From Robust Control to Cyber-Resilience: A Comprehensive Overview of the Polytopic Framework for Safety-Critical...

Area of Science:

• Control Theory
• Systems Engineering
• Cybersecurity

Background:

• Complex systems exhibit nonlinear dynamics and uncertainties.
• Safety-critical cyber-physical systems face increasing cyber-attack threats.
• Ensuring resilience in these systems is a major challenge.

Purpose of the Study:

• To present the polytopic approach as a unifying paradigm beyond mere modeling.
• To explore its application in enhancing cyber-resilience for safety-critical systems.
• To bridge complex system dynamics, convex analysis, and control synthesis.

Main Methods:

• Reviewing and synthesizing recent developments in polytopic approaches.
• Focusing on applications in cyber-resilient estimation and control.
• Examining techniques for uncertainty structuring and decision-making.

Main Results:

• Polytopic representations serve as a methodological principle for managing uncertainty and nonlinear behavior.
• Extended polytopic methods address false-data injection attacks and enable simultaneous state/attack estimation.
• Developments include resilient observer-based control and event-triggered control under constraints.

Conclusions:

• The polytopic approach is a structured methodology linking representation, uncertainty management, and control synthesis.
• It evolves into a unifying paradigm for nonlinear dynamics, cyber-attacks, and network constraints.
• Enhances resilience, reliability, and operational safety of safety-critical cyber-physical systems.