Assessing the resilience of stochastic dynamic systems under partial observability

Area of Science:

• Complex Systems Analysis
• System Resilience Engineering
• Probabilistic Modeling

Background:

• Resilience is crucial for complex systems, enabling them to maintain services despite disruptions.
• Existing formal definitions of resilience are limited in modeling real-world stochasticity and partial observability.
• Hidden Markov Models (HMMs) offer a probabilistic framework suitable for dynamic, uncertain environments.

Purpose of the Study:

• To adapt formal resilience definitions for constraint-based systems into a probabilistic framework using HMMs.
• To develop an efficient and exact algorithm for inference queries in probabilistic resilience checking.
• To analyze the computational complexity of probabilistic resilience and resistance checking.

Main Methods:

• Formal adaptation of constraint-based resilience definitions to a probabilistic HMM framework.
• Development and analysis of an exact algorithm for inference queries in the proposed framework.
• Evaluation of the algorithm's time complexity against state-of-the-art methods.
• Application and performance assessment in diverse scenarios: disaster management, macroeconomics, aerospace computing, and robotic swarms.

Main Results:

• A probabilistic framework for resilience analysis in complex systems, incorporating stochasticity and partial observability.
• An efficient and exact algorithm for property checking with linear time complexity relative to the time horizon.
• Demonstrated flexibility and performance of the approach across four distinct application domains.
• Insights into the complexity of probabilistic resilience and resistance checking.

Conclusions:

• The proposed probabilistic framework and algorithm provide a robust and efficient method for analyzing system resilience.
• The approach realistically models complex real-world systems and facilitates accurate property checking.
• The demonstrated applications highlight the broad applicability and practical value of the developed methodology.