Department: Mechanical & Aerospace Engineering
Name: Andrey S Smyshlyaev
Email: asmyshly @ ucsd.edu
Grad Year: 2006
We consider a problem of stabilization of distributed parameter systems with unknown reaction, advection, and diffusion parameters. Both sensing and actuation are performed at the boundary and the unknown parameters are allowed to be spatially varying. With only a scalar input, a scalar output, and infinite-dimensional plant and parameter states, the problem is of ultimate challenge. First we construct a special transformation of the original system into the PDE analog of "observer canonical form," with unknown parameters multiplying the measured output. We then use the so-called swapping method for parameter estimation. Filters of the input and the output are implemented so that a dynamic parametrization of the problem is converted into a static parametrization where a least squares estimation algorithm is used. The control gain is computed through the numerical solution of an ordinary integro-differential equation. The adaptive closed-loop scheme is shown to be robust with respect to the numerical error introduced in the online gain computation. The controller is capable of tracking an arbitrary reference signal prescribed at the boundary. The results are illustrated by simulations.
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