Exact Recovery Guarantees for Parameterized Nonlinear System Identification Problem under Adversarial Attacks
Keywords: System identification, robust control, exact recovery
Abstract: In this work, we study the system identification problem for parameterized nonlinear systems using basis functions under adversarial attacks. Motivated by the LASSO-type estimators, we analyze the exact recovery property of a nonsmooth estimator, which is generated by solving an embedded $\ell_1$-loss minimization problem. First, we derive necessary and sufficient conditions for the well-specifiedness of the estimator and the uniqueness of global solutions to the underlying optimization problem. Next, we provide exact recovery guarantees for the estimator under two different scenarios of boundedness and Lipschitz continuity of the basis functions. The non-asymptotic exact recovery is guaranteed with high probability, even when there are more severely corrupted data than clean data. Finally, we numerically illustrate the validity of our theory. This is the first study on the sample complexity analysis of a nonsmooth estimator for the nonlinear system identification problem.
Supplementary Material: pdf
Primary Area: learning on time series and dynamical systems
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Submission Number: 591
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