Jorge Cortés


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


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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Mechanical and Aerospace Engineering, University of California, San Diego
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