Global Finite-Time Stabilization for Uncertain Systems With Unknown Measurement Sensitivity

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Systems Theory

Background:

• Existing control strategies for nonlinear systems often rely on precise output measurements.
• Limited sensor accuracy introduces measurement errors, challenging observer-based control design.
• Finite-time stabilization is crucial for systems requiring rapid convergence.

Purpose of the Study:

• To develop a finite-time output feedback stabilization scheme for uncertain nonlinear systems.
• To address the challenge of unknown measurement sensitivity and sensor errors.
• To design a novel observer that does not require knowledge of system nonlinearities.

Main Methods:

• A new finite-time convergent observer is proposed, avoiding explicit use of nonlinearity information.
• The observer design combines homogeneous domination and power integrator techniques.
• An output feedback controller using multiple nested sign functions is developed.

Main Results:

• The proposed observer achieves finite-time convergence despite unknown measurement sensitivity.
• The integrated output feedback controller guarantees global finite-time stabilization.
• The effectiveness of the stabilization scheme is demonstrated through a numerical example.

Conclusions:

• The developed method provides a robust solution for finite-time stabilization of uncertain nonlinear systems with measurement errors.
• This approach overcomes limitations of existing methods that require precise output measurements.
• The novel observer design offers a significant advancement in handling sensor inaccuracies in control systems.