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We consider the problem of nonlinear system identification when priorknowledge is available on the region of attraction (ROA) of an equilibriumpoint. We propose an identification method in the form of an optimizationproblem, minimizing the fitting error and guaranteeing the desired stabilityproperty. The problem is approached by joint identification the dynamics and aLyapunov function verifying the stability property. In this setting, thehypothesis set is a reproducing kernel Hilbert space, and with respect to eachpoint of the given subset of the ROA, the Lie derivative inequality of theLyapunov function imposes a constraint. The problem is a non-convexinfinite-dimensional optimization with infinite number of constraints. Toobtain a tractable formulation, only a suitably designed finite subset of theconstraints are considered. The resulting problem admits a solution in form ofa linear combination of the sections of the kernel and its derivatives. Anequivalent optimization problem with a quadratic cost function subject tolinear and bilinear constraints is derived. A suitable change of variable givesa convex reformulation of the problem. To reduce the number of hyperparameters,the optimization problem is adapted to the case of diagonal kernels. The methodis demonstrate by means of an example.

Nonlinear System Identification with Prior Knowledge of the Region of Attraction