Robust Cooperative Optimal Sliding-Mode Control for High-Order Nonlinear Systems: Directed Topologies

Area of Science:

• Control Theory
• Robotics
• Artificial Intelligence

Background:

• Nonlinear multiagent systems (MASs) are susceptible to external disturbances and internal modeling uncertainties.
• Existing control methods often require specific network topologies and struggle with robustness.

Purpose of the Study:

• To develop a robust cooperative optimal control strategy for nonlinear MASs.
• To address external disturbances and modeling uncertainties in high-order nonlinear MASs.
• To design a control protocol that is less restrictive regarding system topology.

Main Methods:

• Utilized the super-twisting algorithm for a continuous sliding-mode control protocol.
• Employed the Takagi-Sugeno fuzzy approach to model the sliding-mode dynamics.
• Designed a nominal control protocol for robust optimization of the cost function.
• Developed a protocol applicable to directed network topologies, removing common assumptions.

Main Results:

• Demonstrated a robust cooperative optimal control protocol for nonlinear MASs.
• Successfully handled external disturbances and modeling uncertainties.
• The protocol accommodates directed topologies, offering greater flexibility.
• Effectiveness and improved performance were validated through three numerical examples.

Conclusions:

• The presented super-twisting based sliding-mode control protocol offers robust cooperative optimal control for nonlinear MASs.
• The Takagi-Sugeno fuzzy modeling approach enhances the system's ability to handle uncertainties.
• The protocol's applicability to directed topologies signifies a significant advancement in MAS control.
• Numerical simulations confirm the protocol's effectiveness and superior performance compared to existing methods.