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Fundamental Constraints on Uncertainty Evolution in Hamiltonian Systems

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2 Author(s)
Fu-Yuen Hsiao ; Dept. of Aerospace Eng., Tamkang Univ., Tamsui ; Scheeres, D.J.

A realization of Gromov's nonsqueezing theorem and its applications to uncertainty analysis in Hamiltonian systems are studied in this note. Gromov's nonsqueezing theorem describes a fundamental property of symplectic manifolds, however, this theorem is usually started in terms of topology and its physical meaning is vague. In this note we introduce a physical interpretation of the linear symplectic width, which is the lower bound in the nonsqueezing theorem, in terms of the eigenstructure of a positive-definite, symmetric matrix. Since uncertainty is often represented in terms of a positive definite, symmetric matrix in control theory, our study can be applied to uncertainty analysis by applying the nonsqueezing theorem to the uncertainty ellipsoid. We find a fundamental inequality for the evolving uncertainty in a linear dynamical system and provide some numerical examples

Published in:

Automatic Control, IEEE Transactions on  (Volume:52 ,  Issue: 4 )