Adaptive, cautious, predictive control with gaussian process priors

Murray-Smith, Roderick; Sbárbaro, Daniel; Rasmussen, Carl Edward; Girard, Agathe

doi:10.1016/s1474-6670(17)34915-7

Cited by 51 publications

(45 citation statements)

References 12 publications

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“…Alpcan investigated active optimal control with Gaussian processes in the context of dual control [1]. Murray-Smith et al have explored Gaussian processes in the context of dual adaptive control [38], [39]. Nguyen-Tuong and Peters combined a physics based model with a Gaussian Process model for learning inverse dynamics of stable systems such as robotic arms [44].…”

Section: A Related Workmentioning

confidence: 99%

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Chowdhary

Kingravi

How

et al. 2015

IEEE Trans. Neural Netw. Learning Syst.

143

160

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Abstract-Most current Model Reference Adaptive Control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element are Radial Basis Function Networks (RBFNs), with RBF centers pre-allocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become non-effective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semi-global in nature. This paper investigates a Gaussian Process (GP) based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

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Section: A Related Workmentioning

confidence: 99%

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Chowdhary

Kingravi

How

et al. 2015

IEEE Trans. Neural Netw. Learning Syst.

143

160

View full text Add to dashboard Cite

show abstract

“…Explicitly using the predictive variance has been recently successfully used in a control context [21] and also the propagation of uncertainty methodology, in a model predictive control framework where knowledge of the accuracy of the model predictions over the whole prediction horizon is required (see [22]). …”

Section: Discussionmentioning

confidence: 99%

Switching and Learning in Feedback Systems

Murray-Smith

Shorten²

2005

Lecture Notes in Computer Science

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Abstract.With the Gaussian Process model, the predictive distribution of the output corresponding to a new given input is Gaussian. But if this input is uncertain or noisy, the predictive distribution becomes non-Gaussian. We present an analytical approach that consists of computing only the mean and variance of this new distribution (Gaussian approximation). We show how, depending on the form of the covariance function of the process, we can evaluate these moments exactly or approximately (within a Taylor approximation of the covariance function). We apply our results to the iterative multiple-step ahead prediction of non-linear dynamic systems with propagation of the uncertainty as we predict ahead in time. Finally, using numerical examples, we compare the Gaussian approximation to the numerical approximation of the true predictive distribution by simple Monte-Carlo.

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“…And, most importantly, the model quantifies its ignorance due to missing data [3]. Many application utilize GPs in a model predictive control scheme [4], [5] or reinforcement learning [6]. Inverse models for robotic manipulators are also obtained using semiparametric methods, see [7].…”

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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Adaptive, cautious, predictive control with gaussian process priors

Cited by 51 publications

References 12 publications

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Switching and Learning in Feedback Systems

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

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