Tracking analysis for general linearly coupled dynamical systems

Tracking analysis problem is studied for general linearly coupled dynamical systems in this paper. One challenging and essential question for this issue is that: At least how many nodes should be informed about the objective tracking signal? This paper is devoted to answer this question. Two dynamical network models are considered. The first one, each individual has its own dynamics and simultaneously influenced by its neighbors’ information. The dynamics of itself could be stable, periodic, semi-periodic, and chaotic. The second one, each individual update its state just according to the error states different from its communicated neighbors. The main contribution of this paper is that the minimum number of controllers is designed to force the state of each agent to the desired objective by fully utilizing the structure of the network. The convergence rate can also be estimated. The topology of the underlying network can be directed and hierarchical. Some simple criteria are given to judge whether the tracking control can be successful. In addition, numerical examples are given to show the validity of the analytical results.