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Notion of Opacity Considering Security Levels for Piecewise Affine Systems.
Taiga Matsumae1, Koichi Kobayashi1, Yuh Yamashita1
1Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan.
Sensors (Basel, Switzerland)
|June 26, 2026
Summary
This study introduces a new security measure for cyber-physical systems (CPSs) by extending the concept of opacity to discrete-time piecewise affine (DT-PWA) systems. It proposes a method to quantify security levels, moving beyond binary classifications for enhanced system protection.
Area of Science:
- Control Systems Engineering
- Cybersecurity
- Hybrid Systems
Background:
- Cyber-physical systems (CPSs) are vulnerable to cyber attacks due to their interconnected nature.
- Opacity is a crucial security property for preventing information leakage in discrete-event systems.
- Existing opacity analysis is often binary and insufficient for systems with continuous dynamics.
Purpose of the Study:
- To extend the concept of opacity to discrete-time piecewise affine (DT-PWA) systems, a key class of hybrid systems modeling CPSs.
- To introduce a notion of opacity that quantifies security levels, addressing the limitations of binary characterization.
- To develop a verification method for assessing the degree of security in DT-PWA systems.
Main Methods:
- Formulation of opacity for DT-PWA systems.
- Derivation of a necessary and sufficient condition for opacity in these systems.
- Development of a verification method utilizing polytope computations.
Main Results:
- A novel, quantifiable notion of opacity for DT-PWA systems is proposed.
- A condition for opacity is derived, enabling precise security level assessment.
- A computational method for verifying opacity is presented and demonstrated.
Conclusions:
- The proposed method provides a more nuanced evaluation of security in CPSs compared to traditional binary opacity.
- The introduced security levels offer a practical way to manage and enhance the protection of sensitive information in DT-PWA systems.
- The numerical example confirms the effectiveness of the developed verification technique for assessing system opacity.
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