Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Chowdhary, Girish; Kingravi, Hassan A.; How, Jonathan P.; Vela, Patricio A.

doi:10.1109/tnnls.2014.2319052

Cited by 149 publications

(170 citation statements)

References 57 publications

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“…It uses estimates (11) to control the system based on (13). We run the simulation for T sim = 50s three times: Without any data D none = ∅, with D frac and D full .…”

Section: A Setupmentioning

confidence: 99%

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Feedback linearization using Gaussian processes

Umlauft

Beckers

Kimmel

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. This paper utilizes Gaussian processes, a Bayesian nonparametric approach, to learn a model for feedback linearization. By using a proper kernel structure, the training data for identification is collected while an existing controller runs the system. Using the identified dynamics, an improved controller, based on feedback linearization, is proposed. The analysis shows that the resulting system is globally uniformly ultimately bounded. We further derive a relationship between the training data of the system and the size of the ultimate bound to which the system converges with a certain probability. A simulation of a robotic system illustrates the proposed method.

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“…It uses estimates (11) to control the system based on (13). We run the simulation for T sim = 50s three times: Without any data D none = ∅, with D frac and D full .…”

Section: A Setupmentioning

confidence: 99%

“…Also [11] considers uncertainties in the given dynamics, but without specifying how these are obtained. The methods in [12], [13] use an adaptive scheme, however, nonparametric identification methods for control affine systems have not been exploited.…”

Section: Introductionmentioning

confidence: 99%

Feedback linearization using Gaussian processes

Umlauft

Beckers

Kimmel

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

View full text Add to dashboard Cite

show abstract

“…The first of the BD criteria (2) can be minimized using (25), (26) and the cautious control component u c k is given as…”

Section: Control Law Derivationmentioning

confidence: 99%

“…Typically, it is necessary to consider some kind of GP approximation to counteract the problem of increasing data size. Recently increased effort has been given to the design of original algorithms, which eliminate this drawback [22][23][24][25][26].…”

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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“…However, none of these perform a stability analysis of the controlled system. This is first considered in an adaptive control scheme in [8], followed by a computed torque approach in [9] and a feedback linearization control in [10]. These approaches focus on ultimate boundedness, but do not ensure asymptotic convergence.…”

Section: Introductionmentioning

confidence: 99%

An Uncertainty-Based Control Lyapunov Approach for Control-Affine Systems Modeled by Gaussian Process

Umlauft

Pohler

Hirche

2018

IEEE Control Syst. Lett.

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Abstract-Data-driven approaches in control allow for identification of highly complex dynamical systems with minimal prior knowledge. However, properly incorporating model uncertainty in the design of a stabilizing control law remains challenging. Therefore, this article proposes a control Lyapunov function framework which semiglobally asymptotically stabilizes a partially unknown fully actuated control affine system with high probability. We propose an uncertainty-based control Lyapunov function which utilizes the model fidelity estimate of a Gaussian process model to drive the system in areas near training data with low uncertainty. We show that this behavior maximizes the probability that the system is stabilized in the presence of power constraints using equivalence to dynamic programming. A simulation on a nonlinear system is provided.

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Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Cited by 149 publications

References 57 publications

Feedback linearization using Gaussian processes

Feedback linearization using Gaussian processes

Functional Dual Adaptive Control with Recursive Gaussian Process Model

An Uncertainty-Based Control Lyapunov Approach for Control-Affine Systems Modeled by Gaussian Process

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