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

Convex Nonparametric Formulation for Identification of Gradient Flows