Pinning control of complex networked systems: A decade after and beyond

In practice, directly control every node in a dynamical networked system with a huge number of nodes might be impossible or unnecessary; therefore, pinning control is a desirable approach. This paper surveys advances in pinning control approaches to making a dynamical networked system have a desired behavior. For a network with fixed topology, we review the feasibility, stability and effectiveness of pinning control. We then focus on pinning-based consensus and flocking control of mobile multi-agent networked systems. One of the main challenges with consensus and flocking control is that the topology of the corresponding dynamical network is time-varying, which depends on the states of all the agents in the network. Looking forward to the next decade, we expect to have a much deeper understanding of the relationship between the effectiveness of pinning control and the structural properties of a complex network, which may result in better control of large scale networked systems.