Upper and lower estimates for invariance entropy

Christoph Kawan

doi:10.3934/dcds.2011.30.169

Article Contents

2011, Volume 30, Issue 1: 169-186. Doi: 10.3934/dcds.2011.30.169

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Upper and lower estimates for invariance entropy

Christoph Kawan^1,

1.
Institut für Mathematik, Universität Augsburg, 86135 Augsburg

Received: October 31, 2009

Revised: October 31, 2010

Published: December 2010

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Abstract

Invariance entropy for continuous-time control systems measures how often open-loop control functions have to be updated in order to render a subset of the state space invariant. In the present paper, we derive upper and lower bounds for the invariance entropy of control systems on smooth manifolds, using differential-geometric tools. As an example, we compute these bounds explicitly for projected bilinear control systems on the unit sphere. Moreover, we derive a formula for the invariance entropy of a control set for one-dimensional control-affine systems with a single control vector field.

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Mathematics Subject Classification: Primary: 34C40, 93C15, 94A17.

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References

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