Operator-Theoretic De Bruijn Functional and Robust Safety Control Framework

Key Points

• To develop a framework for safety assessment in safety-critical systems using operator-theoretic concepts and stochastic controls.
• Proposed an operator-theoretic formulation of the De Bruijn functional as a quadratic metric.
• Integrated the framework into a stochastic control model involving belief-state dynamics and robust programming.
• Examined connections between time-domain, frequency-domain representations, and operator structures.
• Established equivalence between time-domain localization and frequency-domain representation.
• Provided a unified mathematical structure for assessing safety through energy metrics and risk measures.
• Demonstrated the framework's efficacy in handling safety-critical system assessments.