Finite-Time Multi-Agent Target Tracking on Riemannian Manifolds via Sliding Mode Control

Abstract

This letter investigates a novel control strategy for finite-time target tracking on Riemannian manifolds, building upon the asymptotic tracking dynamics proposed in existing works. While conventional geometric feedback controllers guarantee asymptotic convergence to the target, such approaches may fall short in practical scenarios where finite-time convergence is desired. To address this limitation, we incorporate a sliding mode control (SMC) mechanism into the existing geometric dynamics to enable finite-time convergence to a preassigned target on Riemannian manifolds. The proposed feedback controller is intrinsically defined with respect to the underlying manifold geometry and ensures rapid convergence. Numerical simulations are presented to validate the theoretical findings. This letter provides a new theoretical framework for finite-time target tracking in Riemannian geometric settings.