5,439 research outputs found
A Global Steering Method for Nonholonomic Systems
In this paper, we present an iterative steering algorithm for nonholonomic
systems (also called driftless control-affine systems) and we prove its global
convergence under the sole assumption that the Lie Algebraic Rank Condition
(LARC) holds true everywhere. That algorithm is an extension of the one
introduced in [21] for regular systems. The first novelty here consists in the
explicit algebraic construction, starting from the original control system, of
a lifted control system which is regular. The second contribution of the paper
is an exact motion planning method for nilpotent systems, which makes use of
sinusoidal control laws and which is a generalization of the algorithm
described in [29] for chained-form systems
Stabilization and controllability of first-order integro-differential hyperbolic equations
In the present article we study the stabilization of first-order linear
integro-differential hyperbolic equations. For such equations we prove that the
stabilization in finite time is equivalent to the exact controllability
property. The proof relies on a Fredholm transformation that maps the original
system into a finite-time stable target system. The controllability assumption
is used to prove the invertibility of such a transformation. Finally, using the
method of moments, we show in a particular case that the controllability is
reduced to the criterion of Fattorini
A kinematic wave theory of capacity drop
Capacity drop at active bottlenecks is one of the most puzzling traffic
phenomena, but a thorough understanding is practically important for designing
variable speed limit and ramp metering strategies. In this study, we attempt to
develop a simple model of capacity drop within the framework of kinematic wave
theory based on the observation that capacity drop occurs when an upstream
queue forms at an active bottleneck. In addition, we assume that the
fundamental diagrams are continuous in steady states. This assumption is
consistent with observations and can avoid unrealistic infinite characteristic
wave speeds in discontinuous fundamental diagrams. A core component of the new
model is an entropy condition defined by a discontinuous boundary flux
function. For a lane-drop area, we demonstrate that the model is well-defined,
and its Riemann problem can be uniquely solved. We theoretically discuss
traffic stability with this model subject to perturbations in density, upstream
demand, and downstream supply. We clarify that discontinuous flow-density
relations, or so-called "discontinuous" fundamental diagrams, are caused by
incomplete observations of traffic states. Theoretical results are consistent
with observations in the literature and are verified by numerical simulations
and empirical observations. We finally discuss potential applications and
future studies.Comment: 29 pages, 10 figure
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