An Approximate Bayesian Approach to Optimal Input Signal Design for System Identification.

Area of Science:

• Control Systems Engineering
• Statistical Inference
• Information Theory

Background:

• Classical system identification relies on Fisher information, which is limited by local approximations and struggles with model uncertainty and non-linearity.
• Designing informative input signals is crucial for accurate system identification, but traditional methods have limitations.

Purpose of the Study:

• To develop a robust Bayesian approach for designing informative input signals for system identification.
• To address the computational challenges associated with maximizing mutual information (MI) for signal design.
• To improve system identification accuracy in the presence of model uncertainty and non-linearity.

Main Methods:

• A Bayesian framework is proposed, utilizing mutual information (MI) between observations and parameters as the objective function.
• A tractable lower bound of MI is maximized to overcome computational intractability.
• An efficient algorithm is developed to reduce the computational complexity of inverting large covariance matrices, enabling application to long experimental data.

Main Results:

• The proposed Bayesian method, based on MI, is shown to be superior to the average D-optimal design and other semi-Bayesian approaches.
• The developed algorithm significantly reduces computational load, making the Bayesian approach feasible for long-term system identification.
• The method effectively designs input signals that maximize information gain for identifying quasi-linear stochastic dynamical systems.

Conclusions:

• The Bayesian approach using a lower bound of mutual information offers a powerful and computationally feasible method for designing informative input signals.
• This technique enhances the accuracy of system identification, particularly in complex scenarios with model uncertainty and non-linearity.
• The method's effectiveness is demonstrated across various applications, including atomic sensor models, highlighting its broad applicability and impact.