In this study, a new fast variable structure adaptive fuzzy controller is presented for nonlinear state-delay systems which are subjected to external disturbances and uncertainties. The undesirable chattering and singularity of the variable structure scheme are eliminated by using a novel fast robust high-precision continuous nonsingular control law which is able to accelerate the finite-time convergence both in reaching and sliding phases of the motion. A fuzzy logic system with a neural network adaptive law is used to approximate the dynamics of the nonlinear system containing the current state and the delayed state. The superiority of the proposed fuzzy neural network in online adjusting the weights of the network is the fast convergence rate of the approximation error to the optimum value in a very short time. The stability of the closed-loop system is proved by using an extended finite-time Lyapunov criterion such that the convergence of the position tracking error, velocity tracking error, and the estimation error to the bounded region is guaranteed in a very short time. Two second-order uncertain nonlinear simulation examples with external disturbances are given to evaluate the efficacy of the proposed control technique. The simulation results show that faster and high-precision tracking performance is obtained compared with the existing recent works focused on robust control of nonlinear state-delay systems with uncertainties.

在这项研究中，提出了一种新的快速变结构自适应模糊控制器，用于受外部干扰和不确定性影响的非线性状态延迟系统。通过使用一种新颖的快速鲁棒高精度连续非奇异控制律消除了变结构方案的不良抖动和奇异性，该控制律能够加速运动的到达和滑动阶段的有限时间收敛。具有神经网络自适应律的模糊逻辑系统用于近似包含当前状态和延迟状态的非线性系统的动力学。所提出的模糊神经网络在在线调整网络权值方面的优越性是逼近误差在很短的时间内快速收敛到最优值。利用扩展的有限时间李雅普诺夫准则证明了闭环系统的稳定性，保证了位置跟踪误差、速度跟踪误差和估计误差在极短时间内收敛到有界区域。给出了两个具有外部干扰的二阶不确定非线性仿真示例，以评估所提出的控制技术的功效。仿真结果表明，与现有的专注于具有不确定性的非线性状态延迟系统的鲁棒控制的近期工作相比，可以获得更快和高精度的跟踪性能。并且在很短的时间内保证了对有界区域的估计误差。给出了两个具有外部干扰的二阶不确定非线性仿真示例，以评估所提出的控制技术的功效。仿真结果表明，与现有的专注于具有不确定性的非线性状态延迟系统的鲁棒控制的近期工作相比，可以获得更快和高精度的跟踪性能。并且在很短的时间内保证了对有界区域的估计误差。给出了两个具有外部干扰的二阶不确定非线性仿真示例，以评估所提出的控制技术的功效。仿真结果表明，与现有的专注于具有不确定性的非线性状态延迟系统的鲁棒控制的近期工作相比，可以获得更快和高精度的跟踪性能。