arXiv subjects

Chams E. Mballo

Publications and source records attributed to Chams E. Mballo.

2 recordsLinked to original sources

arXiv2026

A Spectral Perspective on Stochastic Control Barrier Functions

Stochastic control barrier functions (SCBFs) provide a safety-critical control framework for systems subject to stochastic disturbances by bounding the probability of remaining within a safe set. However, synthesizing a valid SCBF that explicitly reflects the true safety probability of the system, which is the most natural measure of safety, remains a challenge. This paper addresses this issue by adopting a spectral perspective, utilizing the linear operator that governs the evolution of the closed-loop system's safety probability. We find that the dominant eigenpair of this Koopman-like operator encodes fundamental safety information of the stochastic system. The dominant eigenfunction is a natural and valid SCBF, with values that explicitly quantify the relative long-term safety of the state, while the dominant eigenvalue indicates the global rate at which the safety probability decays. A practical synthesis algorithm is proposed, termed power-policy iteration, which jointly computes the dominant eigenpair and an optimized backup policy. The method is validated using simulation experiments on safety-critical dynamics models.

eess.SY↗

arXiv2026

EigenSafe: A Spectral Framework for Learning-Based Probabilistic Safety Assessment

We present EigenSafe, an operator-theoretic framework for safety assessment of learning-enabled stochastic systems. In many robotic applications, the dynamics are inherently stochastic due to factors such as sensing noise and environmental disturbances, and it is challenging for conventional methods such as Hamilton-Jacobi reachability and control barrier functions to provide a well-calibrated safety critic that is tied to the actual safety probability. We derive a linear operator that governs the dynamic programming principle for safety probability, and find that its dominant eigenpair provides critical safety information for both individual state-action pairs and the overall closed-loop system. The proposed framework learns this dominant eigenpair, which can be used to either inform or constrain policy updates. We demonstrate that the learned eigenpair effectively facilitates safe reinforcement learning. Further, we validate its applicability in enhancing the safety of learned policies from imitation learning through robot manipulation experiments using a UR3 robotic arm in a food preparation task.

cs.RO↗