Event-Triggered and Self-Triggered L_∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks

Area of Science:

• Control Systems Engineering
• Stochastic Systems Analysis
• Cybersecurity in Control

Background:

• Markov jump stochastic nonlinear systems are susceptible to denial-of-service (DoS) attacks, which disrupt network communication and can destabilize system performance.
• Existing control strategies often struggle with practical implementation due to reliance on mathematical expectations or susceptibility to Zeno behavior.

Purpose of the Study:

• To develop robust event-triggered and self-triggered L∞ control methods for Markov jump stochastic nonlinear systems under DoS attacks.
• To propose a practical self-triggering scheme (STS) that avoids mathematical expectations and Zeno behavior.
• To ensure system stability (mean-square asymptotical and almost sure exponential) despite network attacks and disturbances.

Main Methods:

• A switched model is developed to represent the impact of DoS attacks, incorporating unstable subsystems.
• The multiple Lyapunov function method is employed to derive sufficient conditions for L∞ performance.
• A novel self-triggering scheme (STS) is designed, featuring a positive lower bound to prevent Zeno behavior and exponent parameters to reduce triggering frequency.

Main Results:

• Sufficient conditions are established for preserving L∞ performance under DoS attacks using the event-triggering scheme (ETS).
• The proposed STS is shown to be implementable without mathematical expectation and effectively avoids Zeno behavior.
• The study demonstrates mean-square asymptotical stability and almost sure exponential stability under STS in the absence of exogenous disturbances.

Conclusions:

• The developed event-triggered and self-triggered control strategies effectively address L∞ control problems in Markov jump stochastic nonlinear systems under DoS attacks.
• The proposed STS offers a practical and efficient approach for real-world implementations, enhancing system robustness and stability.
• The findings are validated through two illustrative examples, confirming the efficacy of the proposed control methodologies.