Distributed RISE-based Control for Exponential Heterogeneous Multi-Agent Target Tracking of Second-Order Nonlinear Systems

A distributed implementation of a Robust Integral of the Sign of the Error (RISE) controller is developed for multi-agent target tracking problems with exponential convergence guarantees. Previous RISE-based approaches for multi-agent systems required 2-hop communication, limiting practical applicability. New insights from a Lyapunov-based design-analysis approach are used to eliminate the need for multi-hop communication required in previous literature, while yielding exponential target tracking. The new insights include the development of a new P-function that works in tandem with the graph interaction matrix in the Lyapunov function. Nonsmooth Lyapunov-based stability analysis methods are used to yield semi-global exponential convergence to the target agent state despite the presence of bounded disturbances with bounded derivatives. The resulting outcome is a controller that achieves exponential target tracking with only local information exchange between neighboring agents.