An innovative modulating functions method for pseudo-state estimation of fractional order systems

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Dynamical Systems Theory

Background:

• Fractional order systems are increasingly used in modeling complex phenomena.
• Estimating system states from discrete, noisy measurements presents significant challenges.
• Existing observers for fractional systems may lack guaranteed convergence speed or robustness.

Purpose of the Study:

• To develop a novel method for estimating the pseudo-state of fractional order systems.
• To achieve non-asymptotic, finite-time estimation robust to noise.
• To outperform existing fractional order observers in terms of speed and robustness.

Main Methods:

• Application of the modulating functions method to the Brunovsky observable canonical form.
• Derivation of an algebraic integral formula for the initial pseudo-state.
• Analysis of modulating function properties and discrete noise error bounds.
• Comparison with fractional order Luenberger-like and H∞-like observers.

Main Results:

• The proposed method provides non-asymptotic, finite-time pseudo-state estimation.
• Demonstrated robustness against corrupting noises.
• Achieved superior performance over existing fractional order observers in numerical examples.
• Error analysis provided for discrete noise cases to enhance accuracy.

Conclusions:

• The modulating functions method is effective for pseudo-state estimation in fractional order systems.
• The method offers a robust and efficient alternative to traditional observers.
• Guaranteed convergence speed and robustness are key advantages for practical applications.