GAUSSIAN PROCESS PRIORS IN CONTROL (original) (raw)

CONTROL USING NONPARAMETRIC GAUSSIAN PROCESS PRIOR MODELS

Abstract: Nonparametric Gaussian Process prior models, taken from Bayesian statistics methodology are used to implement a nonlinear control law. We minimise the expected value of a quadratic cost function, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution), and excitation of the system (exploration).

NONLINEAR ADAPTIVE CONTROL USING NONPARAMETRIC GAUSSIAN PROCESS PRIOR MODELS

2002

Nonparametric Gaussian Process prior models, taken from Bayesian statistics methodology are used to implement a nonlinear adaptive control law. The expected value of a quadratic cost function is minimised, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution), and excitation of the system. The controller has dual features, since it is both tracking a reference signal and learning a model of the system from observed responses. The general method and its main features are illustrated on a simulation example.

Self-tuning control of non-linear systems using Gaussian process prior models

2005

Gaussian Process prior models, as used in Bayesian non-parametric statistical models methodology are applied to implement a nonlinear adaptive control law. The expected value of a quadratic cost function is minimised, without ignoring the variance of the model predictions. This leads to implicit regularisation of the control signal (caution) in areas of high uncertainty. As a consequence, the controller has dual features, since it both tracks a reference signal and learns a model of the system from observed responses.

Adaptive, cautious, predictive control with Gaussian process priors

2003

Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example.

Predictive control with Gaussian process models

2003

Abstract This paper describes model-based predictive control based on Gaussian processes. Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of nonlinear dynamic systems. It offers more insight in variance of obtained model response, as well as fewer parameters to determine than other models.

Gaussian process model based predictive control

2004

Abstract Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes 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. Gaussian process models contain noticeably less coefficients to be optimized.

Nonlinear predictive control with a gaussian process model

2005

Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of nonlinear dynamic systems. The Gaussian processes 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. Gaussian process models contain noticeably less coefficients to be optimized. This chapter illustrates possible application of Gaussian process models within model predictive control.

Modelling and Control of Dynamic Systems Using Gaussian Process Models

2016

This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Highlights: - Explains how theoretical work in Gaussian process models can be applied in the control of real industrial systems - Provides the engineer with practical guidance is not unduly encumbered by complicated theory - Shows the academic researcher the potential for real-world application of a recent branch of control theory More information about the book on the Springer web page (http://www.springer.com/us/book/9783319210209).

Regression on the Basis of Nonstationary Gaussian Processes with Bayesian Regularization

We consider the regression problem, i.e. prediction of a real valued function. A Gaussian process prior is imposed on the function, and is combined with the training data to obtain predictions for new points. We introduce a Bayesian regularization on parameters of a covariance function of the process, which increases quality of approximation and robustness of the estimation. Also an approach to modeling nonstationary cova􏱌 riance function of a Gaussian process on basis of linear expansion in parametric functional dictionary is pro􏱌 posed. Introducing such a covariance function allows to model functions, which have non􏱌homogeneous behaviour. Combining above features with careful optimization of covariance function parameters results in unified approach, which can be easily implemented and applied. The resulting algorithm is an out of the box solution to regression problems, with no need to tune parameters manually. The effectiveness of the method is demonstrated on various datasets.

Gaussian process priors with uncertain inputs: Multiple-step ahead prediction

2002

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time nonlinear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y t = f (y t−1 , . . . , y t−L ), the prediction of y at time t + k is based on the estimatesŷ t+k−1 , . . . ,ŷ t+k−L of the previous outputs. We show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction. In this framework, the problem is that of predicting responses at a random input and we compare the Gaussian approximation to the Monte-Carlo numerical approximation of the predictive distribution. The approach is illustrated on a simulated non-linear dynamic example, as well as on a simple one-dimensional static example.