Asynchronous Control of Networked Markov Jump Linear Systems Under DoS Attacks

Area of Science:

• Control Theory
• Systems Engineering
• Networked Systems

Background:

• Networked Markov jump linear systems (MJLSs) are susceptible to denial-of-service (DoS) attacks, compromising stability and performance.
• Real-world scenarios often involve imperfect mode detection and uncertain probability information, complicating control design.

Purpose of the Study:

• To investigate the asynchronous H∞ control problem for discrete-time MJLSs under aperiodic DoS attacks.
• To address the challenges of imperfect mode detection and imperfectly known probabilities in MJLS control.
• To develop a robust asynchronous control strategy for networked systems.

Main Methods:

• Utilizing a Hidden Markov Model (HMM) to characterize mismatched detected/system modes.
• Employing a general description for imperfectly known transition and observation probabilities (T/OPs).
• Developing an HMM-based asynchronous control law using iterative piecewise Lyapunov functionals and a probability decoupling principle.

Main Results:

• Establishing sufficient conditions for stochastic stability and H∞ performance of the networked MJLS.
• Demonstrating that the asynchronous control law can be designed using an LMI-based convex optimization algorithm.
• Validating the effectiveness of the proposed method through a single-link robotic arm example.

Conclusions:

• The proposed HMM-based asynchronous control law effectively addresses DoS attacks and uncertainties in MJLSs.
• The developed conditions ensure robust stability and H∞ performance for networked systems.
• The LMI-based design approach provides a practical method for implementing the asynchronous control strategy.