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This paper proposes a quadratic programming-based framework for designing almost surely safe and stable controller by integrating stochastic control barrier functions (SCBFs) and stochastic control Lyapunov functions (SCLFs). Following a theoretical analysis of the applicability of SCLFs, SCBFs, and extended high-order stochastic control barrier functions for stochastic systems with high relative degrees, two distinct filters are proposed: one prioritizing safety exclusively and the other concurrently addressing safety and stability. The efficacy of both filters is demonstrated through a comparative case study on robotic formation trajectory tracking.

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Almost Sure Safety-Stabilizing Filter Design for Affine Nonlinear Stochastic Systems

  • 会议论文

  • 发表日期：

    2026年

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  • Yang Wang,
  • Shixian Luo,
  • Yan Jiang

摘要

This paper proposes a quadratic programming-based framework for designing almost surely safe and stable controller by integrating stochastic control barrier functions (SCBFs) and stochastic control Lyapunov functions (SCLFs). Following a theoretical analysis of the applicability of SCLFs, SCBFs, and extended high-order stochastic control barrier functions for stochastic systems with high relative degrees, two distinct filters are proposed: one prioritizing safety exclusively and the other concurrently addressing safety and stability. The efficacy of both filters is demonstrated through a comparative case study on robotic formation trajectory tracking.