相关论文: Natural frames and interacting particles in three …
In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes…
This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces…
Traffic interactions between merging and highway vehicles are a major topic of research, yielding many empirical studies and models of driver behaviour. Most of these studies on merging use naturalistic data. Although this provides insight…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of "neighboring" agents is responsible for maintaining a prescribed target distance between them. In a recent paper…
Symmetries of nonlinear control systems in state representation are considered. To this end, a geometric approach to ordinary differential equations is advocated. Invariant feedback laws for systems with Lie symmetries, i.e. feedback laws…
We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale…
We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum…
A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try…
Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…
The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison…
Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
Rigidity of the interaction graph is a fundamental condition for achieving the desired formation which can be defined in terms of distance or bearing constraints between agents. In this paper, for reaching a unique formation with the same…
Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify…