Detectability of Discrete Event Systems with Dynamic Event Observation.

Area of Science:

• Control Systems Engineering
• Computer Science
• Information Theory

Background:

• Traditional discrete event systems analysis assumes static event observability, where events are always observable once detected.
• Practical systems, like sensor networks, often exhibit dynamic event observation, where event detectability varies with system state.
• This limitation hinders accurate state determination in complex, real-world systems.

Purpose of the Study:

• To generalize the concept of event observation from static to dynamic.
• To introduce and define four novel types of detectability for discrete event systems under dynamic observation.
• To develop efficient methods for analyzing system detectability with dynamic event observation.

Main Methods:

• Formalizing dynamic event observation and its implications for system state determination.
• Defining four distinct classes of detectability tailored to dynamic observation scenarios.
• Developing an observer with exponential complexity for checking detectabilities.
• Proposing a polynomial-complexity detector for efficiently verifying strong detectabilities.

Main Results:

• The study successfully generalizes static event observation to dynamic event observation for discrete event systems.
• Four new types of detectability are formally defined, expanding the analytical framework.
• Efficient algorithms are presented, including a polynomial-time detector for strong detectabilities, mitigating computational complexity.
• Methods for active observation are explored, focusing on minimal policies to maintain detectability.

Conclusions:

• Dynamic event observation is crucial for accurately analyzing modern discrete event systems.
• The proposed detectability framework and efficient algorithms provide practical tools for system analysis and design.
• Findings enable the development of more robust and reliable systems, particularly in sensor networks and similar applications.