Nonparametric adaptive control using Gaussian Processes with online hyperparameter estimation

Grande, Robert C.; Chowdhary, Girish; How, Jonathan P.

doi:10.1109/cdc.2013.6759990

“…Stable adaptive control of nonlinear systems often relies on linearly parameterizable dynamics with known nonlinear basis functions, i.e., features, and the ability to cancel these nonlinearities stably with the control input when the parameters are known exactly [69,70,71,44]. When such features cannot be derived a priori, function approximators such as neural networks [65,33,34] and Gaussian processes [25,23] can be used and updated online in the adaptive control loop. However, fast closed-loop adaptive control with complex function approximators is hindered by the computational effort required to train them; this issue is exacerbated by the practical need for controller gain tuning.…”

Section: B Adaptive Controlmentioning

confidence: 99%

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Richards

¹

,

Azizan

²

,

Slotine

³

et al. 2021

Robotics: Science and Systems XVII

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Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features.Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented metalearning of features to fit input-output data. Specifically, we metalearn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the metaobjective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.

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“…Stable adaptive control of nonlinear systems often relies on linearly parameterizable dynamics with known nonlinear basis functions, i.e., features, and the ability to cancel these nonlinearities stably with the control input when the parameters are known exactly [68,69,70,44]. When such features cannot be derived a priori, function approximators such as neural networks [65,33,34] and Gaussian processes [25,23] can be used and updated online in the adaptive control loop. However, fast closed-loop adaptive control with complex function approximators is hindered by the computational effort required to train them; this issue is exacerbated by the practical need for controller gain tuning.…”

Section: B Adaptive Controlmentioning

confidence: 99%

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Richards¹,

Azizan²,

Slotine³

et al. 2021

Preprint

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Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features.Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented metalearning of features to fit input-output data. Specifically, we metalearn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the metaobjective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.

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“…This sparse approximation scales as O(|BV|) for calculating the GP mean, and scales as O(|BV| 2 ) for variance, resulting in significant computational savings. Algorithms are available for optimizing GP hyperparameters online as well [10], [26].…”

Section: Online Budgeted Inferencementioning

confidence: 99%

Online Regression for Data With Changepoints Using Gaussian Processes and Reusable Models

Grande

¹

,

Walsh

²

,

Chowdhary

³

et al. 2016

IEEE Trans. Neural Netw. Learning Syst.

Self Cite

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Many prediction, decision-making, and control architectures rely on online learned Gaussian process (GP) models. However, most existing GP regression algorithms assume a single generative model, leading to poor predictive performance when the data are nonstationary, i.e., generated from multiple switching processes. Furthermore, existing methods for GP regression over nonstationary data require significant computation, do not come with provable guarantees on correctness and speed, and many only work in batch settings, making them ill-suited for real-time prediction. We present an efficient online GP framework, GP-non-Bayesian clustering (GP-NBC), which addresses these computational and theoretical issues, allowing for real-time changepoint detection and regression using GPs. Our empirical results on two real-world data sets and two synthetic data set show that GP-NBC outperforms state-of-the-art methods for nonstationary regression in terms of both regression error and computation. For example, it outperforms Dirichlet process GP clustering with Gibbs sampling by 98% in computation time reduction while the mean absolute error is comparable.

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Nonparametric adaptive control using Gaussian Processes with online hyperparameter estimation

Cited by 22 publications

References 23 publications

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

Online Regression for Data With Changepoints Using Gaussian Processes and Reusable Models

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