Optimal control for phase locking of synchronized oscillator populations via dynamical reduction techniques

Area of Science:

• Physics
• Applied Mathematics
• Complex Systems

Background:

• Coupled oscillator systems are fundamental in various scientific domains.
• Controlling collective dynamics, especially phase synchronization, remains a challenge.
• External periodic inputs can influence oscillator synchronization.

Purpose of the Study:

• To present a novel framework for controlling the collective phase of coupled oscillators.
• To apply optimal control theory to achieve rapid resynchronization after phase shifts.
• To investigate the impact of control on mutual synchrony in the Kuramoto model.

Main Methods:

• Utilizing dynamical reduction and optimal control theory.
• Employing the Ott-Antonsen ansatz and phase-amplitude reduction for system simplification.
• Deriving one-dimensional equations for collective phase and amplitude.
• Setting up an optimal control problem for rapid phase shift recovery.

Main Results:

• A framework was established for controlling collective phase in coupled oscillators.
• The derived optimal control input effectively manages collective phase.
• Numerical simulations validated the framework's ability to achieve rapid resynchronization.
• The control strategy was shown to maintain or enhance mutual synchrony.

Conclusions:

• The combined approach of dynamical reduction and optimal control offers a powerful tool for managing complex oscillator systems.
• This framework provides a method for addressing synchronization challenges, analogous to real-world phenomena like jet lag.
• The study demonstrates the efficacy of optimal control in restoring synchrony after external perturbations.