Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 4 of 4
Full-Text Articles in Control Theory
Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman
Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be …
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 …
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 …
Flocks And Formations, J. J. P. Veerman, Gerardo Lafferriere, John S. Caughman Iv, A. Williams
Flocks And Formations, J. J. P. Veerman, Gerardo Lafferriere, John S. Caughman Iv, A. Williams
Mathematics and Statistics Faculty Publications and Presentations
Given a large number (the “flock”) of moving physical objects, we investigate physically reasonable mechanisms of influencing their orbits in such a way that they move along a prescribed course and in a prescribed and fixed configuration (or “in formation”). Each agent is programmed to see the position and velocity of a certain number of others. This flow of information from one agent to another defines a fixed directed (loopless) graph in which the agents are represented by the vertices. This graph is called the communication graph. To be able to fly in formation, an agent tries to match the …