Data-Driven Discovery of Block-Oriented Nonlinear Models Using Sparse Null-Subspace Methods.

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• Computational Science

Background:

• Nonlinear system identification is crucial for modeling complex dynamic behaviors.
• Existing methods often face challenges with computational complexity and accuracy.
• Sparse recovery offers a promising approach for efficient model discovery.

Purpose of the Study:

• To develop an efficient and accurate algorithm for nonlinear system identification.
• To formulate the identification problem as a sparse recovery task.
• To enhance computational efficiency by reducing model complexity.

Main Methods:

• Formulating nonlinear system identification as a sparse recovery problem.
• Utilizing an augmented Lagrangian function to relax non-convex optimization.
• Applying an alternating direction method with regularization for solving the sparse recovery problem.

Main Results:

• A novel algorithm for nonlinear system identification is proposed.
• Theoretical analysis guarantees the convergence of the algorithm.
• The method effectively removes redundant terms, significantly improving computational efficiency.
• Numerical simulations demonstrate the algorithm's effectiveness and superiority over existing methods.

Conclusions:

• The developed algorithm provides an efficient and accurate solution for nonlinear system identification.
• The sparse recovery formulation simplifies model discovery and reduces computational load.
• The proposed method holds significant potential for applications in various scientific and engineering domains.