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Full-Text Articles in Control Theory
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Smooth And Analytic Normal And Canonical Forms For Strict Feedforward Systems, Issa Amadou Tall, Witold Respondek
Miscellaneous (presentations, translations, interviews, etc)
Recently we proved that any smooth (resp. analytic) strict feedforward system can be brought into its normal form via a smooth (resp. analytic) feedback transformation. This will allow us to identify a subclass of strict feedforward systems, called systems in special strict feedforward form, shortly (SSFF), possessing a canonical form which is an analytic counterpart of the formal canonical form. For (SSFF)-systems, the step-by-step normalization procedure of Kang and Krener leads to smooth (resp. convergent analytic) normalizing feedback transformations. We illustrate the class of (SSFF)-systems by a model of an inverted pendulum on a cart.
Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall
Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall
Articles and Preprints
We study the feedback group action on multi-input nonlinear control systems with uncontrollable mode. We follow slightly an approach proposed in Kang and Krener [W. Kang and A. J. Krener, SIAM J. Control. Optim., 30 (1992), pp. 1319–1337] which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes, on one hand, the results obtained in the single-input case and, on the other hand, those recently obtained by the same author in the controllable case. We illustrate our results by studying the Caltech Multi-Vehicle Wireless Testbed (MVWT) and the prototype …
A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman
A Note On Lattice Chains And Delannoy Numbers, John S. Caughman Iv, Clifford R. Haithcock, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
Fix nonnegative integers n1,…,nd and let L denote the lattice of integer points (a1,…,ad)∈Zd satisfying 0⩽ai⩽ni for 1⩽i⩽d. Let L be partially ordered by the usual dominance ordering. In this paper we offer combinatorial derivations of a number of results concerning chains in L. In particular, the results obtained are established without recourse to generating functions or recurrence relations. We begin with an elementary derivation of the number of chains in L of a given size, from which one can deduce the classical expression for the total number …
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 …