Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2212.07927

On Disturbance Propagation in Vehicular Platoons with Different Communication Ranges

Chengshuai Wu·Meng Zhang·Dimos V. Dimarogonas
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the control of vehicular platoons, the disturbances acting on one vehicle can propagate and affect other vehicles. If the disturbances do not amplify along the vehicular string, then it is called string stable. However, it is usually difficult to achieve string stability with a distributed control setting, especially when a constant spacing policy is considered. This note considers the string unstable cases and studies disturbance propagation in a nonlinear vehicular platoon consisting of $n+1$ vehicles where the (virtual) leading vehicle provides the reference for a constant spacing policy. Apart from the communications between consecutive vehicles, we also assume that each vehicle can receive information from $r$ neighbors ahead, that is, the vehicular platoon has communication range $r$. For the maximal overshoot of the inter-vehicular spacing errors, we explicitly show that the effect of disturbances, including the external disturbances acting on each vehicle and the acceleration of the leading vehicle, is scaled by $O(\sqrt{ \left \lceil \frac{n}{r} \right \rceil})$ for a fixed $n$. This implies that disturbance propagation can be reduced by increasing communication range. Numerical simulation is provided to illustrate the main results.

Explore related subjects

math.DSmath.OC

Keep this discovery

BibTeXRIS

Chengshuai Wu, Meng Zhang, Dimos V. Dimarogonas. 2022-12-15. On Disturbance Propagation in Vehicular Platoons with Different Communication Ranges. https://arxiv.org/abs/2212.07927

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗