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With the recent development of the joint classification of hyperspectral image (HSI) and light detection and ranging (LiDAR) data, deep learning methods have achieved promising performance owing to their locally sematic feature extracting ability. Nonetheless, the limited receptive field restricted the convolutional neural networks (CNNs) to represent global contextual and sequential attributes, while visual image transformers (VITs) lose local semantic information. Focusing on these issues, we propose a fractional Fourier image transformer (FrIT) as a backbone network to extract both global and local contexts effectively. In the proposed FrIT framework, HSI and LiDAR data are first fused at the pixel level, and both multisource feature and HSI feature extractors are utilized to capture local contexts. Then, a plug-and-play image transformer FrIT is explored for global contextual and sequential feature extraction. Unlike the attention-based representations in classic VIT, FrIT is capable of speeding up the transformer architectures massively and learning valuable contextual information effectively and efficiently. More significantly, to reduce redundancy and loss of information from shallow to deep layers, FrIT is devised to connect contextual features in multiple fractional domains. Five HSI and LiDAR scenes including one newly labeled benchmark are utilized for extensive experiments, showing improvement over both CNNs and VITs.

This article studies the hierarchical sliding-mode surface (HSMS)-based adaptive optimal control problem for a class of switched continuous-time (CT) nonlinear systems with unknown perturbation under an actor–critic (AC) neural networks (NNs) architecture. First, a novel perturbation observer with a nested parameter adaptive law is designed to estimate the unknown perturbation. Then, by constructing an especial cost function related to HSMS, the original control issue is further converted into the problem of finding a series of optimal control policies. The solution to the HJB equation is identified by the HSMS-based AC NNs, where the actor and critic updating laws are developed to implement the reinforcement learning (RL) strategy simultaneously. The critic update law is designed via the gradient descent approach and the principle of standardization, such that the persistence of excitation (PE) condition is no longer needed. Based on the Lyapunov stability theory, all the signals of the closed-loop switched nonlinear systems are strictly proved to be bounded in the sense of uniformly ultimate boundedness (UUB). Finally, the simulation results are presented to verify the validity of the proposed adaptive optimal control scheme.

In this article, the asymptotic tracking control problem for a class of nonlinear multi-agent systems (MASs) is researched by the combination of radial basis function neural networks (RBF NNs) and an improved dynamic surface control (DSC) technology. It’s important to emphasize that the MASs studied in this article are nonlinear and nonstrict-feedback systems, where the nonlinear functions are unknown. In order to satisfy the requirement that all items in the controller must be available, the unknown nonlinearities in the system are flexibly approximated by utilizing RBF NNs technique. Moreover, the issue of “complexity explosion” in the backstepping procedure is handled by improving the traditional DSC technology, and meanwhile, the influences of the boundary layers caused by the filters in the DSC procedure are eliminated skillfully through the compensation terms. In addition, the relative threshold event-triggered strategy is developed for the designed controllers to reduce the waste of communication resources, where Zeno phenomenon is successfully avoided. It is observed that the new presented control strategy ensures that all the closed-loop systems variables are uniformly ultimately bounded (UUB), and furthermore all the outputs of followers are able to track the output of the leader with zero tracking errors. Finally, the simulation results are presented to show the effectiveness of the obtained design scheme.

This study reports a fixed-time tracking control problem for strict-feedback nonlinear systems with quantized inputs and actuator faults where the total number of faults is allowed to be infinite. By taking advantage of radial basis function neural networks (RBFNNs), unknown nonlinear function terms in the system dynamic model can be effectively approached. In addition, based on the sector property of quantization nonlinearities and the structure of the actuator fault model, novel adaptive estimations and innovative auxiliary design signals are constructed to compensate for the influence caused by actuator faults and quantized inputs properly in the fixed-time convergence settings. Then, rigorous theoretical analysis manifests that the proposed control scheme can make the output tracking error converge to a small neighborhood of the origin within a fixed time, and the upper bound of the setting time not only does not depend on initial states of the system but also can be preassigned by selecting parameters appropriately. Meanwhile, all the signals in the closed-loop system remain bounded. Finally, a numerical example and a practical example of a single-link manipulator are presented to demonstrate the effectiveness of the proposed control algorithm.

This article presents a global adaptive neural-network-based control algorithm for disturbed pure-feedback nonlinear systems to achieve zero tracking error in a predefined time. Different from the traditional works that only solve the semiglobal bounded tracking problem for pure-feedback systems, this work not only achieves that the tracking error globally converges to zero but also guarantees that the convergence time can be predefined according to the user specification. In order to get the desired predefined-time controller, first, a mild semibound assumption for nonaffine functions is skillfully proposed so that the design difficulty caused by the structure of pure feedback can be easily solved. Then, we apply the property of radial basis function (RBF) neural networks (NNs) and Young’s inequality to derive the upper bound of the term that contains the unknown nonlinear function and external disturbances, and the designed adaptive parameters decide the derived upper and robust control gain. Finally, the predefined-time virtual control inputs are presented whose derivatives are further estimated by utilizing finite-time differentiators. It is strictly proved that the proposed novel predefined-time controller can guarantee that the tracking error globally converges to zero within predefined time and a practical example is shown to verify the effectiveness and practicability of the proposed predefined-time control method.