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Reduction of Nonlinear Control Systems - A Differential Geometric Approach (Paperback, Softcover reprint of the original 1st ed. 1999)
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Reduction of Nonlinear Control Systems - A Differential Geometric Approach (Paperback, Softcover reprint of the original 1st ed. 1999)
Series: Mathematics and Its Applications, 472
Expected to ship within 10 - 15 working days
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Advances in science and technology necessitate the use of
increasingly-complicated dynamic control processes. Undoubtedly,
sophisticated mathematical models are also concurrently elaborated
for these processes. In particular, linear dynamic control systems
iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are
constants, are often abandoned in favor of nonlinear dynamic
control systems (2) which, in addition, contain a large number of
equations. The solution of problems for multidimensional nonlinear
control systems en counters serious difficulties, which are both
mathematical and technical in nature. Therefore it is imperative to
develop methods of reduction of nonlinear systems to a simpler
form, for example, decomposition into systems of lesser dimension.
Approaches to reduction are diverse, in particular, techniques
based on approxi mation methods. In this monograph, we elaborate
the most natural and obvious (in our opinion) approach, which is
essentially inherent in any theory of math ematical entities, for
instance, in the theory of linear spaces, theory of groups, etc.
Reduction in our interpretation is based on assigning to the
initial object an isomorphic object, a quotient object, and a
subobject. In the theory of linear spaces, for instance, reduction
consists in reducing to an isomorphic linear space, quotient space,
and subspace. Strictly speaking, the exposition of any mathemat
ical theory essentially begins with the introduction of these
reduced objects and determination of their basic properties in
relation to the initial object."
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