Wavelets are designed to have compact support in both time and frequency, giving them the ability to represent a signal in the two-dimensional time–frequency plane. The Gaussian, the Mexican hat and the Morlet wavelets are crude wavelets that can be used only in continuous decomposition. The Morlet wavelet is complex-valued and suitable for feature extraction using the continuous wavelet transform. Continuous wavelets are favoured when high temporal and spectral resolution is required at all scales. In this paper, considering the properties from the Morlet wavelet and based on the structure of a recurrent high-order neural network model, a novel wavelet neural network structure, here called a recurrent Morlet wavelet neural network, is proposed in order to achieve a better identification of the behaviour of dynamic systems. The effectiveness of our proposal is explored through the design of a decentralized neural backstepping control scheme for a quadrotor unmanned aerial vehicle. The performance of the overall neural identification and control scheme is verified via simulation and real-time results. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

In this paper, a decentralized direct model reference adaptive control (MRAC) scheme is proposed in order to achieve the attitude control task for a quadrotor unmanned aerial vehicle (UAV). On the one hand, the nonlinear model for the quadrotor UAV is decomposed in the rotational and translational systems. Thus, a second order subsystem for each attitude angle is extracted from the rotational system dynamics. Then, under the assumption that a linear-in-the-parameters model for each subsystem can be defined, each subsystem is represented by a parameterized model from which a direct MRAC is designed. On the other hand, a PID controller is implemented for altitude control. The performance of our decentralized adaptive control scheme is validated via simulation results taking into account parametric variations, noise in the measurements and external perturbations.

This paper presents a neuro-adaptive control scheme dedicated to solve the motion trajectory tracking problem of robot manipulators under uncertain parameters and external disturbances. A two degrees of freedom direct-drive robot manipulator was taken as a case of study. The proposed controller is able to guarantee asymptotic convergence of the position and velocity tracking errors, and the weights of the artificial neural network are bounded. Artificial neural network weights are updated online using filtered error approach, adaptive laws and signed power function. This scheme does not require any offline training. The neuro-adaptive controller is experimentally validated and compared with a classical one-layer neuro-adaptive controller; the proposed scheme obtains better quantitative metrics related with the RMS values of the position and velocity errors, and a good robust behaviour against external disturbances.

Thanks to recent advances in artificial intelligence, interest in autonomous mobile systems has increased, and consequently, the development and validation of advanced control schemes for them has also seen a rise. This work introduces a two-layer neuro-adaptive compensation control scheme designed to address the trajectory tracking problem for an omnidirectional wheeled mobile robot equipped with four independent Mecanum wheels. The two-layer artificial neural network is used to compensate for the unknown dynamics of the mobile robot; the filtered error technique is used to obtain the weights of the artificial neural network. This approach does not require offline training. A key contribution of this approach is the integration of a novel auxiliary signal to provide robustness, particularly in non-ideal scenarios. This robust term effectively bounds the disturbance commonly encountered in such control approaches. A significant advantage of this approach is its independence from precise knowledge of plant parameters or the overall plant dynamics. Experimental results demonstrate the effectiveness of the proposed controller in achieving desired performance for the 4-wheeled omnidirectional mobile robot.

In this paper, a decentralized control scheme is proposed in order to achieve the control goal of a quadrotor unmanned aerial vehicle (UAV). On the one hand, the nonlinear model for the quadrotor UAV is decomposed in the rotational and translational systems. Thus, a second-order subsystem for each attitude angle is extracted from the rotational system dynamics. Then, under the assumption that a linear-in-the-parameters model for each subsystem can be defined, each subsystem is represented by a parameterized model from which a direct MRAC is designed. On the other hand, a second-order subsystem for each translational coordinate is extracted from the translational system dynamics. Then, a PID controller is implemented for each translational coordinate subsystem. The performance of our decentralized control scheme is validated via simulation results taking into account parametric variations, noise in the measurements and external perturbations.