Sample Complexity for Evaluating the Robust Linear Observers Performance under Coprime Factors Uncertainty
| Autor: | Zhang, Yifei, Ukil, Sourav Kumar, Sperila, Andrei, Sabau, Serban |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback gain. We build on the results from Ding et al. (1994) to bridge the gap between the parameterization of all state-estimators and the celebrated Youla parameterization. Refitting the expression of the relevant closed loop allows for the optimal linear observer problem given a fixed state feedback gain to be recast as a convex problem in the Youla parameter. The robust synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant, such that a min-max optimization problem is formulated for the robust H2 controller via an observer approach. The closed-loop identification scheme follows Zhang et al. (2021), where the nominal model of the true plant is identified by constructing a Hankel-like matrix from a single time-series of noisy, finite length input-output data by using the ordinary least squares algorithm from Sarkar et al. (2020). Finally, a H-infinity bound on the estimated model error is provided, as the robust synthesis procedure requires bounded additive uncertainty on the coprime factors of the model. Comment: 23 pages. 2 Figures |
| Databáze: | arXiv |
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