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Frequency-domain Gaussian Process Models for $H_\infty$ Uncertainties
- Publication Year :
- 2023
-
Abstract
- Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could be used for probabilistic robust control, allowing for robustly safe learning. We investigate sufficient conditions for a general complex-domain Gaussian process to have this property. For the special case of processes whose Hermitian covariance is stationary, we provide an explicit parameterization of the covariance structure in terms of a summable sequence of nonnegative numbers. We then establish how an $H_\infty$ Gaussian process can serve as a prior for Bayesian system identification and as a probabilistic uncertainty model for probabilistic robust control. In particular, we compute formulas for refining the uncertainty model by conditioning on frequency-domain data and for upper-bounding the probability that the realizations of the process satisfy a given integral quadratic constraint.<br />Comment: 20 pages, 2 figures. Submission to SICON. arXiv admin note: substantial text overlap with arXiv:2211.15923
- Subjects :
- Electrical Engineering and Systems Science - Systems and Control
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.10106
- Document Type :
- Working Paper