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Applied Interval Analysis - With Examples in Parameter and State Estimation, Robust Control and Robotics (Paperback, Softcover reprint of the original 1st ed. 2001)
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Applied Interval Analysis - With Examples in Parameter and State Estimation, Robust Control and Robotics (Paperback, Softcover reprint of the original 1st ed. 2001)
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At the core of many engineering problems is the solution of sets of
equa tions and inequalities, and the optimization of cost
functions. Unfortunately, except in special cases, such as when a
set of equations is linear in its un knowns or when a convex cost
function has to be minimized under convex constraints, the results
obtained by conventional numerical methods are only local and
cannot be guaranteed. This means, for example, that the actual
global minimum of a cost function may not be reached, or that some
global minimizers of this cost function may escape detection. By
contrast, interval analysis makes it possible to obtain guaranteed
approximations of the set of all the actual solutions of the
problem being considered. This, together with the lack of books
presenting interval techniques in such a way that they could become
part of any engineering numerical tool kit, motivated the writing
of this book. The adventure started in 1991 with the preparation by
Luc Jaulin of his PhD thesis, under Eric Walter's supervision. It
continued with their joint supervision of Olivier Didrit's and
Michel Kieffer's PhD theses. More than two years ago, when we
presented our book project to Springer, we naively thought that
redaction would be a simple matter, given what had already been
achieved . . ."
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