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Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression

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Document pages: 6 pages

Abstract: Modelling real world systems involving humans such as biological processesfor disease treatment or human behavior for robotic rehabilitation is achallenging problem because labeled training data is sparse and expensive,while high prediction accuracy is required from models of these dynamicalsystems. Due to the high nonlinearity of problems in this area, data-drivenapproaches gain increasing attention for identifying nonparametric models. Inorder to increase the prediction performance of these models, abstract priorknowledge such as stability should be included in the learning approach. One ofthe key challenges is to ensure sufficient flexibility of the models, which istypically limited by the usage of parametric Lyapunov functions to guaranteestability. Therefore, we derive an approach to learn a nonparametric Lyapunovfunction based on Gaussian process regression from data. Furthermore, we learna nonparametric Gaussian process state space model from the data and show thatit is capable of reproducing observed data exactly. We prove that stabilizationof the nominal model based on the nonparametric control Lyapunov function doesnot modify the behavior of the nominal model at training samples. Theflexibility and efficiency of our approach is demonstrated on the benchmarkproblem of learning handwriting motions from a real world dataset, where ourapproach achieves almost exact reproduction of the training data.

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