  In this paper, we develop a nonparametric system identification method for
the nonlinear gradient-flow dynamics. In these systems, the vector field is the
gradient field of a potential energy function. This fundamental fact about the
dynamics of system plays the role of a structural prior knowledge as well as a
constraint in the proposed identification method. While the nature of the
identification problem is an estimation in the space of functions, we derive an
equivalent finite dimensional formulation, which is a convex optimization in
form of a quadratic program. This gives scalability of the problem and provides
the opportunity for utilizing recently developed large-scale optimization
solvers. The central idea in the proposed method is representing the energy
function as a difference of two convex functions and estimating these convex
functions jointly. Based on necessary and sufficient conditions for function
convexity, the identification problem is formulated, and then, the existence,
uniqueness and smoothness of the solution is addressed. We also illustrate the
method numerically for a demonstrative example.
