Adaptation and synchronization over a network: Asymptotic error convergence and pinning

Travis E. Gibson

Abstract: The synchronization of unknown systems is studied for both undirected and directed graphs. In the undirected setting it is shown that consensus can be achieved without an external consensus protocol (that is, without a high gain linear error input usually written as a function of the graph laplacian and the states in the network), but solely through local adaptive feedback. In the directed case several different scenarios are addressed. An emphasis is placed on analyzing the simplest possible control design to achieve the goal of consensus. This breaks from the pinning adaptive control literature where the most general case is usually addressed, inadvertently obscuring what is, and what is not needed to achieve stability. Also breaking from the literature in the area of Distributed Adaptive Control with Synchronization (DACS) we do not assume a-priori knowledge of a uniform bound on the plant state.