Sliding Mode Control for Uncertain 2-D FMII Systems Under Stochastic Scheduling

Area of Science:

• Control Systems Engineering
• Systems Theory
• Stochastic Processes

Background:

• Two-dimensional (2-D) systems are crucial in various applications, but their control is complex.
• Stochastic communication protocols introduce challenges in maintaining system stability and performance.
• The Fornasini-Marchesini (FMII) model is a common framework for representing 2-D systems.

Purpose of the Study:

• To develop a robust sliding mode control (SMC) strategy for 2-D FMII systems with Markovian-switched communication.
• To design a compensator for unavailable controller nodes under stochastic scheduling.
• To ensure the reachability of the sliding surface and the uniform ultimate boundedness of the closed-loop system.

Main Methods:

• A novel sliding function is constructed, incorporating system states from present and previous positions.
• A scheduling signal-dependent SMC law is designed to handle stochastic communication.
• Token- and parameter-dependent Lyapunov functionals are utilized for stability analysis.
• A differential evolution algorithm is employed to optimize the control parameters and minimize the convergence bound.

Main Results:

• Sufficient conditions for the reachability of the sliding surface and mean-square boundedness of the closed-loop system are derived.
• The proposed SMC law effectively manages the stochastic communication protocol.
• The optimization approach successfully minimizes the system's convergent bound.

Conclusions:

• The developed control scheme provides a stable and efficient solution for controlling 2-D FMII systems with stochastic communication.
• The integration of SMC with stochastic scheduling and optimization offers a promising direction for advanced control applications.
• Simulation results validate the effectiveness of the proposed control strategy.