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<p>The work presented concerns how to achieve suitable behavior with stability guarantees. Currently, the best way to fit a system’s response or to predict decisions is to use artificial neural networks as predictive models. However, the stability of the closed-loop system is not ensured. The main idea of this work is to use artificial neural networks to approximate a linear stable system. By using a wide domain of approximation, the initial controller is transformed into the desired one with stability constraints. To achieve this goal, a stable linear filter is synthesized by minimizing the <i>l</i><sup>2</sup> or <i>l</i><sup>∞</sup> norms using Linear Matrix Inequalities, without employing a Lyapunov matrix or a finite impulse response, thanks to the proposed algorithm. Thus, we can avoid the weaknesses of artificial neural networks in closed-loop systems by using Youla-Kucera parametrization, ensuring stability in the <i>l</i><sup>1</sup> space, learning from a previous stable linear filter.</p>

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Learning Control and Stability Strategies

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Mohamed Abbas Turki

摘要

The work presented concerns how to achieve suitable behavior with stability guarantees. Currently, the best way to fit a system’s response or to predict decisions is to use artificial neural networks as predictive models. However, the stability of the closed-loop system is not ensured. The main idea of this work is to use artificial neural networks to approximate a linear stable system. By using a wide domain of approximation, the initial controller is transformed into the desired one with stability constraints. To achieve this goal, a stable linear filter is synthesized by minimizing the l2 or l∞ norms using Linear Matrix Inequalities, without employing a Lyapunov matrix or a finite impulse response, thanks to the proposed algorithm. Thus, we can avoid the weaknesses of artificial neural networks in closed-loop systems by using Youla-Kucera parametrization, ensuring stability in the l1 space, learning from a previous stable linear filter.