This paper proposes an adaptive and robust adaptive control strategy based on type-2 fuzzy neural network (T2FNN) for tracking the desired trajectories of a quadrotor. The designed methods can control both the position and the orientation of a quadrotor. Contrary to common sliding mode controllers (SMCs), the robust adaptive trajectory tracking scheme presented here is based on SMC with exponential reaching law; which helps reduce the phenomenon of chattering. Moreover, parameters including the gains of sliding surfaces, are optimized by cuckoo optimization algorithm (COA), and the results are compared with those obtained by genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO). The designed methods in this study are called adaptive T2FNN controller and the exponential SMC (ESMC)-T2FNN. The law for updating the T2FNN is obtained online by using the Lyapunov stability theory. Considering undesired factors such as uncertainties, external disturbances and control signal saturation, the results of our controllers are compared with those of the adaptive type-1 fuzzy neural network controller (T1FNN) and ESMC-T1FNN. The extensive simulations demonstrate the effectiveness of the proposed COA-based ESMC-AT2FNN approach compared to the other tested techniques (i.e. GA, PSO and ACO) in terms of the improved transient and steady-state trajectory-tracking performance. The mean and standard deviation values concerning the COA are obtained through statistical analyses at 0.00006173 and 0.000092, respectively. This paper also examines the complexity of COA in optimizing the trajectory tracking control of quadrotor and investigates the effects of COA parameters on optimization results. The stable performance of the cuckoo algorithm is demonstrated by varying its parameters and analyzing the obtained results. These results also show the convergence of COA for the considered problem.

本文提出了一种基于类型 2 模糊神经网络 (T2FNN) 的自适应和鲁棒自适应控制策略，用于跟踪四旋翼飞行器的所需轨迹。所设计的方法可以控制四旋翼飞行器的位置和方向。与常见的滑模控制器 (SMC) 不同，这里提出的鲁棒自适应轨迹跟踪方案基于具有指数到达定律的 SMC；这有助于减少抖动现象。此外，通过布谷鸟优化算法（COA）对包括滑动面增益在内的参数进行优化，并将结果与​​遗传算法（GA）、粒子群优化（PSO）、蚁群优化（ACO）的结果进行比较。本研究中设计的方法称为自适应 T2FNN 控制器和指数 SMC (ESMC)-T2FNN。利用李雅普诺夫稳定性理论在线获得更新T2FNN的规律。考虑到不确定性、外部干扰和控制信号饱和等不利因素，我们的控制器的结果与自适应类型 1 模糊神经网络控制器 (T1FNN) 和 ESMC-T1FNN 的结果进行了比较。广泛的模拟证明了所提出的基于 COA 的 ESMC-AT2FNN 方法与其他测试技术相比的有效性（即GA、PSO 和 ACO）在改进的瞬态和稳态轨迹跟踪性能方面。COA 的平均值和标准偏差值分别通过统计分析在 0.00006173 和 0.000092 处获得。本文还考察了优化四旋翼飞行器轨迹跟踪控制时 COA 的复杂性，并研究了 COA 参数对优化结果的影响。通过改变其参数并分析获得的结果，证明了布谷鸟算法的稳定性能。这些结果还显示了 COA 对所考虑问题的收敛性。