Dynamic Programming for Finite Ensembles of Nanomagnetic Particles
This work provides a theoretical framework for optimal control of nanomagnetic particle ensembles, which is relevant for applications in spintronics and data storage, but the results are theoretical with only illustrative simulations.
The authors apply dynamic programming to optimally control an ensemble of interacting nanomagnetic particles via an external field, proving existence of a unique strong solution and using a Hopf-Cole transformation to derive a linear PDE solved via Monte Carlo simulations for optimal switching.
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 = (S^2)^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.