Unifying the most important methodology in this field,
Multi-Resolution Methods for Modeling and Control of Dynamical
Systems explores existing approximation methods as well as develops
new ones for the approximate solution of large-scale dynamical
system problems. It brings together a wide set of material from
classical orthogonal function approximation, neural network
input-output approximation, finite element methods for distributed
parameter systems, and various approximation methods employed in
adaptive control and learning theory.
With sufficient rigor and generality, the book promotes a
qualitative understanding of the development of key ideas. It
facilitates a deep appreciation of the important nuances and
restrictions implicit in the algorithms that affect the validity of
the results produced. The text features benchmark problems
throughout to offer insights and illustrate some of the
computational implications. The authors provide a framework for
understanding the advantages, drawbacks, and application areas of
existing and new algorithms for input-output approximation. They
also present novel adaptive learning algorithms that can be
adjusted in real time to the various parameters of unknown
mathematical models.
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