The control design problem for a class of constrained uncertain systems is considered in this paper. The uncertainty in the system, including unknown system parameters and external disturbance, is nonlinear and time-varying. The bound of the uncertainty is described via a fuzzy set. The states of the system are constrained to be bounded. A one-to-one state transformation is proposed to convert the bounded state constrained system into the unconstrained system. A new robust control scheme is then proposed for the transformed system, which is in deterministic form and not fuzzy if–then rule based. By fuzzy description of the uncertainty bound, the optimal design of the control gain is proposed, which minimizes a fuzzy performance index associated with both the fuzzy system performance and the control effort. The analytic solution to the optimization problem is demonstrated to always exist and be unique. The resulting control can guarantee uniform boundedness and uniform ultimate boundedness of the uncertain system, while minimizing the fuzzy-based performance index. In addition, the state constraint can be always guaranteed.

中文翻译：

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约束不确定系统的最优鲁棒控制设计：模糊集理论方法

本文考虑了一类约束不确定系统的控制设计问题。系统中的不确定性，包括未知系统参数和外部扰动，是非线性和时变的。不确定性的界限是通过模糊集来描述的。系统的状态被约束为有界。提出了一对一的状态转换，将有界状态约束系统转换为无约束系统。然后为转换后的系统提出了一种新的鲁棒控制方案，该方案是确定性形式的，而不是基于模糊 if-then 规则的。通过对不确定性界限的模糊描述，提出了控制增益的优化设计，它最小化了与模糊系统性能和控制努力相关的模糊性能指标。优化问题的解析解被证明始终存在并且是唯一的。由此产生的控制可以保证不确定系统的统一有界和统一的最终有界，同时最小化基于模糊的性能指标。此外，状态约束总是可以得到保证的。