Searcharxiv⌕ Search

arXiv subjects

Quang-Cuong Pham

Publications and source records attributed to Quang-Cuong Pham.

61 records · Page 4Linked to original sources
arXiv2013

Stochastic Contraction in Riemannian Metrics

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic contraction results and sharp associated performance bounds have been established only in the specialized context of state-independent metrics, which restricts their applicability. This paper extends stochastic contraction analysis to the case of general time- and state-dependent Riemannian metrics, in both discrete-time and continuous-time settings, thus extending its applicability to a significantly wider range of nonlinear stochastic dynamics.

math.OC↗
arXiv2012

Affine invariance of human hand movements: a direct test

Geometrical invariance, in particular affine invariance, has been recently proposed as an important principle underlying the production of hand movements. However, tests of affine invariance have traditionally been applied to the consequences of this principle rather to the principle itself. Here, we designed and performed an original, direct, test of affine invariance in a scribbling experiment. In each of the 10800 pairs of randomly-selected scribbling segments, we compared the time parameterizations obtained by transforming the first segment using four different transportation rules - affine, equi-affine, Euclidian and constant - with the experimentally-observed parameterization of the second segment. We observed that, when the two paths are affinely-similar, the affine transportation of the first segment yields the time parameterization that best matches the experimental parameterization of the second segment, which directly demonstrates the existence of affine invariance in the production of hand movements.

q-bio.OT↗
arXiv2011

Affine trajectory correction for nonholonomic mobile robots

Planning trajectories for nonholonomic systems is difficult and computationally expensive. When facing unexpected events, it may therefore be preferable to deform in some way the initially planned trajectory rather than to re-plan entirely a new one. We suggest here a method based on affine transformations to make such deformations. This method is exact and fast: the deformations and the resulting trajectories can be computed algebraically, in one step, and without any trajectory re-integration. To demonstrate the possibilities offered by this new method, we use it to derive position and orientation correction algorithms for the general class of planar wheeled robots and for a tridimensional underwater vehicle. These algorithms allow in turn achieving more complex applications, including obstacle avoidance, feedback control or gap filling for sampling-based kinodynamic planners.

cs.RO↗
arXiv2009

How synchronization protects from noise

Synchronization phenomena are pervasive in biology. In neuronal networks, the mechanisms of synchronization have been extensively studied from both physiological and computational viewpoints. The functional role of synchronization has also attracted much interest and debate. In particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore it may play a role in temporal binding and in attention and sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called "collective enhancement of precision." We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations -- intrinsic neuronal noise -- which affect all neurons in the nervous system. This property may allow reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates), as mathematically it is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Using stochastic contraction theory, we show how synchronization of nonlinear dynamical systems helps protect these systems from random perturbations. Our main contribution is a mathematical proof that, under specific quantified conditions, the impact of noise on each individual system and on the spatial mean can essentially be cancelled through synchronization. Similar concepts may be applicable to questions in systems biology.

q-bio.NC↗
arXiv2008

Analysis of Discrete and Hybrid Stochastic Systems by Nonlinear Contraction Theory

We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and hybrid resetting systems. In particular, we show that the mean square distance between any two trajectories of a discrete (or hybrid resetting) contracting stochastic system is upper-bounded by a constant after exponential transients. Using these results, we study the synchronization of noisy nonlinear oscillators coupled by discrete noisy interactions.

math.OC↗
arXiv2006

Stable Concurrent Synchronization in Dynamic System Networks

In a network of dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. In the brain, concurrent synchronization may occur at several scales, with multiple ``rhythms'' interacting and functional assemblies combining neural oscillators of many different types. Mathematically, stable concurrent synchronization corresponds to convergence to a flow-invariant linear subspace of the global state space. We derive a general condition for such convergence to occur globally and exponentially. We also show that, under mild conditions, global convergence to a concurrently synchronized regime is preserved under basic system combinations such as negative feedback or hierarchies, so that stable concurrently synchronized aggregates of arbitrary size can be constructed. Robustnesss of stable concurrent synchronization to variations in individual dynamics is also quantified. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.

q-bio.NC↗