On the controllability of transitions between equilibrium states in small inductively coupled arrays of Josephson junctions: A computational approach

• Published in: Journal of computational physics 2020-02, Vol.403 (C), p.109023, Article 109023
• Main Authors: Glowinski, Roland, López, Jorge, Juárez, Héctor, Braiman, Yehuda
• Format: Article
• Language: English
• Subjects: Algorithms; Arrays; Computational physics; Conjugate gradient algorithms; Controllability; Cost analysis; Cost function; Cryogenic memory; Josephson junction; Josephson junctions; Memory operators; Nonlinear differential equations; Nonlinear equations; Nonlinear programming; Optimal control; Optimization; Ordinary differential equations; Perturbation methods; Robust control; Stability
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.109023

In this article, we investigate computationally some controllability properties of a physical system consisting of three inductively coupled Josephson junctions. This system is modeled by nonlinear ordinary differential equations. A particular attention is given to the optimal control of the transition between equilibrium states, possibly unstable. After defining the control problem cost function, we use a perturbation analysis to compute its differential and formulate an optimality system. After appropriate time discretization of the control problem, we use a conjugate gradient algorithm to solve the discrete analogue of the above optimality system. The methodology we briefly described above has been applied successfully to the current pulse driven transition between two stable equilibrium states. This type of transitions was used in [1–5], to study Read/Write cryogenic memory cell operations based on the dynamics of small Josephson junction arrays. In order to show the robustness of our control-based approach we apply it also to the transitions from a stable equilibrium state to an unstable one. •Optimal transition between two steady states of a system consisting of three inductively coupled Josephson junctions.•Robust methodology based on a conjugate gradient algorithm for nonquadratic functionals in L2.•More general controls than Gaussian pulses.