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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. [ABSTRACT FROM AUTHOR]

A novel approach for output synchronization for uncertain general complex networks with non-identical nodes is proposed. This goal can be solved applying to a small fraction of network nodes (pinned ones) a neural controller; this controller is composed of an on-line identifier based on a recurrent high-order neural network, and a sliding-mode controller. An illustrative example is included, which is composed of a network of ten nodes, with different self-dynamics, illustrating the effectiveness and good performance of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a pinning control scheme for adaptive trajectory tracking of networked nonlinear systems is proposed. The desired trajectory tracking objective is achieved via a novel adaptive control strategy, in which the existing concept of pinning control is extended to an adaptive pinning control. The adaptive control is based on a recurrent high‐order neural network identification strategy for unknown pinned nodes dynamics. The combined pinning‐neural features in tracking control constitute the novelty of this approach. The proposed control law operates properly with a different reference along with unknown dynamics and coupling variations. In contrast to the linearization approach, less restrictive assumptions for node dynamics are imposed. Moreover, matrix conditions that include network topology and control properties for both pinned and non‐pinned nodes are obtained. The applicability of this control scheme is illustrated via simulations. [ABSTRACT FROM AUTHOR]