SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1370-1392, January 2021.
New combined finite-differential versions of nonsmooth speed-gradient (SG) algorithms are proposed and examined. Sufficient conditions for stability and robustness of the closed loop system are established. In addition, new passivity definitions suitable for the nonsmooth setting are proposed and passivity of the system with nonsmooth SG algorithms is examined. The proposed finite-differential algorithms possess enhanced dynamic properties and provide extra flexibility for control system design. Particularly, they may operate under a broad uncertainty of plant parameters and disturbances, and they have improved convergence rate and robustness. An illustrative example of adaptive control of Duffing system demonstrates better performance of a combination of smooth and nonsmooth finite-differential SG-algorithms in comparison with performance of the smooth or nonsmooth algorithm.

中文翻译：

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有限差分非平稳速度梯度控制：稳定性，无源性，鲁棒性

SIAM控制与优化杂志，第59卷，第2期，第1370-1392页，2021年1月。
提出并研究了非平稳速度梯度（SG）算法的新组合有限差分版本。建立了闭环系统的稳定性和鲁棒性的充分条件。此外，提出了适用于非平滑设置的新的无源性定义，并研究了具有非平滑SG算法的系统的无源性。所提出的有限差分算法具有增强的动态特性，并为控制系统设计提供了额外的灵活性。特别地，它们可以在植物参数和干扰的广泛不确定性下运行，并且它们具有提高的收敛速度和鲁棒性。