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Gradient realization of nonlinear control systems
J. Cortés, A.J. van der Schaft, P.E. Crouch
IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Seville, Spain, 2003, pp. 73-78

Abstract

We investigate necessary and sufficient conditions under which a 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 input-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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