Gaussian Control Barrier Functions: Safe Learning and Control

Khan, Mouhyemen; Chatterjee, Abhijit

doi:10.1109/cdc42340.2020.9303753

Cited by 9 publications

(2 citation statements)

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“…However, utilizing an uncertain or inaccurate system model for control synthesis may lead to safety violations. As such, control engineers often seek to compensate for model uncertainty in one of the following ways: by taking a robust approach [22,25,50], assuming some worst-case bound on the perturbation to the system dynamics; by using adaptive techniques [27,44,51], defining parameter-adaptation laws according to which estimates of unknown system parameters are modified online; or by employing learning algorithms [21,23,45], using data to learn a representation of system behavior.…”

Section: Introductionmentioning

confidence: 99%

“…Controllers designed using adaptive-CBFs (aCBFs) and parameter estimators may adjust quickly to changes in the system dynamics online, but can lead to undesirable chattering [44] or require strict assumptions on persistently excited (PE) signals in the system dynamics [31]. And while learning-based control algorithms have found success empirically in certain scenarios, they lack guarantees of safety and stabilization [23]. In this paper, we seek to design a control framework that leverages the fast reactivity of adaptation-based controllers and the strong robustness properties of rCBFs to guarantee the following: 1) that uncertainty represented by a class of additive, parameter-affine perturbations in the system dynamics is learned within a finite time independent of the initial parameter estimates, and 2) that the system trajectories remain safe at all times.…”

Section: Introductionmentioning

confidence: 99%

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Fixed-Time Parameter Adaptation for Safe Control Synthesis

Black¹,

Arabi²,

Panagou³

2022

Preprint

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We propose a fixed-time stable parameter adaptation law that guarantees that an additive, parameter-affine disturbance appearing in the dynamics of a class of nonlinear, control-affine systems is learned within a fixed time. We then provide an upper bound on the parameter estimation error as an explicit function of time, and use such knowledge to formulate a control barrier function condition to guarantee safety of the system trajectories at all times. We further show that our proposed parameter adaptation law is robust against bounded perturbations to the system dynamics in that the resulting estimated parametric disturbance converges to a known neighborhood of the true parametric disturbance within a fixed time. To illustrate the advantages of our proposed approach, we conduct a comparative numerical study against various controllers from the literature. Finally, we validate our approach on a trajectory-tracking problem subject to safety requirements using a 6 degree-of-freedom quadrotor model in an unknown wind field.

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