Algorithm

Control (management)

Engineering

Pure mathematics

Biology

Identification (biology)

Discrete mathematics

Support vector machine

Control engineering

Applied mathematics

Variable kernel density estimation

Data mining

Polynomial kernel

Computer science

Botany

Mathematical optimization

Kernel smoother

Kernel embedding of distributions

Radial basis function kernel

Kernel (algebra)

Kernel principal component analysis

Mathematics

Impulse response

Kernel method

System identification

Mathematical analysis

Artificial intelligence

Measure (data warehouse)

Control theory (sociology)

Machine learning

Automatica

There are two key issues for the kernel-based regularization method: one is how to design a suitable kernel to embed in the kernel the prior knowledge of the LTI system to be identified, and the other one is how to tune the kernel such that the resulting regularized impulse response estimator can achieve a good bias–variance tradeoff. In this paper, we focus on the issue of kernel design. Depending on the type of the prior knowledge, we propose two methods to design kernels: one is from a machine learning perspective and the other one is from a system theory perspective. We also provide analysis results for both methods, which not only enhances our understanding for the existing kernels but also directs the design of new kernels.

On kernel design for regularized LTI system identification