Achieving Synchrony in Physical Systems with Mutual Adaptation

The concept of behavioural synchrony was originally formulated after a series of studies of groups exhibiting collectively common behaviour. It has become the basis of several engineered systems, and some of these applications use model reference adaptive control. However, the existence of a reference model is not always assured in practical scenarios. In this paper, we pose behavioural synchronisation of systems as a mutual adaptation problem. In this novel strategy, the system states are synchronised in the absence of the reference model. Since mutual adaptation can be shown to be asymptotically stable, a stable approach to behavioural synchrony is guaranteed with our strategy. Effectiveness of the approach is demonstrated with three example systems with tunable parameters. The systems interact mutually to ensure that the error between the states converges to zero, thereby exhibiting a consensus on the overall behaviour.