Dynamic Programming for Finite Ensembles of Nanomagnetic Particles

2018/06/18 by Jensen, Max, Majee, Ananta, Prohl, Andreas +1
#45K05 #46S50 #49L20 #49L25 #91A23 #93E20 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1806.06592

Abstract

We use optimal control via a distributed exterior field to steer the dynamics of an ensemble of N interacting ferromagnetic particles which are immersed into a heat bath by minimizing a quadratic functional. By using dynamic programing principle, we show the existence of a unique strong solution of the optimal control problem. By the Hopf-Cole transformation, the related Hamilton-Jacobi-Bellman equation from dynamic programming principle may be re-cast into a linear PDE on the manifold M = (S²)^N, whose classical solution may be represented via Feynman-Kac formula. We use this probabilistic representation for Monte-Carlo simulations to illustrate optimal switching dynamics.

Related

• Optimal control of nonequilibrium systems through automatic differentiation
• Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field
• Gradient projection method and stochastic search for some optimal control models with spin chains. I
• Deterministic classical limit of the optimal control problem of quantum particles with spin
• Finite elements and moving asymptotes accelerate quantum optimal control - FEMMA