Learning complexity dimensions for a continuous-time control system

Pirkko Kuusela; Daniel Ocone; Eduardo D. Sontag

doi:10.1137/S0363012901384302

Learning complexity dimensions for a continuous-time control system

Pirkko Kuusela, Daniel Ocone, Eduardo D. Sontag

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that inputs are generated randomly from a known class consisting of linear combinations of k sinusoidals. The output of the system is classified at some single instant of time. The main result establishes that the number of samples needed for identification with small error and high probability, independently from the distribution of inputs, scales polynomially with n, the system dimension, and logarithmically with k.

Original language	English (US)
Pages (from-to)	872-898
Number of pages	27
Journal	SIAM Journal on Control and Optimization
Volume	43
Issue number	3
DOIs	https://doi.org/10.1137/S0363012901384302
State	Published - 2005

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

Keywords

Learning theory
Linear systems identification
VC dimension

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10.1137/S0363012901384302

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AB - This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that inputs are generated randomly from a known class consisting of linear combinations of k sinusoidals. The output of the system is classified at some single instant of time. The main result establishes that the number of samples needed for identification with small error and high probability, independently from the distribution of inputs, scales polynomially with n, the system dimension, and logarithmically with k.

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KW - VC dimension

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Learning complexity dimensions for a continuous-time control system

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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