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A necessary condition for dynamic equivalence

Abstract : If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different dimensions, the one of higher dimension must ruled. A ruled system is one whose equations define at each point in the state manifold, a ruled submanifold of the tangent space. Dynamic equivalence is also known as equivalence by endogenous dynamic feedback, or by a Lie-Bäcklund transformation when control systems are viewed as underdetermined systems of ordinary differential equations; it is very close to absolute equivalence for Pfaffian systems. It was already known that a differentially flat system must be ruled; this is a particular case of the present result, in which one of the systems is assumed to be "trivial" (or linear controllable).
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https://hal.inria.fr/inria-00277531
Contributor : Jean-Baptiste Pomet <>
Submitted on : Monday, November 24, 2008 - 4:12:33 PM
Last modification on : Tuesday, October 15, 2019 - 1:15:38 AM
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Jean-Baptiste Pomet. A necessary condition for dynamic equivalence. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2009, 48 (2), pp.925-940. ⟨10.1137/080723351⟩. ⟨inria-00277531v2⟩

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