Free Final Time Input Design Problem for Robust Entropy-Like System Parameter Estimation.

Area of Science:

• Control Systems Engineering
• System Identification
• Optimization Theory

Background:

• System identification relies on optimal input signals for accurate model estimation.
• Real-world experiments face constraints on input design and duration, impacting cost and efficiency.
• Robustness to outlying data is crucial for reliable system identification.

Purpose of the Study:

• To propose a novel method for designing free final time input signals for robust system identification.
• To investigate the economic trade-offs between input signal constraints and experiment duration.
• To enhance the robustness of system identification against outlying data.

Main Methods:

• Formulating the constrained optimal input design problem by minimizing a free final time scaling factor.
• Incorporating D-efficiency and input energy constraints into the optimization.
• Utilizing an Entropy-like estimator for the objective function to ensure robustness to outlying data.
• Comparing Least Squares and Entropy-Like estimators using ellipsoidal confidence regions.

Main Results:

• A novel method for free final time input signal design is presented.
• The method effectively balances input constraints and experiment duration for economic efficiency.
• The Entropy-like estimator demonstrates robustness to additive white noise in measurements.
• Numerical examples validate the applicability to general systems.

Conclusions:

• The proposed method offers an efficient approach to designing input signals for robust system identification.
• Economic considerations in experiment design can be effectively managed by optimizing input signals.
• The Entropy-like estimator provides a robust alternative for system parameter validation in noisy environments.