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Local controllability of observables in finite and infinite dimensional nonlinear control systems

Local controllability of observables in finite and infinite dimensional nonlinear control systems LetA, ℬ be evolution operators (possibly nonlinear) which act within a Banach spaceB andu(·) a measurable, real valued, control function. We study control systems of the form ∂υ t /∂t=A υ t +u(t)ℬυ t , υ0=ϕ ∈B. An observation of this system is defined to be a continuous linear mapg:B→ℝ k . Our main result gives a computable sufficient condition to assure that fort > 0 and sufficiently small, the observation of the reference solution (which corresponds tou(t)≡0) at timet is interior to the set of observations of all solutions at timet. An example to illustrate the theory is the local controllability, via tension, of various observations of a vibrating string. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Local controllability of observables in finite and infinite dimensional nonlinear control systems

Applied Mathematics and Optimization , Volume 5 (1) – Mar 23, 2005

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References (11)

Publisher
Springer Journals
Copyright
Copyright © 1979 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01442549
Publisher site
See Article on Publisher Site

Abstract

LetA, ℬ be evolution operators (possibly nonlinear) which act within a Banach spaceB andu(·) a measurable, real valued, control function. We study control systems of the form ∂υ t /∂t=A υ t +u(t)ℬυ t , υ0=ϕ ∈B. An observation of this system is defined to be a continuous linear mapg:B→ℝ k . Our main result gives a computable sufficient condition to assure that fort > 0 and sufficiently small, the observation of the reference solution (which corresponds tou(t)≡0) at timet is interior to the set of observations of all solutions at timet. An example to illustrate the theory is the local controllability, via tension, of various observations of a vibrating string.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 23, 2005

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