Identification and control of LPV systems using orthonormal
basis functions
Project members: P.M.J. Van den Hof, C.W. Scherer, V. Verdult, P.S.C. Heuberger, R.T. Tóth
Sponsored by:
NWO
Orthogonal basis functions have a long history in the context of
system approximation and identification. Examples are the standard
pulse basis and the Laguerre basis. These are both special cases of a
more general construction in which the basis functions are generated
by a cascaded network of allpass filters. Typically basis
function models are parameterized as
where denotes the set of basis functions and
is the set of coefficients (parameters). An important
advantage of this parameterization is that the model parameters appear
linearly (this implies that in least squares settings the optimum is
unique and easily calculated). Furthermore it leads to an output error
structure (consistent estimation of the transfer function,
irrespective of noise). This project aims at the exploration of the
possible advantages of orthogonal basis functions for the modeling and
control of nonlinear systems.
Many practical (control) systems involve phenomena that are not only
functions of time, but also of other independent variables, such as,
e.g., space coordinates. Furthermore, these functions are sometimes
nonlinear and/or nonstationary. As a result the accurate modeling of
such systems is in general a complex and tedious task, involving the
use of nonlinear partial differential equations, leading to models
with a huge number of parameters and high computational complexity. On
the other hand accurate and efficient control of the relevant process
variables is of paramount importance to satisfy the increasing
performance demands. In order to achieve these goals, control
algorithms and methods have to be applied that require process models
of low complexity. This project aims at the development and
application of a new generation of tools for identification and
control of these processes, enhancing results recently obtained in
systems and control theory, with the goal to bridge this obvious gap
between modeling and control requirements by the creation of
relatively simple models, that are both accurate in the representation
of the overall system behavior, suited for control design. One of the
approaches taken will consist of interpolation of locally linear
models, combining the theory on LPV (linear parameter varying) systems
and the theory on orthogonal basis functions.
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