Nonlinear System Identification With Prior Knowledge on the Region of Attraction


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Date

2021-07

Publication Type

Journal Article

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yes

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Abstract

We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing the fitting error and guaranteeing the desired stability property. The problem is approached by joint identification of the dynamics and a Lyapunov function verifying the stability property. In this setting, the hypothesis set is a reproducing kernel Hilbert space, and with respect to each point of the given subset of the ROA, the Lie derivative inequality of the Lyapunov function imposes a constraint. The problem is a non-convex infinite-dimensional optimization with an infinite number of constraints. To obtain a tractable formulation, only a suitably designed finite subset of the constraints are considered. The resulting problem admits a solution in form of a linear combination of the sections of the kernel and its derivatives. An equivalent finite dimension optimization problem with a quadratic cost function subject to linear and bilinear constraints is derived. A suitable change of variable gives a convex reformulation of the problem. The method is demonstrated by several examples.

Publication status

published

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Volume

5 (3)

Pages / Article No.

1091 - 1096

Publisher

IEEE

Event

Edition / version

Methods

Software

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Subject

Nonlinear system identification; Region of attraction; Prior knowledge; Convex optimization

Organisational unit

08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former) check_circle

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