Self-synchronization and controlled synchronization

An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give

Adaptive synchronization of nonlinear networks with delayed couplings under incomplete control and incomplete measurements

Passification based adaptive synchronization method for decentralized control of dynamical networks proposed in (I. A. Dzhunusov and A. L. Fradkov. Adaptive Synchronization of a Network of Interconnected Nonlinear Lur'e Systems. Automation and Remote Control, 2009, Vol. 70, No. 7, pp. 1190-1205) is extended to the networks with delayed couplings. In the contrast to the existing papers the case of incomplete control and incomplete measurements is examined (both number of inputs and the number of outputs are less than the number of the state variables). Delay independent synchronization conditions are provided. The solution is based on passification in combination with using Lyapunov-Krasovskii functional

Self-synchronization and controlled synchronization of dynamical systems

A general definition of synchronization of dynamical systems is given capturing features of both self-synchronized systems and systems synchronized by means of control. It has been demonstrated for important special cases of "master-slave" and coupled systems that synchronizing control may be designed using feedback linearization or passification methods

Passification based controlled synchronization of complex networks

In the paper an output synchronization problem for a networks of linear dynamical agents is examined based on passification method and recent results in graph theory. The static output feedback and adaptive control are proposed and sufficient conditions for synchronization are established ensuring synchronization of agents under incomplete measurements and incomplete control. The results are extended to the networks with sector bounded nonlinearities in the agent dynamics and information delays

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

Oscillatority of Nonlinear Systems with Static Feedback

New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for consideration of nonperiodic, e.g., chaotic modes. Upper and lower bounds for oscillations amplitude are obtained. The relation between the oscillatority bounds and excitability indices for the systems with the input are established. Control design procedure providing nonlinear systems with oscillatority property is proposed. Examples illustrating proposed results for Van der Pol system, Lorenz system, and Hindmarsh–Rose neuron model as well as computer simulation results are given

A controlled closing theorem

In a number of problems in the theory of nonlinear oscillations and the theory of nonlinear control systems, one must investigate the behavior of solutions of differential systems under small changes of right-hand sides. In particular, the following problem is of interest: is it possible to transform a nearly periodic motion (for example, an almost periodic or recurrent motion) into a periodic motion with the use of small admissible changes of the right-hand side? The positive answer to this question was given in the so-called closing lemma proved by C. Pugh. However, in problems of control of oscillations, which have been intensively studied in the recent years, arbitrary variations of the right-hand sides are not allowed; only variations compatible with the actual capabilities of the control are admissible. Therefore, it is of interest to generalize the closing lemma to controlled systems. Some conditions of this type have been stated in the previous works by the authors. They essentially pertain to control theory and provide a criterion for the controllability of a nonlinear system near a recurrent trajectory by controls small in the uniform metric. In the present paper, we give a rigorous statement and a complete proof of this assertion (referred to as the controlled closing theorem)