dynamical systems based on tensors notations via a model reduction approach. Here, we want to show how this algorithm can be constructed for general nonlinear control problems and to illustrate its performances on a number of challenging numerical tests. Our numerical results indicate a large decrease in memory requirements, as well as computational time, for the proposed problems. Moreover, we prove the convergence of the algorithm and give some hints on its implementation