Sliding Mode Control for Discrete-Time Systems With Markovian Packet Dropouts

Area of Science:

• Control Systems Engineering
• Networked Systems
• Stochastic Processes

Background:

• Networked control systems (NCS) are susceptible to packet dropouts, which can degrade performance and stability.
• Packet losses in NCS often exhibit temporal correlation, necessitating advanced modeling techniques.
• Sliding mode control (SMC) offers robustness but requires adaptation for packet loss scenarios.

Purpose of the Study:

• To design a robust sliding mode controller for NCS with successive Markovian packet dropouts.
• To develop an update scheme for controller state estimation under packet loss.
• To ensure system stability and convergence to the sliding surface despite data loss.

Main Methods:

• Utilizing the Gilbert-Elliott channel model to capture temporal correlations in packet losses.
• Implementing an update scheme for assumed available states in the SMC law.
• Applying discrete-time Markov jump linear system techniques.
• Introducing Lyapunov functions dependent on packet loss indicators.

Main Results:

• The designed sliding mode controller drives system states into the integral sliding surface neighborhood in a mean-square sense.
• Lyapunov inequalities are derived to guarantee controller performance.
• The system is shown to remain within the sliding surface neighborhood after convergence.
• Simulated case studies validate the effectiveness of the proposed control law.

Conclusions:

• The proposed sliding mode controller effectively manages packet dropouts in NCS.
• The methodology ensures system stability and convergence in the presence of correlated packet losses.
• This approach provides a robust solution for NCS operating over unreliable communication channels.