Pinning Control of Lag-Consensus for Second-Order Nonlinear Multiagent Systems

Abstract

Lag consensus means that the corresponding state vectors of the followers are behind the leader with a lag time. In this paper, Lyapunov functional and matrix theory are applied to analyze pinning-controlled lag consensus of second-order nonlinear multiagent systems. The focus is twofold: 1) to find out which agents should be pinned and 2) to determine what the coupling strength should be, so that the multiagent systems can reach lag consensus. Moreover, the practical problem in a noisy environment is considered. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed pinning control protocol.

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

“…Remark When ρ 3 = 0, Assumption becomes the Lipschitz condition. Therefore, the restrictions on the unknown nonlinearities of multiagent systems are more relaxed than those in other works …”

“…Therefore, the restrictions on the unknown nonlinearities of multiagent systems are more relaxed than those in other works. [19][20][21][22][23][24][25] Assumption 2. The external disturbances of all followers are bounded by a positive constant , that is, |d i | ⩽ .…”

“…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.…”

Quasi-Synchronization of Heterogeneous Networks With a Generalized Markovian Topology and Event-Triggered Communication

“…In the literature, many control strategies have been proposed to enable the network to be stabilized. These include pinning control [8]- [11], fuzzy control [12], impulsive control [13], and fixed-time control [14], etc. As it is generally rather expensive, and not necessary to impose controllers on all network nodes, pinning control stands out as a good choice since it can be realized by controlling only a subset of network nodes.…”