2023/01/31 by Giacomo Albi, Marco Caliari, Albi, Giacomo +5
Engineering · Mathematics · Physics and Astronomy · #35Q49 #35Q89 #49N80 #65L04 #65M12 #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2302.00127
openalex publication_date 2023/01/31 · openalex created_date 2023/02/04 · openalex updated_date 2026/07/28
In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally derived in a general framework, accounting for boundary conditions. Hence, the optimality system is used to construct a reduced gradient method, where we introduce a novel algorithm for the numerical realization of the forward and the backward equations, based on exponential integrators. We illustrate extensive numerical experiments on different control problems for collective motion in the context of opinion formation and pedestrian dynamics.