The optimal design problem of adaptive robust control for fuzzy mechanical systems with uncertainty is investigated in this paper. The uncertainty that may be nonlinear and (possibly fast) time-varying is assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. Based on the Udwadia and Kalaba's approach, an adaptive robust controller, which is deterministic and is not the usual if-then rules-based is proposed to render the system to follow a class of prespecified constraints approximately. The adaptive law is of leakage type that can adjust the magnitude of the adaptive parameter based on the nonlinear performance-dependent gain. The resulting controlled system is uniformly bounded and uniformly ultimately bounded, which is proved via the Lyapunov minimax approach. Furthermore, we propose a novel concept: fuzzy confidence to measure the expectation value of a fuzzy number. Then, a fuzzy-based system performance index that includes the expectation value of the uniform ultimate boundedness (the average fuzzy performance) and the control cost is formulated. The optimal design problem associated with the control can then be solved by minimizing the performance index. As a result, the performance of the fuzzy mechanical system is both deterministically guaranteed and fuzzily optimized under this control.

中文翻译：

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模糊机械系统鲁棒控制的优化设计：基于性能的泄漏和置信指数测度

本文研究了具有不确定性的模糊机械系统的自适应鲁棒控制优化设计问题。可能是非线性和（可能快速）随时间变化的不确定性被假定为有界的，并且界的知识仅位于规定的模糊集合内。基于 Udwadia 和 Kalaba 的方法，提出了一种自适应鲁棒控制器，它是确定性的，而不是通常的基于 if-then 规则的控制器，以使系统近似遵循一类预先指定的约束。自适应律是泄漏型的，可以根据非线性性能相关增益来调整自适应参数的大小。由此产生的受控系统是一致有界和一致最终有界的，这通过 Lyapunov 极小极大方法得到了证明。此外，我们提出了一个新概念：模糊置信度来衡量一个模糊数的期望值。然后，制定了一个基于模糊的系统性能指标，该指标包括统一极限有界的期望值（平均模糊性能）和控制成本。然后可以通过最小化性能指标来解决与控制相关的优化设计问题。因此，在这种控制下，模糊机械系统的性能得到确定性保证和模糊优化。然后可以通过最小化性能指标来解决与控制相关的优化设计问题。因此，在这种控制下，模糊机械系统的性能得到确定性保证和模糊优化。然后可以通过最小化性能指标来解决与控制相关的优化设计问题。因此，在这种控制下，模糊机械系统的性能得到确定性保证和模糊优化。