Multivariable Generalized Minimum Variance Control Based on Artificial Neural Networks and Gaussian Process Models

Sbárbaro, Daniel; Murray-Smith, Roderick; Valdes, Arturo

doi:10.1007/978-3-540-28648-6_8

Cited by 9 publications

(10 citation statements)

References 10 publications

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“…Increasing the size of the covariance matrix, i.e., 'blow-up model', with the instreaming data and repeating model optimisation is used in papers [19,20,[30][31][32], where more attention is devoted to control algorithms and their benefits based on information gained from the GP model and not on the model identification itself.…”

Section: Adaptive Control Algorithms Based On Gaussian Process Modelsmentioning

confidence: 99%

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Closed-Loop Control with Evolving Gaussian Process Models

Kocijan

Petelin

2016

Complex Systems

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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.

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Section: Adaptive Control Algorithms Based On Gaussian Process Modelsmentioning

confidence: 99%

“…The minimisation can be done analytically, but also numerically, using any appropriate optimisation method. The cost function (24.11) can be expanded with a penalty terms and generalised to multiple-input multiple-output case leading to generalised minimum-variance control [31].…”

Section: Adaptive Control Algorithms Based On Gaussian Process Modelsmentioning

confidence: 99%

Closed-Loop Control with Evolving Gaussian Process Models

Kocijan

Petelin

2016

Complex Systems

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“…Adaptive control of nonlinear stochastic systems with unknown functions offers an interesting challenge [1], [2], [3], [4]. It can be understood as a natural effort of extension of the adaptive control from a class of linear systems and nonlinear systems with unknown parameters to the complex systems with functional uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Gaussian process based dual adaptive control of nonlinear stochastic systems

Král

Prüher

Šimandl

2014

22nd Mediterranean Conference on Control and Automation

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The paper proposes a suboptimal adaptive control for a nonlinear stochastic system subject to functional uncertainty. The problem of a real-time identification of the unknown nonlinear system is tackled by using the Gaussian process based non-parametric model. The covariance function of the Gaussian process is chosen in such a way that allows deriving the control law in a closed form. The control action stems from the bicriterial dual approach that uses two separate criteria to introduce both of the mutually opposing aspects between estimation and control. Properties of the novel dual controller are tested and validated in a numerical example by Monte Carlo analysis.

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“…The problem of adaptive control of non-linear stochastic systems with unknown functions offers an interesting challenge [1][2][3][4]. It can be understood as a natural extension of the adaptive control from a class of linear systems and non-linear systems with unknown parameters to the complex systems with functional uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…So far, GP modelling was utilised in functional adaptive approach only in a few pioneering works [3,27]. It should be noted, that the GP models were implemented exclusively in a nonrecursive form, causing a continuous increase of the computational demands with time, which significantly reduces their practical applicability.…”

Section: Introductionmentioning

confidence: 99%

Functional Dual Adaptive Control with Recursive Gaussian Process Model

Prüher

Král

2015

J. Phys.: Conf. Ser.

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Abstract. The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded.

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Multivariable Generalized Minimum Variance Control Based on Artificial Neural Networks and Gaussian Process Models

Cited by 9 publications

References 10 publications

Closed-Loop Control with Evolving Gaussian Process Models

Closed-Loop Control with Evolving Gaussian Process Models

Gaussian process based dual adaptive control of nonlinear stochastic systems

Functional Dual Adaptive Control with Recursive Gaussian Process Model

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