Prescribed-Time Semi-Global Control for a Class of Nonlinear Uncertain Systems by Linear Time-Varying Feedback.
IEEE Transactions on Cybernetics
|March 3, 2025
Summary
This study presents a new control method for uncertain time-varying systems, achieving precise control within a set time using linear feedback. The approach handles complex uncertainties and is validated in mechatronics simulations.
Area of Science:
- Control Theory
- System Dynamics
- Nonlinear Systems
Background:
- Controlling time-varying uncertain systems presents significant challenges.
- Existing methods often struggle with nonlinear uncertainties and achieving finite-time convergence.
- Semi-global control is crucial for practical applications requiring predictable performance.
Purpose of the Study:
- To develop a prescribed-time semi-global control strategy for time-varying uncertain systems.
- To address both matched and unmatched nonlinear uncertainties.
- To design both state feedback and observer-based output feedback controllers.
Main Methods:
- Utilizing linear time-varying feedback for control.
- Categorizing nonlinear uncertainties into matched (time-dependent) and unmatched (state- and time-dependent) types.
- Employing parametric Lyapunov equations and solving scalar differential equations for time-varying gains.
- Implementing a separation principle for observer and state feedback design.
Main Results:
- Successfully designed a prescribed-time semi-global controller for the specified system class.
- Demonstrated the effectiveness of the observer-based output feedback approach.
- Validated the control scheme through simulations on a complex mechatronics system.
Conclusions:
- The proposed linear time-varying feedback control effectively achieves prescribed-time semi-global stability for uncertain systems.
- The separation principle simplifies the design of observer-based output feedback controllers.
- The method shows practical applicability in complex mechatronic systems.
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