Robust multi-step interval observer via convex LMIs with applications to UAV and BMS

Area of Science:

• Control Systems Engineering
• Robust Control Theory
• State Estimation

Background:

• Accurate state estimation is critical for safety-critical systems but is challenged by uncertainties.
• Traditional point observers (e.g., Kalman, Luenberger) are often unreliable under disturbances and model errors.
• Interval observers (IOs) offer guaranteed robustness by providing bounded estimates, ensuring safety.

Purpose of the Study:

• To propose a robust multi-step interval observer (IO) for discrete-time systems.
• To enhance state estimation accuracy, disturbance rejection, and delay resilience using a predictive structure.
• To ensure computational efficiency and scalability for real-time applications.

Main Methods:

• A q-step predictive structure aggregates system dynamics over a selectable horizon.
• Convex linear matrix inequality (LMI) design is employed to compute observer gains.
• The method ensures non-negative error dynamics without complex transformations or iterative tuning.

Main Results:

• The proposed IO achieves significantly tighter interval bounds (±0.1% vs. ±2.5%) in benchmark applications.
• Demonstrated improved accuracy, faster convergence, and reduced computational load compared to existing methods.
• Validated effectiveness on a non-minimum phase UAV and a Lithium-ion battery management system (BMS).

Conclusions:

• The robust multi-step IO offers superior performance and reliability for state estimation under uncertainty.
• The LMI-based design ensures computational efficiency and scalability for real-time deployment.
• This framework presents promising advancements for interval observer design in aerospace, automotive, and energy sectors.