Confidence set-membership state estimation for LPV systems with inexact scheduling variables

Area of Science:

• Control Systems Engineering
• Estimation Theory
• Uncertainty Quantification

Background:

• Linear Parameter Varying (LPV) systems are widely used to model complex dynamic systems.
• Estimating system states accurately in the presence of uncertainties is crucial for control and monitoring.
• Existing methods often struggle with simultaneous set-bounded and Gaussian uncertainties in inexact scheduling variable scenarios.

Purpose of the Study:

• To develop a confidence set-membership state estimator for polytopic LPV systems with inexact scheduling variables.
• To simultaneously account for set-bounded and Gaussian uncertainties in process disturbances and measurement noises.
• To achieve a state estimation with a specified confidence level and minimize the size of the confidence set.

Main Methods:

• Utilized a polytopic LPV uncertain enclosure model to characterize state uncertainties.
• Employed a worst-case strategy to determine set-bounded and Gaussian uncertainties.
• Adopted constrained zonotopes for accurate representation of set-bounded uncertainties.
• Minimized the confidence set size to derive optimal estimator gains.

Main Results:

• The proposed confidence set-membership state estimator effectively handles polytopic LPV systems with inexact scheduling variables.
• Simultaneous consideration of set-bounded and Gaussian uncertainties leads to robust state estimation.
• The use of constrained zonotopes improves the accuracy of uncertainty representation.
• Demonstrated effectiveness through a vehicle dynamics example.

Conclusions:

• The developed state estimator provides a reliable method for state estimation in uncertain LPV systems.
• The approach offers a practical solution for applications requiring guaranteed confidence levels in state estimates.
• The methodology is validated by its successful application to a real-world engineering problem.