Sufficient Conditions for Parameter Convergence Over Embedded Manifolds Using Kernel Techniques

doi:10.1109/TAC.2022.3148716

Sufficient Conditions for Parameter Convergence Over Embedded Manifolds Using Kernel Techniques

2023-02-01

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DOI：10.1109/TAC.2022.3148716

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The persistence of excitation (PE) condition is sufficient to ensure parameter convergence in adaptive estimation problems. Recent results on adaptive estimation in reproducing kernel Hilbert spaces (RKHS) introduce PE conditions for RKHS. This article presents sufficient conditions for PE for the particular class of uniformly embedded RKHS defined over smooth Riemannian manifolds. This article also studies the implications of the sufficient condition in the case when the RKHS is finite or infinite-dimensional. When the RKHS is finite-dimensional, the sufficient condition implies parameter convergence as in the conventional analysis. On the other hand, when the RKHS is infinite-dimensional, the same condition implies that the function estimate error is ultimately bounded by a constant that depends on the approximation error in the infinite-dimensional RKHS. We illustrate the effectiveness of the sufficient condition in a practical example.

Keywords:

Sufficient conditions

Kernel

Convergence

Adaptive estimation

Manifolds

Hilbert space

Space vehicles

parameter convergence

persistence of excitation (PE)

reproducing kernel Hilbert spaces (RKHS)

Sufficient Conditions for Parameter Convergence Over Embedded Manifolds Using Kernel Techniques

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