Reduced-size kernel models for nonlinear hybrid system identification.

Area of Science:

• Dynamical Systems Theory
• Machine Learning
• Nonlinear System Identification

Background:

• Hybrid dynamical systems exhibit multiple switching nonlinear behaviors.
• Identifying these systems requires learning from input-output data without prior group knowledge.
• Kernel methods are suitable for approximating arbitrary nonlinearities.

Purpose of the Study:

• To develop an efficient method for identifying nonlinear hybrid dynamical systems.
• To learn an ensemble of kernel submodels from a single dataset.
• To address computational efficiency for large datasets.

Main Methods:

• Proposed four preprocessing approaches inspired by least-squares support vector machines, feature selection, and kernel principal component regression.
• Focused on building sparse kernel submodels by fixing submodel sizes and limiting optimization variables.
• Employed a regression setting without prior data grouping.

Main Results:

• The proposed methods enable efficient and accurate simultaneous classification of data points and approximation of nonlinear behaviors.
• Numerical experiments validated the effectiveness of the developed approaches.
• The techniques successfully handle large datasets by limiting computational complexity.

Conclusions:

• The presented approach offers an effective solution for identifying complex nonlinear hybrid dynamical systems.
• The method provides a way to learn multiple nonlinear behaviors from data efficiently.
• This work contributes to advancing the field of system identification for complex dynamical systems.