Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework.

Area of Science:

• Systems Engineering
• Control Theory
• Signal Processing

Background:

• Linear systems with quadratic output (LQO) are prevalent in various engineering disciplines.
• Accurate modeling of LQO systems is crucial for analysis and controller design.
• Existing modeling techniques may not fully capture the complexities of LQO dynamics.

Purpose of the Study:

• To develop a novel data-driven modeling framework for linear systems with quadratic output (LQO).
• To extend the Adaptive Antoulas-Anderson (AAA) algorithm for LQO system identification.
• To establish theoretical foundations for LQO system representation and interpolation.

Main Methods:

• Extension of the Adaptive Antoulas-Anderson (AAA) algorithm to handle LQO systems.
• Establishment of joint barycentric representations for LQO transfer functions.
• Development of an interpolation theory tailored for LQO system identification.
• Integration of transfer function interpolation with least-squares minimization on sampled data.

Main Results:

• Introduction of the AAA-LQO algorithm for data-driven LQO model construction.
• Demonstration of reliable LQO model identification through interpolation and least-squares fitting.
• Validation of the AAA-LQO algorithm's efficiency via two numerical test cases.

Conclusions:

• The proposed AAA-LQO algorithm provides an effective data-driven approach for modeling linear systems with quadratic output.
• The method successfully combines interpolation and least-squares techniques for robust system identification.
• The framework offers a reliable tool for analyzing and controlling complex LQO systems.