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Optimal Adaptive Robust Control Based on Cooperative Game Theory for a Class of Fuzzy Underactuated Mechanical Systems
IEEE Transactions on Cybernetics ( IF 11.8 ) Pub Date : 2020-09-10 , DOI: 10.1109/tcyb.2020.3016003
Xiaolong Chen , Han Zhao , Hao Sun , Shengchao Zhen , Abdullah Al Mamun

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.

中文翻译:

一类模糊欠驱动机械系统基于合作博弈的最优自适应鲁棒控制

在为一类欠驱动机械系统 (UMS) 设计控制时,应考虑不确定性和规定的非完整跟踪轨迹。本文考虑的不确定性是时变有界的,不确定性的界是用模糊集理论来描述的,即模糊UMS。采用基于分析动力学的观点,其中规定的跟踪轨迹被视为伺服约束,可以是线性的、非线性的、完整的和非完整的。使用这种观点,找到了一种具有泄漏型自适应律的自适应鲁棒控制的新封闭形式解决方案,以保证确定性系统性能,包括一致有界和一致最终有界。为了找到设计控制的最佳双增益参数,提出了一种两人合作博弈,始终可以保证帕累托最优。通过对两轮倒立摆车辆的数值模拟显示了所提出控制的有效性。
更新日期:2020-09-10
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