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approximating linearizations for nonlinear systemsThe following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.
Document ID
19860020106
Document Type
Technical Memorandum (TM)
Authors
Hunt, L. R.
(Texas Univ. Dallas., United States)
Su, R.
(Colorado Univ. Boulder., United States)
Meyer, G.
(NASA Ames Research Center Moffett Field, CA, United States)
Date Acquired
September 5, 2013
Publication Date
January 1, 1986
Subject Category
NUMERICAL ANALYSIS
Report/Patent Number
NASA-TM-88772
NAS 1.15:88772
Funding Number(s)
CONTRACT_GRANT: NAG2-203
CONTRACT_GRANT: N00014-76-C1136
CONTRACT_GRANT: NAG2-189
CONTRACT_GRANT: NAG2-366
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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