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Closed-Loop Control with Evolving Gaussian Process Models

Part of the Studies in Systems, Decision and Control book series (SSDC,volume 55)

Abstract

This contribution presents a new development in the design of control system based on evolving Gaussian process (GP) models . GP models provide a probabilistic, nonparametric modelling approach for black-box identification of nonlinear dynamic systems. They can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. GP models contain noticeably less coefficients to be optimised than commonly used parametric models. While GP models are Bayesian models, their output is normal distribution, expressed in terms of mean and variance. Latter can be interpreted as a confidence in prediction and used in many fields, especially in control system. Evolving GP model is the concept approach within which various ways of model adaptations can be used. Successful control system needs as much as possible data about process to be controlled . If the prior knowledge about the system to be controlled is scarce or the system varies with time or operating region, this control problem can be solved with an iterative method which adapts model with information obtained with streaming data and concurrently optimises hyperparameter values. This contribution provides: a survey of adaptive control algorithms for dynamic systems described in publications where GP models have been used for control design, a novel and improved closed-loop controller with evolving GP models and an example for the illustration of proposed control algorithm.

Keywords

  • Dynamic systems modelling
  • Gaussian process regression
  • Evolving Gaussian process model
  • Adaptive control

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Notes

  1. 1.

    It should be noted that for calculation of the negative log marginal likelihood the inverse of the covariance matrix is needed. In our case the inverse of the covariance matrix should be calculated for every subset. But, this computational demanding task can be speeded up by calculating the Cholesky decomposition of the exceeded active set of length n only once and then downdates it for every data in it by using low-rank updates [33].

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Acknowledgments

This work has been supported by the Slovenian Research Agency, grant No. P2-0001

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Correspondence to Juš Kocijan .

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Kocijan, J., Petelin, D. (2016). Closed-Loop Control with Evolving Gaussian Process Models. In: Dimirovski, G. (eds) Complex Systems. Studies in Systems, Decision and Control, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-28860-4_24

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  • DOI: https://doi.org/10.1007/978-3-319-28860-4_24

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