The content discusses the problem of efficient adaptive control for discrete-time nonlinear systems with matched uncertainty. The key highlights are:
The authors consider a discrete-time system with matched uncertainty, where the unknown dynamics can be parameterized by an unknown parameter vector and a known feature matrix.
They propose a novel recursive proximal learning (RPL) algorithm and analyze its performance in terms of asymptotic stability and regret. RPL is shown to achieve finite regret scaling with the time required to satisfy a weak persistence of excitation (PE) condition.
The authors also analyze the well-established recursive least squares with exponential forgetting (RLSFF) algorithm in this setting. RLSFF is shown to achieve finite regret under a stronger PE condition, with a similar bound to RPL.
The regret bounds for both RPL and RLSFF consist of three terms: a constant term, an exponentially decaying term, and a linear term in the PE time. The linear term arises from the non-expansive properties of the parameter estimates during the initial non-PE phase.
The authors demonstrate the performance of the proposed algorithms on a discrete-time model reference adaptive control (MRAC) numerical example, showcasing the superior tracking and regret performance of RPL compared to RLSFF and a command governor-based MRAC controller.
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by Aren Karapet... às arxiv.org 04-03-2024
https://arxiv.org/pdf/2404.02023.pdfPerguntas Mais Profundas