Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings

Abstract

Abstract-In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.Index Terms-Bernoulli stochastic variables, complex dynamical networks, distributed synchronization, multi-agent systems, multiple random nonlinearities, multiple random updating laws.

Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

“…The first one is to simplify the complex controller, as a simple controller can be applied in practice more easily [41]. The second interesting topic would be to study finite-time distributed synchronization between two different coupled dynamical networks [42,43]. A distributed controller could improve the control efficiency, and reduce the control cost.…”

Nonlinear Consensus Protocol Modified from Doubly Stochastic Quadratic Operators in Networks of Dynamic Agents

“…However, most nonlinear protocols are based on the Lyapunov function theory, which means that it has remained hard to shape nonlinear protocols based on a realistic Lyapunov function for MAS [5,23,30,31]. Furthermore, the recent research completed in the study of nonlinear protocols was constructed on fractional second-order and second-order of calculus such as in [32][33][34][35][36][37][38][39].…”

Synchronization of fractional-order chaotic systems with multiple delays by a new approach

“…The systems with time-delays are difficult to achieve satisfying performance. The stability issue of time-delay systems is of practical importance [15,17,23,24,28].…”