Synchronization of Kuramoto oscillators via HEOL, and a discussion on AI

Artificial neural networks and their applications in deep learning have recently made an incursion into the field of control. Deep learning techniques in control are often related to optimal control, which relies on the Pontryagin maximum principle or the Hamilton-Jacobi-Bellman equation. They imply control schemes that are tedious to implement. We show here that the new HEOL setting, resulting from the fusion of the two established approaches, namely differential flatness and model-free control, provides a solution to control problems that is more sober in terms of computational resources. This communication is devoted to the synchronization of the popular Kuramoto’s coupled oscillators, which was already considered via artificial neural networks by L. Bttcher et al. (Nature Commun., 2022), where, contrarily to this communication, only the single control variable case is examined. One establishes the flatness of Kuramotos coupled oscillator model with multiplicative control and develops the resulting HEOL control. Unlike many examples, this system reveals singularities that are avoided by a clever generation of phase angle trajectories. The results obtained, verified in simulations, show that it is not only possible to synchronize these oscillators in finite time, and even to follow angular frequency profiles, but also to exhibit robustness concerning model mismatches. To the best of our knowledge that has never been done before. Concluding remarks advocate a viewpoint, which might be traced back to Wiener’s cybernetics: control theory belongs to AI.