This study presents a nonlinear auto-regressive moving average (NARMA) based online learning controller algorithm providing adaptability, robustness and the closed loop system stability. Both the controller and the plant are identified by the proposed NARMA based input–output models of Wiener and Hammerstein types, respectively. In order to design the NARMA controller, not only the plant but also the closed loop system identification data are obtained from the controlled plant during the online supervised learning mode. The overall closed loop model parameters are determined in suitable parameter regions to provide Schur stability. The identification and controller parameters are calculated by minimizing the \(\varepsilon \)-insensitive error functions. The proposed controller performances are not only tested on two simulated models such as the quadrotor and twin rotor MIMO system (TRMS) models but also applied to the real TRMS with having severe cross-coupling effect between pitch and yaw. The tracking error performances of the proposed controller are observed better compared to the conventional adaptive and proportional–integral–derivative controllers in terms of the mean squared error, integral squared error and integral absolute error. The most noticeable superiority of the developed NARMA controller over its linear counterpart, namely the adaptive auto-regressive moving average (ARMA) controller, is observed on the TRMS such that the NARMA controller shows a good tracking performance not only for the simulated TRMS model but also the real TRMS. On the other hand, it is seen that the adaptive ARMA is incapable of producing feasible control inputs for the real TRMS whereas it works well for the simulated TRMS model.

中文翻译：

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用于无人机的学习稳定鲁棒自适应NARMA控制器及其在双旋翼MIMO系统中的应用

这项研究提出了一种基于非线性自回归移动平均值（NARMA）的在线学习控制器算法，该算法提供了适应性，鲁棒性和闭环系统稳定性。控制器和工厂都分别通过建议的基于NARMA的Wiener和Hammerstein类型的输入-输出模型进行识别。为了设计NARMA控制器，在在线监督学习模式下，不仅从受控工厂中获取工厂，而且从闭环系统中获取闭环系统识别数据。在合适的参数区域中确定总体闭环模型参数，以提供Schur稳定性。通过最小化\（\ varepsilon \）来计算识别和控制器参数-不敏感的错误功能。所提出的控制器性能不仅在两个仿真模型（如四旋翼和双旋翼MIMO系统（TRMS）模型）上进行了测试，而且还应用于在俯仰和偏航之间具有严重交叉耦合作用的实际TRMS。在均方误差，积分平方误差和积分绝对误差方面，与传统的自适应和比例-积分-微分控制器相比，所提出的控制器的跟踪误差性能更好。在TRMS上观察到已开发的NARMA控制器相对于其线性同类产品最明显的优势，即自适应自回归移动平均（ARMA）控制器，这样NARMA控制器不仅对模拟的TRMS模型而且对模拟的TRMS模型都表现出良好的跟踪性能也是真正的TRMS。另一方面，