Abstract In the presence of unmodelled dynamics and uncertainties with no a priori constant bounds, conventional robust adaptation strategies for switched systems cannot allow the control gains of inactive subsystems to remain constant during inactive intervals: vanishing gains are typically required in order to prove bounded stability. As a consequence, these strategies, known in literature as leakage-based adaptive methods, might introduce poor transients at each switching instant. Leakage-based adaptive control becomes even more problematic in the switched nonlinear case, where non-conservative state-dependent upper bounds for uncertainties and unmodelled dynamics are required. This work shows that, for a class of switched Euler–Lagrange systems, such difficulties can be mitigated: a novel leakage-based stable mechanism is introduced which allows the gains of inactive subsystems to remain constant. At the same time, unmodelled dynamics and uncertainties with no a priori bounds can be handled by a quadratic state-dependent upper bound structure that reduces conservativeness as compared to state-of-the-art structures. The proposed design is validated analytically and its performance is studied in simulation with a pick-and-place robotic manipulator example.

中文翻译：

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关于切换系统鲁棒适应的消失增益：一类欧拉-拉格朗日动力学的基于泄漏的新结果

摘要 在存在没有先验常数界限的未建模动力学和不确定性的情况下，切换系统的传统鲁棒适应策略不能允许非活动子系统的控制增益在非活动间隔期间保持恒定：通常需要消失增益以证明有界稳定性。因此，这些在文献中称为基于泄漏的自适应方法的策略可能会在每个开关瞬间引入不良瞬态。在切换非线性情况下，基于泄漏的自适应控制变得更加成问题，在这种情况下，不确定性和未建模动态需要非保守的状态相关上限。这项工作表明，对于一类切换欧拉-拉格朗日系统，可以减轻这些困难：引入了一种新颖的基于泄漏的稳定机制，允许非活动子系统的增益保持恒定。同时，没有先验界限的未建模动力学和不确定性可以通过二次状态相关的上限结构来处理，与最先进的结构相比，该结构降低了保守性。所提出的设计经过分析验证，并通过拾取和放置机器人机械手示例在仿真中研究其性能。