Nonlinear pinning control of stochastic network systems

We propose a constructive method to design a pinning control law that synchronizes a network of stochastic dynamical systems. Different from traditional pinning control, we add to the standard proportional controller a nonlinear feedback term that, in the absence of coupling, would minimize a given cost functional. We then derive analytic guarantees that the proposed control law can effectively synchronize coupled noisy systems described by stochastic differential equations. Building on our theoretical results, we provide an algorithm for control design, whose effectiveness is illustrated on numerical testbeds. Finally, we perform extensive Monte Carlo simulations to evaluate the performance of the proposed nonlinear pinning strategy and compare it against the traditional proportional law.