Estimating Controllability Boundaries for Uncertain Systems

Grantham, Walter J.

doi:10.1007/978-3-642-46436-2_11

Walter J. Grantham³

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 40))

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Abstract

Two methods, combining controllability and Lyapunov stability, are presented for estimating reachability boundaries for nonlinear control systems. The controllability method is exact, but lacks appropriate boundary conditions in certain cases and is effectively restricted to two-dimensional problems. The approximate Lyapunov method combines Lyapunov stability theory with a controllability maximum principle. The Lyapunov estimate of the reachable set generally differs from the actual reachable set, but the estimate is conservative (i.e., guaranteed to contain the actual reachable set), does not require integration of the equations of motion, and is applicable to n-dimensional systems. Both methods are applied to an example of a prey-predator fishery with bounded harvesting efforts.

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Authors and Affiliations

Department of Mechanical Engineering, Washington State University, Pullman, Washington, USA, 99164
Walter J. Grantham

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Walter J. Grantham
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Editors and Affiliations

Aerospace and Mechanical Engineering, University of Arizona, 85705, Tucson, AZ, USA
Thomas L. Vincent
Department of Mathematics, University of Queensland, 4067, St. Lucia, Queensland, Australia
Janislaw M. Skowronski

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Grantham, W.J. (1981). Estimating Controllability Boundaries for Uncertain Systems. In: Vincent, T.L., Skowronski, J.M. (eds) Renewable Resource Management. Lecture Notes in Biomathematics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46436-2_11

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DOI: https://doi.org/10.1007/978-3-642-46436-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10566-4
Online ISBN: 978-3-642-46436-2
eBook Packages: Springer Book Archive

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