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Journal Articles SIAM Journal on Control and Optimization Year : 2009

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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Dates and versions

inria-00277531 , version 1 (06-05-2008)
inria-00277531 , version 2 (24-11-2008)

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Jean-Baptiste Pomet. A necessary condition for dynamic equivalence. SIAM Journal on Control and Optimization, 2009, 48 (2), pp.925-940. ⟨10.1137/080723351⟩. ⟨inria-00277531v2⟩
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