This paper proposes an optimal indirect approach for asymmetric bounds in constraint-following in mechanical systems with (possibly fast) time-varying fuzzy uncertainty. The uncertainty is described with fuzzy set theory. We aim at optimal controller to drive the constraint-following error of the concerned fuzzy system to lie within a desired (possibly asymmetric) bound all the time and get to be sufficiently small eventually. For deterministic performance, we transform the fuzzy original system into a constructed fuzzy system, for which a deterministic (not the usual if-then rules-based) adaptive robust control is designed for uniform boundedness and uniform ultimate boundedness. For optimal performance, a performance index is proposed based on the fuzzy information, by minimizing which an optimal control gain design problem is formulated and solved. When the constructed fuzzy system is uniform boundedness and uniform ultimate boundedness, the constraint-following error of the original fuzzy system is proved to be bounded. As a result, the control design can render out deterministic performance and minimum performance index.

中文翻译：

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模糊机械系统有界约束跟随误差的自适应鲁棒控制的优化设计

本文提出了一种具有（可能是快速的）时变模糊不确定性的机械系统约束跟踪中非对称边界的最优间接方法。用模糊集理论描述不确定性。我们的目标是使所有相关模糊系统的约束跟随误差始终处于所需的（可能是非对称的）界限之内并最终变得足够小的最优控制器。为了获得确定性性能，我们将模糊原始系统转换为构造的模糊系统，为此，针对统一有界和统一最终有界设计了确定性（不是通常的基于if-then规则的自适应鲁棒控制）。为了获得最佳性能，基于模糊信息提出了性能指标，通过最小化提出和解决最佳控制增益设计问题。当所构造的模糊系统是一致有界和一致的最终有界时，证明原始模糊系统的约束跟随误差是有界的。结果，控制设计可以提供确定的性能和最低性能指标。