Consensus Tracking in Multi-dimensional Systems

This paper considers the tracking control problem of a network of identical linear state-space models with directed topology. It is assumed that communication topology contains a rooted directed spanning tree, where root has the knowledge of the states and control input of reference trajectory. Though the control input of reference is not known to all, the structure of the dynamics of reference control input is known to all agents. A distributive consensus-type tracking control protocol is proposed based on the relative information of states in the neighbourhood of each agent with a consensus-based estimator that estimates the reference input. Condition on coupling strength has been derived such that errors between states of the agents and the reference trajectory, and the estimated control inputs and control input of reference trajectory decay at a determined rate. Computational complexity reduces abundantly for an undirected communication topology. The effectiveness of the proposed controller is demonstrated through numerical simulations.