Experimental study of the robust global synchronization of Brockett oscillators

International audienceThis article studies the experimental synchronization of a family of a recently proposed oscillator model, i.e. the Brockett oscillator [Brockett, 2013]. Due to its structural property, Brockett oscillator can be considered as a promising benchmark nonlinear model for investigating synchronization and the consensus phenomena. Our experimental setup consists of analog circuit realizations of a network of Brockett oscillators. Experimental results obtained in this work correspond to the prior theoretical findings

Output Global Oscillatory Synchronization of Heterogeneous Systems

International audienceThe global output synchronization problem for heterogeneous nonlinear systems having relative degree 2 or higher is studied. The proposed approach consists in two steps. First, a partial projection of individual subsystems into the Brockett oscillators is performed using a sliding-mode control. Second, the network of these oscillators is synchronized using the global synchronization results of a particular second order nonlinear oscillator model from Ahmed et al. (2019). Our approach is based on output feedback and uses a higher order sliding mode observer to estimate the states and perturbations of the synchronized nonlinear systems. Along with numerical simulations, the performance of the proposed synchronization scheme is experimentally verified on a network of Van der Pol oscillators

Robust global synchronization of Brockett oscillators

In this article, motivated by a recent work of R. Brockett [Brockett, 2013], a robust global synchronization problem of multistable Brockett oscillators has been studied within an Input-to-State Stability (ISS) framework. Following a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, two synchronization protocols are designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The conditions obtained in our work are global and applicable to families of non-identical oscillators in contrast to the local analysis of [Brockett, 2013]. Numerical simulation examples illustrate our theoretical results