Title:
Approximate Feedback Linearization: A Homotopy Operator Approach

dc.contributor.author Banaszuk, Andrzej
dc.contributor.author Hauser, John
dc.contributor.corporatename Georgia Institute of Technology. School of Mathematics
dc.contributor.corporatename University of Colorado, Boulder. Electrical and Computer Engineering
dc.date.accessioned 2009-12-04T20:43:33Z
dc.date.available 2009-12-04T20:43:33Z
dc.date.issued 1995-01-12
dc.description.abstract In this paper, we present an approach for finding feedback linearizable systems that approximate a given single-input nonlinear system on a given compact region of the state space. First, we show that if the system is close to being involutive then it is also close to being linearizable. Rather than working directly with the characteristic distribution of the system, we work with characteristic one-forms, i.e., with the one-forms annihilating the characteristic distribution. We show that homotopy operators can be used to decompose a given characteristic one-form into an exact and antiexact part. The exact part is used to define a change of coordinates to a normal form that looks like a linearizable part plus nonlinear perturbation terms. The nonlinear terms in this normal form depend continuously on the antiexact part and they vanish whenever the antiexact part does. Thus, the antiexact part of a given characteristic one-form is a measure of nonlinearizability of the system. If the nonlinear terms are small, by neglecting them we obtain a linearizable system approximating the original system. One can design control for the original system by designing it for the approximating linearizable system and applying it to the original one. We apply this approach for design of locally stabilizing feedback laws for nonlinear systems that are close to being linearizable. en
dc.description.sponsorship NSF under grant PYI ECS-9157835 and DMS-9207703 en
dc.identifier.uri http://hdl.handle.net/1853/31285
dc.language.iso en_US en
dc.publisher Georgia Institute of Technology en
dc.relation.ispartofseries SOM0794-018 en
dc.subject Nonlinear systems
dc.subject Linearizable systems
dc.subject Feedback linearizable systems
dc.title Approximate Feedback Linearization: A Homotopy Operator Approach en
dc.type Text
dc.type.genre Pre-print
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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