In this paper, two efficient robust fuzzy model predictive control algorithms are investigated for discrete nonlinear systems with multiple time delays and bounded disturbances. The famous Takagi–Sugeno (T–S) fuzzy systems are utilized to represent nonlinear systems. Instead of the Lyapunov–Krasovskii functional, the Lyapunov–Razumikhin function is adopted to deal with time delays because it involves invariant sets in the original state space of the system. A sequence of explicit control laws corresponding to a sequence of constraint sets are computed offline so that the online computational burden associated with the classical model predictive control algorithms is significantly reduced. In particular, the set invariance theory behind the Razumikhin approach, which is more complicated than the one for nondelayed systems, is directly observed. Additionally, it is proved that all (delayed) states can enter the terminal set in finite time. Moreover, robust positive invariance and input-to-state stability for time-delay systems concerning disturbances are realized. Additionally, an online optimization algorithm is also provided based on the offline computed ellipsoidal sets. Therefore, the conservatism induced by the Razumikhin approach is relaxed, while the computational cost is not significantly increased.

中文翻译：

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基于 Razumikhin 方法的离散非线性时滞系统的高效鲁棒模糊模型预测控制

在本文中，针对具有多个时滞和有界扰动的离散非线性系统，研究了两种有效的鲁棒模糊模型预测控制算法。著名的 Takagi-Sugeno (T-S) 模糊系统被用来表示非线性系统。代替Lyapunov-Krasovskii泛函，Lyapunov-Razumikhin函数被用来处理时间延迟，因为它涉及系统原始状态空间中的不变集。离线计算对应于一系列约束集的一系列显式控制律，从而显着减少与经典模型预测控制算法相关的在线计算负担。特别是，可以直接观察到 Razumikhin 方法背后的集合不变性理论，它比非延迟系统的方法更复杂。此外，证明了所有（延迟）状态都可以在有限时间内进入终端集。此外，实现了关于扰动的时滞系统的鲁棒正不变性和输入到状态稳定性。此外，还提供了基于离线计算的椭球集的在线优化算法。因此，Razumikhin 方法引起的保守性得到放松，而计算成本并没有显着增加。