Frequency Automata: A novel formal model of hybrid systems in combined time and frequency domains

2025-05-30

AI Summary

To address the longstanding limitation of hybrid system modeling—its exclusive reliance on time-domain representations, which hinders integration of frequency-domain advantages essential for control design—this paper introduces the Frequency Automaton (FA), the first formal hybrid model unifying time- and frequency-domain semantics. FA explicitly incorporates spectral properties (e.g., signal spectra) into its semantics, enabling control-oriented spectral modeling and precise event-triggered simulation. We propose a sound translation method from Hybrid Automata (HA) to FA and develop a robust hierarchical crossing detection algorithm supporting equality constraints. Experimental evaluation demonstrates that FA-based simulation achieves 118×–1129× speedup over Simulink/Stateflow, while successfully detecting equality-guarded crossing events that Simulink fails to identify. These advances significantly enhance cross-domain modeling, formal verification, and high-fidelity simulation capabilities for cyber-physical and control systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health

Abstract

Hybrid systems are mostly modelled, simulated, and verified in the time domain by computer scientists. Engineers, however, use both frequency and time domain modelling due to their distinct advantages. For example, frequency domain modelling is better suited for control systems, using features such as spectra of the signal. Considering this, we introduce, for the first time, a formal model called frequency automata for hybrid systems modelling and simulation, which are represented in combined time and frequency domains. We propose a sound translation from Hybrid Automata (HA) to Frequency Automata (FA). We also develop a numerical simulator for FA and compare it with the performance of HA. Our approach provides precise level crossing detection and efficient simulation of hybrid systems. We provide empirical results comparing simulation of HA via its translation to FA and its simulation via Matlab Simulink/Stateflow. The results show clear superiority of the proposed technique with the execution times of the proposed technique 118x to 1129x faster compared to Simulink/Stateflow. Moreover, we also observe that the proposed technique is able to detect level crossing with complex guards (including equality), which Simulink/Stateflow fail.

Problem

• Introducing frequency automata for hybrid systems modeling in combined time and frequency domains
• Proposing a sound translation from Hybrid Automata to Frequency Automata
• Developing a faster and more precise simulator for hybrid systems

Innovation

• Introduces frequency automata for hybrid systems
• Proposes translation from Hybrid to Frequency Automata
• Develops efficient numerical simulator for FA