Robust observer design for LPV systems using Kronecker sum and direct searching.

Area of Science:

• Control Systems Engineering
• Nonlinear System Analysis
• Robust Control Theory

Background:

• Linear parameter varying (LPV) systems present challenges due to parameter uncertainties.
• Designing robust observers for LPV systems is crucial for accurate state estimation.
• Existing methods may struggle with the inherent uncertainties in LPV system dynamics.

Purpose of the Study:

• To develop a robust Luenberger observer for uncertain LPV systems.
• To propose an algorithm for systematically designing observer gains.
• To ensure reliable estimation of system states under parameter variations.

Main Methods:

• Utilizes direct searching, Kronecker sum, and small gain theorem.
• Employs an algorithm to analyze and prune the observer design space.
• Checks for singularity of the Kronecker sum matrix of the estimation error.

Main Results:

• Successfully identified and excluded undesirable regions of the observer design space.
• Demonstrated the feasibility of the remaining design space for selecting observer gains.
• Validated the observer's performance using numerical examples and an electric ground vehicle (EGV) system.

Conclusions:

• The proposed method provides a robust approach for Luenberger observer design in uncertain LPV systems.
• The algorithm effectively handles design space limitations and ensures suitable observer gain selection.
• The approach is validated for practical applications, such as estimating sideslip angle and yaw rate in EGVs.