Safe and Stable Filter Design Using a Relaxed Compatibitlity Control Barrier -- Lyapunov Condition
In this paper, we propose a quadratic programming-based filter for safe and stable controller design, via a Control Barrier Function (CBF) and a Control Lyapunov Function (CLF). Our method guarantees safety and local asymptotic stability without the need for an asymptotically stabilizing control law. Feasibility of the proposed program is ensured under a mild regularity condition, termed relaxed compatibility between the CLF and CBF. The resulting optimal control law is guaranteed to be locally Lipschitz continuous. We also analyze the closed-loop behaviour by characterizing the equilibrium points, and verifying that there are no equilibrium points in the interior of the control invariant set except at the origin. For a polynomial system and a semi-algebraic safe set, we provide a sum-of-squares program to design a relaxed compatible pair of CLF and CBF. The proposed approach is compared with other methods in the literature using numerical examples, exhibits superior filter performance and guarantees safety and local stability.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Secure Safety Filter Design for Sampled-data Nonlinear Systems under Sensor Spoofing Attacks
This paper presents a secure safety filter design for nonlinear systems under sensor spoofing attacks. Existing approaches primarily focus on linear systems which limits their applications in real-world scenarios. In thi…
State EstimationRed-Teaming the Stable Diffusion Safety Filter
Stable Diffusion is a recent open-source image generation model comparable to proprietary models such as DALLE, Imagen, or Parti. Stable Diffusion comes with a safety filter that aims to prevent generating explicit image…
Image GenerationRed TeamingInverse Optimal Safety Filters
CBF-QP safety filters are pointwise minimizers of the control effort at a given state vector, i.e., myopically optimal at each time instant. But are they optimal over the entire infinite time horizon? What does it even m…
On the Impossibility of Separating Intelligence from Judgment: The Computational Intractability of Filtering for AI Alignment
With the increased deployment of large language models (LLMs), one concern is their potential misuse for generating harmful content. Our work studies the alignment challenge, with a focus on filters to prevent the genera…
ECO-DKF: Event-Triggered and Certifiable Optimal Distributed Kalman Filter under Unknown Correlations
This paper presents ECO-DKF, the first Event-Triggered and Certifiable Optimal Distributed Kalman Filter. Our algorithm addresses two major issues inherent to Distributed Kalman Filters: (i) fully distributed and scalabl…