1. A new kernel-based approach to system identification with quantized output data
- Author
-
Håkan Hjalmarsson, Gianluigi Pillonetto, Giulio Bottegal, and Control Systems
- Subjects
FOS: Computer and information sciences ,0209 industrial biotechnology ,Mathematical optimization ,Quantized data ,Machine Learning (stat.ML) ,02 engineering and technology ,Systems and Control (eess.SY) ,Kernel principal component analysis ,symbols.namesake ,Kernel-based methods ,020901 industrial engineering & automation ,Statistics - Machine Learning ,Reglerteknik ,Gibbs sampler ,0202 electrical engineering, electronic engineering, information engineering ,FOS: Electrical engineering, electronic engineering, information engineering ,Electrical and Electronic Engineering ,Expectationâ maximization ,System identification ,Gaussian process ,Mathematics ,Expectationâmaximization ,Control and Systems Engineering ,020208 electrical & electronic engineering ,Expectation–maximization ,Control Engineering ,Variable kernel density estimation ,Kernel embedding of distributions ,Kernel (statistics) ,Radial basis function kernel ,symbols ,Computer Science - Systems and Control ,Kernel regression ,Algorithm - Abstract
In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data., Comment: 10 pages, 4 figures
- Published
- 2016
- Full Text
- View/download PDF