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Bilinear Control Systems
ISBN-13:
9781402096136
Veröffentl:
2009
Seiten:
281
Autor:
David Elliott
Serie:
169, Applied Mathematical Sciences
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups.
"This book introduces and surveys bilinear control systems theory from a mathematical viewpoint. The exposition is at the first-year graduate level. Topics include an introduction to Lie algebras, matrix groups and semigroups; the controllability, stabilization, and observability of bilinear systems; nonlinear systems analytically equivalent to bilinear systems; series representations for input-outputmappings; and random inputs. To assist the reader there are exercises; Mathematica scripts; and appendices on matrix analysis, differentiable maps and manifolds, Lie algebra, and Lie groups."
Symmetric Systems: Lie Theory.- Systems with Drift.- Discrete-Time Bilinear Systems.- Systems with Outputs.- Examples.- Linearization.- Input Structures.- Matrix Algebra.- Lie Algebras and Groups.- Algebraic Geometry.- Transitive Lie Algebras.
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