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Safety criteria for aperiodically forced systems. (English) Zbl 1151.37310

Summary: The theory of uniform hyperbolicity is used to obtain sets of forcing functions for which the response of a dynamical system remains in a prescribed ‘safe’ region. The resulting safety criteria are asymptotically optimal as the size of the safe region goes to zero.

MSC:

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37C75 Stability theory for smooth dynamical systems
70K40 Forced motions for nonlinear problems in mechanics
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