arXiv AI By Shimin Wang, Martin Guay, Richard D. Braatz

Nonadaptive Learning in Robust Nonlinear Output Regulation

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This paper presents a nonadaptive approach to robust nonlinear output regulation for general nonlinear systems with high relative degree in an output‑feedback setting. The design combines an input‑driven filter, a generic internal model, and a recursive backstepping law, transforming the regulation problem into robust input‑to‑state stabilization of an augmented error system. Under standard exosystem assumptions and a minimum‑phase input‑to‑state stability condition, the authors prove global asymptotic regulation and provide explicit inequalities for selecting design gains, demonstrating the method on a benchmark Duffing system.

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arXiv Machine Learning
Aug 27

Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

The paper studies least squares parameter estimation for discrete‑time, unstable, closed‑loop nonlinear stochastic systems with linearly parametrised uncertainty and additive i.i.d. process noise. By perturbing the control policy with exploratory input and assuming a sub‑exponential input‑to‑state growth property, the authors derive non‑asymptotic bounds on the estimation error whenever the state trajectory remains in an informative region of the state space. When the entire state space is informative, the bounds hold with high probability for all time steps, and the authors illustrate the applicability of their results with examples that extend beyond existing work.

By Seth Siriya, Jingge Zhu, Dragan Ne\v{s}i\'c, Ye Pu