Safe MPC-based disturbance rejection control for uncertain nonlinear systems with state constraints

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Robotics and Automation

Background:

• Uncertain nonlinear systems pose challenges for control due to modeling inaccuracies and external disturbances.
• Ensuring system safety under complex state constraints is critical in many applications.
• Existing control methods may struggle to simultaneously address uncertainty, safety, and performance.

Purpose of the Study:

• To develop a robust control strategy for uncertain nonlinear systems that guarantees safety and effective disturbance rejection.
• To improve system stability and reduce state deviations from the equilibrium point.
• To provide a framework that integrates state estimation, uncertainty compensation, and constrained control.

Main Methods:

• Design of an extended state observer (ESO) to estimate system states and total uncertainty.
• Real-time uncertainty compensation using ESO outputs.
• Implementation of a control barrier function (CBF)-based model predictive control (MPC) for the compensated system.
• Integration of safety constraints within the MPC framework using CBFs.

Main Results:

• The proposed control framework guarantees system safety and effective disturbance rejection.
• Significant enhancement in system stability compared to baseline CBF-MPC.
• Reduced root mean square (RMS) error of the system state from the equilibrium point.
• Validation through rigorous theoretical analysis and simulation experiments.

Conclusions:

• The developed safe MPC strategy effectively handles uncertain nonlinear systems with complex safety constraints.
• The proposed method offers superior performance in terms of stability and accuracy over existing approaches.
• This research provides a valuable tool for applications requiring reliable and safe control of uncertain dynamic systems.