Adaptive Leader–Follower Synchronization Over Heterogeneous and Uncertain Networks of Linear Systems Without Distributed Observer

A challenging task in network synchronization is steering the network toward a coherent solution, when the dynamics of the constituent systems are heterogeneous and uncertain. In this situation, synchronization can be achieved via adaptive protocols (with adaptive feedback gains or adaptive coupling gains, or both). However, as state-of-the-art synchronization methods adopt a distributed observer architecture, they require to communicate extra observer variables among neighbors, in addition to the neighbors' states (or outputs). The distinguishing feature of this article is to show that for heterogeneous and uncertain networks of some classes of linear systems, synchronization is possible without the need for any distributed observer. Such classes are in line with those in model reference adaptive control literature. Lyapunov analysis is used to derive a new adaptive synchronization protocol with the simplest communication architecture, in which both feedback and coupling gains are adapted without any extra communication other than neighbors' states (in the full-state information case) or neighbors' outputs (in the partial-state information case).