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Adaptive estimation for nonlinear systems using reproducing kernel Hilbert spaces
- Source :
- Advances in Computational Mathematics. 45:869-896
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. This paper 1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, 2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and 3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis.<br />Comment: 24 pages, Submitted to CMAME
- Subjects :
- Applied Mathematics
Mathematical analysis
Hilbert space
Systems and Control (eess.SY)
010103 numerical & computational mathematics
Function (mathematics)
01 natural sciences
Exponential function
010101 applied mathematics
Computational Mathematics
symbols.namesake
Nonlinear system
Distributed parameter system
Kernel (statistics)
Convergence (routing)
FOS: Electrical engineering, electronic engineering, information engineering
68T05, 93C41, 93C15, 68T30, 93C40
symbols
Computer Science - Systems and Control
0101 mathematics
Reproducing kernel Hilbert space
Mathematics
Subjects
Details
- ISSN :
- 15729044 and 10197168
- Volume :
- 45
- Database :
- OpenAIRE
- Journal :
- Advances in Computational Mathematics
- Accession number :
- edsair.doi.dedup.....af6518f4d985c7d996fea9edcba686a5