Asymptotic tracking of a continuum target through a continuum model on Riemannian manifolds

We provide a sufficient framework for the asymptotic tracking of a continuum target on Riemannian manifolds. To achieve this, we adopt the target tracking model studied in the existing literature as the backbone of our approach, and extend it into a differential-integral equation through continuum modeling. We then present several sufficient conditions on initial data, system parameters, and kernel functionals to ensure the exponential weak target tracking property of this continuum model on Riemannian manifolds. Finally, we also demonstrate the occurrence of exponential strong target tracking in this system.