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Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.
Document ID
19880008947
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Hunt, L. R. (Texas Univ. at Dallas Richardson, TX, United States)
Villarreal, Ramiro (Texas Univ. at Dallas Richardson, TX, United States)
Date Acquired
September 5, 2013
Publication Date
January 1, 1987
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.26:182487
NASA-CR-182487
Accession Number
88N18331
Funding Number(s)
CONTRACT_GRANT: NAG2-366
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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