1. Informative input design for Kernel-Based system identification
- Author
-
Toshiharu Sugie and Yusuke Fujimoto
- Subjects
0209 industrial biotechnology ,Computer science ,Bayesian probability ,02 engineering and technology ,computer.software_genre ,Measure (mathematics) ,Kernel (linear algebra) ,020901 industrial engineering & automation ,0202 electrical engineering, electronic engineering, information engineering ,Information theory and measure theory ,Entropy (information theory) ,Electrical and Electronic Engineering ,Mathematics ,Sequence ,business.industry ,Conditional mutual information ,020208 electrical & electronic engineering ,System identification ,Pattern recognition ,Mutual information ,Information diagram ,Control and Systems Engineering ,Kernel (statistics) ,A priori and a posteriori ,Algorithm design ,Artificial intelligence ,Data mining ,business ,computer ,Algorithm ,Energy (signal processing) - Abstract
This paper discusses the design of input sequence for Kernel-Based system identification. From the Bayesian point of view, the kernel reflects a priori information about the target system, which implies that the information obtained from I/O data differs over kernels. This paper focuses on finding an input sequence which maximizes the information obtained through an observation according to the kernel which is given in advance. As an appropriate measure of such information, the mutual information is adopted. For the given kernel, a concrete procedure is proposed to find the input sequence maximizing the mutual information subject to the input energy constraints. Numerical examples are given to illustrate the effectiveness of the proposed input design. Furthermore, it is shown analytically that the impulse input is optimal for a special class of kernels.
- Published
- 2018