Characterization of gradient control systems

Details Characterization of gradient control systems Characterization of gradient control systems

2003-03-29

arxiv.org/abs/math/0303371v1

Mathematics

Optimization and Control

21 pages, no figures

Scientific paper

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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