First- and Second-Order Sliding Mode Control Design for Networked 2-D Systems Under Round-Robin Protocol

Area of Science:

• Control Systems Engineering
• Systems Theory
• Robotics

Background:

• Uncertain two-dimensional (2-D) systems described by Roesser models are susceptible to bounded disturbances.
• Limited communication bandwidth necessitates efficient control strategies, especially in networked actuator systems.

Purpose of the Study:

• To develop sliding mode control (SMC) schemes for uncertain 2-D systems with reduced communication usage.
• To design robust control strategies that accommodate periodic scheduling and zero-order hold (ZOH) effects.
• To enhance robustness against bounded disturbances using second-order SMC.

Main Methods:

• A novel 2-D common sliding function and token-dependent SMC schemes (first- and second-order) were developed.
• A 2-D round-robin protocol was designed to manage actuator access, coupled with zero-order holders (ZOHs).
• Token-dependent Lyapunov-like functions were used to establish system stability conditions.

Main Results:

• Sufficient conditions were derived to guarantee the ultimate boundedness of system states and the sliding function.
• Two optimization algorithms were formulated to determine optimal gain matrices for enhanced control performance.
• Comparative examples demonstrated the effectiveness of the proposed first- and second-order 2-D SMC schemes under round-robin scheduling.

Conclusions:

• The proposed token-dependent 2-D SMC schemes effectively manage communication constraints and ensure system stability.
• The second-order SMC scheme offers improved robustness against bounded disturbances.
• The developed methods provide a viable approach for controlling uncertain 2-D systems in resource-constrained environments.