Distributed cooperative adaptive identification and control for a group of continuous-time systems with a cooperative PE condition via consensus

In this paper, we first address the uniformly exponential stability (UES) problem of a group of distributed cooperative adaptive systems in a general framework. Inspired by consensus theory, distributed cooperative adaptive laws are proposed to estimate the unknown parameters of these systems. It is shown that not only is the entire closed-loop system stable, but also both the identification/tracking error and the parameter estimation error converge to zero uniformly exponentially under a cooperative persistent excitation (PE) condition of a regressor matrix in each system which is weaker than the traditionally defined PE condition. The effects of network topology on UES of the closed-loop system are also explored. If the topology is time-invariant, it needs to be undirected and connected. However, when the topology is time-varying, it is just required that the integration of the topology over an interval with fixed length is undirected and connected. The established results are then employed to identify and control several classes of linearly parameterized systems. Simulation examples are also provided to demonstrate the effectiveness and applications of the proposed distributed cooperative adaptive laws.