Robust Control Barrier-Value Functions for Safety-Critical Control

Choi, Jason J.; Lee, Donggun; Sreenath, Koushil; Tomlin, Claire J.; Herbert, Sylvia L.

doi:10.48550/arxiv.2104.02808

Cited by 9 publications

(17 citation statements)

References 25 publications

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“…For example, Control Lyapunov Function [5], [6], [24] ensures the existence of a controller so that the system converges to desired behavior. Control Barrier Function [11], [12], [13], [14], [15], [16], [17], [39] ensures the existence of a controller that keep the system inside a safe invariant set. However, the existing controller synthesis with safety certificate heavily relies on a whitebox model of the system dynamics.…”

Section: Safety Certificate and Control Barrier Functionsmentioning

confidence: 99%

SABLAS: Learning Safe Control for Black-box Dynamical Systems

Qin¹,

Sun²,

Fan³

2022

Preprint

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Control certificates based on barrier functions have been a powerful tool to generate probably safe control policies for dynamical systems. However, existing methods based on barrier certificates are normally for white-box systems with differentiable dynamics, which makes them inapplicable to many practical applications where the system is a black-box and cannot be accurately modeled. On the other side, model-free reinforcement learning (RL) methods for black-box systems suffer from lack of safety guarantees and low sampling efficiency. In this paper, we propose a novel method that can learn safe control policies and barrier certificates for black-box dynamical systems, without requiring for an accurate system model. Our method re-designs the loss function to back-propagate gradient to the control policy even when the black-box dynamical system is non-differentiable, and we show that the safety certificates hold on the black-box system. Empirical results in simulation show that our method can significantly improve the performance of the learned policies by achieving nearly 100% safety and goal reaching rates using much fewer training samples, compared to state-of-the-art blackbox safe control methods. Our learned agents can also generalize to unseen scenarios while keeping the original performance. The source code can be found at https://github.com/Zengyi-Qin/bcbf.

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Section: Safety Certificate and Control Barrier Functionsmentioning

confidence: 99%

SABLAS: Learning Safe Control for Black-box Dynamical Systems

Qin¹,

Sun²,

Fan³

2022

Preprint

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“…The resulting value function can then be used to enforce safety by means of a backup controller [8], [9], and is completely agnostic in the task formulation. Another closely related approach is control barrier functions (CBFs) [10], [11], which generalizes the backup controller of HJ reachability with sets of safety-preserving control inputs, which can again be used as task-agnostic backup controllers. This agnosticism is a double-edged feature.…”

Section: A Related Workmentioning

confidence: 99%

“…Intuitively, Q V is the set of state-control pairs that transition into the viability kernel [36]. Condition (11) compares the worst-case scenario of the best safe controller to the best-case scenario of an unsafe controller, and ensures that the former achieves a higher return than the latter.…”

Section: A Safety As a Property Of The Value Functionmentioning

confidence: 99%

Safe Value Functions

Massiani¹,

Heim²,

Solowjow³

et al. 2021

Preprint

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The relationship between safety and optimality in control is not well understood, and they are often seen as important yet conflicting objectives. There is a pressing need to formalize this relationship, especially given the growing prominence of learning-based methods. Indeed, it is common practice in reinforcement learning to simply modify reward functions by penalizing failures, with the penalty treated as a mere heuristic. We rigorously examine this relationship, and formalize the requirements for safe value functions: value functions that are both optimal for a given task, and enforce safety. We reveal the structure of this relationship through a proof of strong duality, showing that there always exists a finite penalty that induces a safe value function. This penalty is not unique, but upperunbounded: larger penalties do not harm optimality. Although it is often not possible to compute the minimum required penalty, we reveal clear structure of how the penalty, rewards, discount factor, and dynamics interact. This insight suggests practical, theory-guided heuristics to design reward functions for control problems where safety is important.

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“…The most closely related work on robust CBFs is briefly summarized. Robust control barrier functions have been developed for guaranteeing safety in the presence of L ∞ bounded disturbances [10], [11], [12], [13] or stochastic disturbances [14]. The work in [15] and [16] considers robust CBFs to account for variations in the model (changes to the vector fields) and input (sector-bounded) nonlinearities, respectively.…”

Section: Introductionmentioning

confidence: 99%

Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints

Seiler¹,

Janković²,

Hellström³

2021

Preprint

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This paper presents a control design method that achieves safety for systems with unmodeled dynamics at the plant input. The proposed method combines control barrier functions (CBFs) and integral quadratic constraints (IQCs). Simplified, low-order models are often used in the design of the controller. Parasitic, unmodeled dynamics (e.g. actuator dynamics, time delays, etc) can lead to safety violations. The proposed method bounds the input-output behavior of these unmodeled dynamics in the time-domain using an α-IQC. The α-IQC is then incorporated into the CBF constraint to ensure safety. The approach is demonstrated with a simple example.

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Robust Control Barrier-Value Functions for Safety-Critical Control

Cited by 9 publications

References 25 publications

SABLAS: Learning Safe Control for Black-box Dynamical Systems

SABLAS: Learning Safe Control for Black-box Dynamical Systems

Safe Value Functions

Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraints

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