Criteria for stochastic pinning control of networks of chaotic maps

Abstract

This paper investigates the controllability of discrete-time networks of coupled chaotic maps through stochastic pinning. In this control scheme, the network dynamics are steered towards a desired trajectory through a feedback control input that is applied stochastically to the network nodes. The network controllability is studied by analyzing the local mean square stability of the error dynamics with respect to the desired trajectory. Through the analysis of the spectral properties of salient matrices, a toolbox of conditions for controllability are obtained, in terms of the dynamics of the individual maps, algebraic properties of the network, and the probability distribution of the pinning control. We demonstrate the use of these conditions in the design of a stochastic pinning control strategy for networks of Chirikov standard maps. To elucidate the applicability of the approach, we consider different network topologies and compare five different stochastic pinning strategies through extensive numerical simulations.

Pinning control design for bounded synchronization of complex networks of nonidentical systems

“…A classical example is formation control in multi-vehicle systems [4]. To solve this problem, pinning control have been suggested where a master node is added to the network and coupled unidirectionally to a small fraction of the network nodes [5]- [10]. In pinning control problems, the aim is to synchronize a complex network onto a desired trajectory s(t), which is a solution of the uncoupled node dynamics.…”

Pinning synchronization of fractional-order complex networks with Lipschitz-type nonlinear dynamics

“…Thus, an effective method to solve this problem is adding controllers to just a limited subset of the network nodes. This approach is known as pinning control, which was first proposed to control chaos in spatiotemporal systems [20][21][22] and proved to be a viable strategy to tame complex networks with different topological structures [23][24][25][26][27][28][29][30][31].…”

Sampled‐data leader‐following consensus of second‐order nonlinear multiagent systems without velocity measurements

“…For instance, in previous works, the leader‐following consensus problem for second‐order nonlinear multiagent systems has been investigated; in some other works, when the agent has a higher‐order nonlinear dynamics, corresponding results were given. On the other hand, there are many results focusing on the pinning control of complex networks, which is closely related to the leader‐following consensus of multiagent systems …”

“…On the other hand, there are many results focusing on the pinning control of complex networks, which is closely related to the leader-following consensus of multiagent systems. [25][26][27][28][29][30] In practical engineering systems, it is usually difficult or even impossible to obtain velocity measurements of agents; therefore, it is of great significance to consider the consensus protocol design without velocity measurements. 19,[31][32][33][34][35] In the works of Zhang and Yang 31 and Zhao et al, 32 the finite-time consensus for second-order multiagent systems without velocity measurements was studied.…”