Optimal iterative learning control design for multi-agent systems consensus tracking

Under a repeatable operation environment, this paper proposes an iterative learning control scheme that can be applied to multi-agent systems to perform consensus tracking under the fixed communication topology. The agent dynamics are modeled by time-varying nonlinear equations which satisfy the global Lipschitz continuous condition. In addition, the desired consensus trajectory is only accessible to a subset of the followers. By using the concept of the graph dependent matrix norm, the convergence conditions can be specified at the agent level, which depend on a set of eigenvalues that are associated with the communication topology. The results are first derived for homogeneous agent systems and then extended to heterogeneous systems. Next, optimal controller gain design methods are proposed in the sense that the λλ-norm of tracking error converges at the fastest rate, which imposes a tightest bounding function for the actual tracking error in the λλ-norm analysis framework. In the end, an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods.