Publication
Learning Non-Parametric Models with Guarantees: A Smooth Lipschitz Interpolation Approach
Abstract
We propose a non-parametric regression method that does not rely on the structure of the ground-truth, but only on its regularity properties. The methodology can be readily used for learning surrogate models of nonlinear dynamical systems from data, while providing bounds on the prediction error. In contrast with the well known Set Membership and Kinky Inference techniques that yield non-differentiable functions, the approach presented herein produces a smooth regressor. Consequently, it is more suitable to optimization-based controllers that heavily rely on gradient computations. A numerical example is provided to show the effectiveness of the method we call Smooth Lipschitz Interpolation (SLI) when compared to the aforementioned alternatives in a Model Predictive Control problem.
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Ontological neighbourhood
Related concepts (36)
Model predictive control
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification.
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Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced ˈloʊɛs. They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model.
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