Abstract

In this paper we consider a system of three nonlinear ordinary differential equations that model a three Josephson Junctions Array (JJA). Our goal is to stabilize the system around an unstable equilibrium employing an optimal control approach. We first define the cost functional and calculate its differential by using perturbation analysis and variational calculus. For the computational solution of the optimality system we consider a conjugate gradient algorithm for quadratic functionals in Hilbert spaces,  combined with a finite difference discretization of the involucrated differential equations.