@Article{IJNAM-11-1,
author = {},
title = {A Numerical Algorithm for Set-Point Regulation of Non-Linear Parabolic Control Systems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2014},
volume = {11},
number = {1},
pages = {54--85},
abstract = {<p style="text-align: justify;">In this paper we hope to draw attention to a particularly simple and extremely flexible
design strategy for solving a wide class of &quot;set-point&quot; regulation problems for nonlinear parabolic
boundary control systems. By this we mean that the signals to be tracked and disturbances to be
rejected are time independent. The theoretical underpinnings of our approach is the well known
regulator equations from the geometric theory of regulation applicable in the neighborhood of an
equilibrium. The most important point of this work is the wide applicability of the design methodology.
In the examples we have employed unbounded sensing and actuation but the method works
equally well for bounded input and output operators and even finite dimensional nonlinear control
systems. Our examples include: multi-input multi-output regulation for a boundary controlled
viscous Burgers&#39; equation; control of a Navier-Stokes flow in two dimensional forked channel; control
problem for a non-Isothermal Navier-Stokes flow in two dimensional box domain. Along the
way we provide some discussion to demonstrate how the method can be altered to provide many
alternative control mechanisms. In particular, in the last section we show how the method can be
adapted to solve tracking and disturbance rejection for piecewise constant time dependent signals.</p>},
issn = {2617-8710},
doi = {https://doi.org/2014-IJNAM-514},
url = {https://global-sci.com/article/83320/a-numerical-algorithm-for-set-point-regulation-of-non-linear-parabolic-control-systems}
}