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Characterization of gradient control systems

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arxiv math/0303371 v1 pith:YL3AP3IV submitted 2003-03-29 math.OC math.DG

Characterization of gradient control systems

Jorge Cortes , Arjan van der Schaft , Peter E. Crouch This is my paper
classification math.OC math.DG
keywords systemaffinecontrolgradientconnectionassociatedbehaviorcharacterization
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We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given affine connection, and on the output behavior of the prolonged system and the gradient extension. The symmetric product associated with an affine connection plays a key role in the discussion.

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