Bayesian Input Design for Linear Dynamical Model Discrimination

Area of Science:

• Control Systems Engineering
• Statistical Signal Processing
• Information Theory

Background:

• Model discrimination is crucial for understanding complex systems.
• Traditional methods often rely on predefined or suboptimal input signals.
• Optimizing input signals can significantly enhance discrimination performance.

Purpose of the Study:

• To develop a Bayesian framework for designing optimal input signals for linear dynamical model discrimination.
• To maximize the mutual information between model parameters and outputs under signal energy constraints.
• To compare the proposed Bayesian design with existing methods.

Main Methods:

• Formulating model discrimination as a parameter estimation problem.
• Utilizing a lower bound of mutual information as the utility function.
• Maximizing the utility function under a signal energy constraint.
• Analyzing small and large energy limits, involving eigenvector solutions and signal properties.

Main Results:

• The optimal signal in the small energy limit is related to the eigenvector of a Hermitian matrix.
• High energy signals can achieve maximum information transfer if model impulse responses differ.
• The proposed Bayesian signal design significantly reduces error probability compared to step or square signals.
• Bayesian design demonstrated superiority over classical average D-optimal design in an illustrative example.

Conclusions:

• The proposed Bayesian input signal design is effective for linear dynamical model discrimination.
• This approach offers improved performance and reduced error probability.
• The method shows potential for extension to nonlinear and non-Gaussian models.