Seminar talk, 15 February 2012: Difference between revisions
Created page with "{{Talk | speaker = Vladimir Chetverikov | title = Flat systems and covering over them: description and control methods | abstract = The talk will discuss flat control systems, i...." |
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| speaker = Vladimir Chetverikov | | speaker = Vladimir Chetverikov | ||
| title = Flat systems and covering over them: description and control methods | | title = Flat systems and covering over them: description and control methods | ||
| abstract = The talk will discuss flat control systems, i.e., the systems that are C-diffeomorphic to infinite jet spaces. By analogy with the theory of differential invariants we consider finite jets of flat systems and corresponding C-diffeomorphisms. We construct a map that takes every 2-jet of C-diffeomorphism to 1-jet of flat system. This map preserves the Cartan distribution and thus lifts to a jet map of higher order. The image of k | | abstract = The talk will discuss flat control systems, i.e., the systems that are <math>\mathcal{C}</math>-diffeomorphic to infinite jet spaces. By analogy with the theory of differential invariants we consider finite jets of flat systems and corresponding <math>\mathcal{C}</math>-diffeomorphisms. We construct a map that takes every <math>2</math>-jet of <math>\mathcal{C}</math>-diffeomorphism to <math>1</math>-jet of flat system. This map preserves the Cartan distribution and thus lifts to a jet map of higher order. The image of <math>k</math>th prolongation consists of <math>(k+1)</math>-jets of flat systems. The analogs of differential invariants are functions constant on the image of k-th prolongation. If <math>k<3</math> then there exists only one such function. It will be presented in the talk. | ||
Besides, we shall show how to generalize the control methods developed for flat systems to coverings over them. | Besides, we shall show how to generalize the control methods developed for flat systems to coverings over them. | ||
Latest revision as of 14:22, 11 February 2012
Speaker: Vladimir Chetverikov
Title: Flat systems and covering over them: description and control methods
Abstract:
The talk will discuss flat control systems, i.e., the systems that are -diffeomorphic to infinite jet spaces. By analogy with the theory of differential invariants we consider finite jets of flat systems and corresponding -diffeomorphisms. We construct a map that takes every -jet of -diffeomorphism to -jet of flat system. This map preserves the Cartan distribution and thus lifts to a jet map of higher order. The image of th prolongation consists of -jets of flat systems. The analogs of differential invariants are functions constant on the image of k-th prolongation. If then there exists only one such function. It will be presented in the talk.
Besides, we shall show how to generalize the control methods developed for flat systems to coverings over them.