Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Non-linear Dynamics
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Mathematics and Statistics Faculty Publications and Presentations
We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also …
Stability Of Large Flocks: An Example, J. J. P. Veerman, F. M. Tangerman
Stability Of Large Flocks: An Example, J. J. P. Veerman, F. M. Tangerman
Mathematics and Statistics Faculty Publications and Presentations
The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then …
Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman
Symmetry And Stability Of Homogeneous Flocks, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The study of the movement of flocks, whether biological or technological, is motivated by the desire to understand the capability of coherent motion of a large number of agents that only receive very limited information. In a biological flock a large group of animals seek their course while moving in a more or less fixed formation. It seems reasonable that the immediate course is determined by leaders at the boundary of the flock. The others follow: what is their algorithm? The most popular technological application consists of cars on a one-lane road. The light turns green and the lead car …
Stability Of Linear Flocks On A Ring Road, J. J. P. Veerman, Carlos Martins Da Fonseca
Stability Of Linear Flocks On A Ring Road, J. J. P. Veerman, Carlos Martins Da Fonseca
Mathematics and Statistics Faculty Publications and Presentations
We discuss some stability problems when each agent of a linear flock on the line interacts with its two nearest neighbors (one on either side).
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Stable Motions Of Vehicle Formations, Anca Williams, Gerardo Lafferriere, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We investigate stable maneuvers for a group of autonomous vehicles while moving in formation. The allowed decentralized feeback laws are factored through the Laplacian matrix of the communication graph. We show that such laws allow for stable circular or elliptical motions for certain vehicle dynamics. We find necessary and sufficient conditions on the feedback gains and the dynamic parameters for convergence to formation. In particular, we prove that for undirected graphs there exist feedback gains that stabilize rotational (or elliptical) motions of arbitrary radius (or eceentricity). In the directed graph case we provide necessary and sufficient conditions on the curvature …
Decentralized Control Of Vehicle Formations, Gerardo Lafferriere, Anca Williams, John S. Caughman Iv, J. J. P. Veerman
Decentralized Control Of Vehicle Formations, Gerardo Lafferriere, Anca Williams, John S. Caughman Iv, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified communication digraph, G. A feedback control is designed using relative information between a vehicle and its in-neighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including …