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

Umlauft, Jonas; Pohler, Lukas; Hirche, Sandra

doi:10.1109/lcsys.2018.2841961

Cited by 75 publications

(56 citation statements)

References 20 publications

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“…The work in [25] considers the control of Lagrangian systems and shows boundedness of the tracking error. The identification of a priori known stable systems with GPs is analyzed in [26], and [27] proposes an uncertaintybased control approach for which asymptotic stability is proven. However, none of these techniques updates the model while controlling the system.…”

Section: A Related Workmentioning

confidence: 99%

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Umlauft

Hirche

2020

IEEE Trans. Automat. Contr.

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Combining control engineering with nonparametric modeling techniques from machine learning allows to control systems without analytic description using data-driven models. Most existing approaches separate learning, i.e. the system identification based on a fixed dataset, and control, i.e. the execution of the model-based control law. This separation makes the performance highly sensitive to the initial selection of training data and possibly requires very large datasets. This article proposes a learning feedback linearizing control law using online closed-loop identification. The employed Gaussian process model updates its training data only if the model uncertainty becomes too large. This event-triggered online learning ensures high data efficiency and thereby reduces the computational complexity, which is a major barrier for using Gaussian processes under realtime constraints. We propose safe forgetting strategies of data points to adhere to budget constraint and to further increase data-efficiency. We show asymptotic stability for the tracking error under the proposed event-triggering law and illustrate the effective identification and control in simulation.

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Section: A Related Workmentioning

confidence: 99%

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Umlauft

Hirche

2020

IEEE Trans. Automat. Contr.

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“…The work in [1] considers to enforce linear operator constraints into GP models. Furthermore, [56] and [58] utilize GPs in a feedback linearizing scheme and [8] and [9] consider safe exploration of the state-space with an initially unknown dynamics. Nevertheless, it is not investigated how the assumption of system stability can be enforced during the learning of the model.…”

Section: Related Workmentioning

confidence: 99%

“…Second, a GP model provides, beside the most likely function value (the GP mean function), an uncertainty measure (the GP variance function), which encodes the precision of the model for any state x ∈ X . This model fidelity allows to apply risk-sensitive [34], uncertainty-aware [58] or path integral [53] control techniques.…”

Section: Problem Formulationmentioning

confidence: 99%

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Learning stochastically stable Gaussian process state–space models

Umlauft

Hirche

2020

IFAC Journal of Systems and Control

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Control systems are increasingly applied in domains where an analytic description of the system dynamics does not exist or is difficult to obtain. Example applications include autonomous robots in unstructured environments, human behavior modeling for prediction and action recognition in human-machineinteraction, and chemical process industry. In many of these cases, classical system identification is challenging, because a parametric model structure is unknown. Data-driven nonparametric models such as Gaussian process statespace models (GPSSMs) offer a suitable alternative: GPSSMs are known for their data-efficiency and rely on Bayesian principles to include prior knowledge.However, properties like stability or boundedness are often known a priori, but rarely exploited during modeling. We therefore propose a novel approach for learning GPSSMs subject to stability constraints. Our approach enforces the convergence using control Lyapunov functions which are also obtained in a datadriven fashion. We analyze the resulting dynamics with respect to convergence radius and data collection. In simulation, we illustrate the precision of the identified model on a real-world dataset of goal-directed motions. 1 .

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“…Our approach is related to several techniques that have been provided in the literature. Using the GP in control community has been attracted much attention in recent years [18]- [21], [23]- [26]. In particular, our approach is related to the ones based on optimal control framework, see, e.g., [19]- [21], [24]- [26].…”

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confidence: 99%

Learning Self-Triggered Controllers With Gaussian Processes

Hashimoto

Yoshimura

Ushio

2021

IEEE Trans. Cybern.

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This paper investigates the design of self-triggered controllers for networked control systems (NCSs), where the dynamics of the plant is unknown apriori. To deal with the unknown transition dynamics, we employ the Gaussian process (GP) regression in order to learn the dynamics of the plant. To design the self-triggered controller, we formulate an optimal control problem, such that the optimal pair of the inter-communication time step and control input can be determined based on the GP dynamics of the plant. Moreover, we provide an overall implementation algorithm that jointly learns the dynamics of the plant and the self-triggered controller based on a reinforcement learning framework. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.

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

Cited by 75 publications

References 20 publications

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Feedback Linearization Based on Gaussian Processes With Event-Triggered Online Learning

Learning stochastically stable Gaussian process state–space models

Learning Self-Triggered Controllers With Gaussian Processes

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