北京雁栖湖应用数学研究院

System identification is concerned with estimating models of dynamical systems based on observed input and output signals. Mathematically, system identification is an inverse problem and may suffer from numerical instability. The Russian researcher Tikhonov suggested in the 1940s a general way to curb the number of solutions for inverse problems which he called regularization. A simple regularization method applied to linear regression became known as ridge regression.

Around 2000 other ideas were put forward for achieving regularization. They had links to general function estimation with mathematical foundations in Reproducing Kernel Hilbert Spaces (RKHS) and kernel techniques.

In this course, we will provide a comprehensive overview of the development of system identification. Starting from the bias-variance trade-off, we will first discuss the traditional regularized linear system identification, and move on to the kernel-based approaches. Regularization in reproducing kernel Hilbert spaces will then be described in details. Finally, we will introduce modern methods for nonlinear system identification.