Control Barriers in Bayesian Learning of System Dynamics

Dhiman, Vikas; Khojasteh, Mohammad Javad; Franceschetti, Massimo; Atanasov, Nikolay

doi:10.48550/arxiv.2012.14964

Cited by 3 publications

(8 citation statements)

References 50 publications

(82 reference statements)

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“…Thus, "energy deficit" CBF defined by (11) has relative degree 2, from the voltage input, according to the perspective in [42], which inherits the backstepping change of variable ( 13) from [36].…”

Section: Nonovershooting Regulation By Backstepping For Multiple Cbfsmentioning

confidence: 99%

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Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Koga¹,

Krstić²

2021

Preprint

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High-relative-degree control barrier functions (hirel-deg CBFs) play a prominent role in automotive safety and in robotics. In this paper we launch a generalization of this concept for PDE control, treating a specific, physically-relevant model of thermal dynamics where the boundary of the PDE moves due to a liquid-solid phase change-the so-called Stefan model. The familiar QP design is employed to ensure safety but with CBFs that are infinite-dimensional (including one control barrier "functional") and with safe sets that are infinite-dimensional as well. Since, in the presence of actuator dynamics, at the boundary of the Stefan system, this system's main CBF is of relative degree two, an additional CBF is constructed, by backstepping design, which ensures the positivity of all the CBFs without any additional restrictions on the initial conditions. It is shown that the "safety filter" designed in the paper guarantees safety in the presence of an arbitrary operator input. This is similar to an automotive system in which a safety feedback law overrides-but only when necessary-the possibly unsafe steering, acceleration, or braking by a vigorous but inexperienced driver. Simulations have been performed for a process in metal additive manufacturing, which show that the operator's heatand-cool commands to the Stefan model are being obeyed but without the liquid ever freezing.

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Section: Nonovershooting Regulation By Backstepping For Multiple Cbfsmentioning

confidence: 99%

“…Due to the addition of the solid phase temperature dynamics, the energy deficit σ in (11) is reformulated. We consider the following CBFs for the two-phase problem:…”

Section: B Nonovershooting Regulation and Guaranteed Safetymentioning

confidence: 99%

Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Koga¹,

Krstić²

2021

Preprint

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“…moving obstacles), which cannot be controlled. 3 The size of σ(X t ) is determined from the uncertainties in the disturbance, unmodeled dynamics [8], [10], [11], [20], and the prediction errors of the environmental variables [13], [21]. Examples of these cases include when the unmodeled dynamics are captured using statistical models such as Gaussian Processes 4 and when the motion of the environment variables are estimated using physics-based models such as Kalman filters [13], [21].…”

Section: A System Description and Design Specificationsmentioning

confidence: 99%

“…The mapping K is either (19) or (20), depending on the choice of control policies. In the next section, we present out main theorems.…”

Section: Safe Probabilitymentioning

confidence: 99%

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Safe Control in the Presence of Stochastic Uncertainties

Chern¹,

Wang²,

Iyer³

et al. 2021

Preprint

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Accurate quantification of safety is essential for the design of autonomous systems. In this paper, we present a methodology to characterize the exact probabilities associated with invariance and recovery in safe control. We consider a stochastic control system where control barrier functions, gradient-based methods, and barrier certificates are used to constrain control actions and validate safety. We derive the probability distributions of the minimum and maximum barrier function values during any time interval and the first entry and exit times to and from any super level sets of the barrier function. These distributions are characterized by deterministic convection-diffusion equations, and the approach used is generalizable to other safe control methods based on barrier functions. These distributions can be used to characterize various quantities associated with invariance and recovery, such as the safety margin, the probability of entering and recovering from safe and unsafe regions, and the mean and tail distributions of failure and recovery times.

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Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty

Castañeda

Choi

Zhang

et al. 2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. Then, we use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization program, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.

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Control Barriers in Bayesian Learning of System Dynamics

Cited by 3 publications

References 50 publications

Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Safe Control in the Presence of Stochastic Uncertainties

Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty

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