Parallels between control PDE's and systems of ODE'sSystem 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 differential 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 paralled 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
19890041232
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Hunt, L. R. (Texas Univ. at Dallas Richardson, TX, United States)
Villarreal, Ramiro (Texas, University Richardson, United States)