Asymptotic tracking of moving target clouds under uncertain communications
Hyunjin Ahn, Seung‐Yeal Ha · Kinetic and Related Models · 2024
We study the asymptotic stochastic tracking of target point and continuum clouds under uncertain communications. For this, we first propose two stochastic multi-agent systems with multiplicative white noises, and present sufficient frameworks leading to asymptotic stochastic tracking. Under the proposed frameworks, we introduce generalized energy functionals which are equivalent to the stochastic counterparts of the energy functionals for deterministic models, and then use the decay estimates for energy functionals to show that asymptotic tracking emerges asymptotically in a probabilistic sense. In our previous works for deterministic tracking models, we used the LaSalle invariance principle together with energy functionals to derive asymptotic target tracking without convergence rate. Thus, we generalize earlier results on asymptotic tracking even for the deterministic models. Moreover, we also show that the same analytical tools can be generalized to the corresponding kinetic systems, which can be derived from the stochastic multi-agent systems in the mean-field limit so that the resulting coupled kinetic system exhibits asymptotic target tracking exponentially fast in a probabilistic sense.