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The performance of dimensionality reduction shows the superiorities of the proposed methods over the state of the art.A single dataset could hide a significant number of relationships among its feature set. Learning these relationships simultaneously avoids the time complexity associated with running the learning algorithm for every possible relationship, and affords the learner with an ability to recover missing data and substitute erroneous ones by using available data. In our previous research, we introduced the gate-layer autoencoders (GLAEs), which offer an architecture that enables a single model to approximate multiple relationships simultaneously. GLAE controls what an autoencoder learns in a time series by switching on and off certain input gates, thus, allowing and disallowing the data to flow through the network to increase network\textquoteright s robustness. However, GLAE is limited to binary gates. In this article, we generalize the architecture to weighted gate layer autoencoders (WGLAE) through the addition of a weight layer to update the error according to which variables are more critical and to encourage the network to learn these variables. This new weight layer can also be used as an output gate and uses additional control parameters to afford the network with abilities to represent different models that can learn through gating the inputs. We compare the architecture against similar architectures in the literature and demonstrate that the proposed architecture produces more robust autoencoders with the ability to reconstruct both incomplete synthetic and real data with high accuracy.This article studies the finite-time tracking control problem for the single-link flexible-joint robot system with actuator failures and proposes an adaptive fuzzy fault-tolerant control strategy. More precisely, the issue of ``explosion of complexity is successfully solved by incorporating the command filtering technology and the backstepping method. The unknown nonlinearities are identified with the help of the fuzzy logic system. An event-triggered mechanism with the relative threshold strategy is exploited to save communication resources. Furthermore, the proposed control design can guarantee that the tracking error converges to a small neighborhood of origin within a finite time by taking full advantage of the finite-time stability theory. Finally, the simulation example is presented to further verify the validity of the proposed control method.Wavelet transform is being widely used in classical image processing. One-dimension quantum wavelet transforms (QWTs) have been proposed. Generalizations of the 1-D QWT into multilevel and multidimension have been investigated but restricted to the quantum wavelet packet transform (QWPTs), which is the direct product of 1-D QWPTs, and there is no transform between the packets in different dimensions. A 2-D QWT is vital for image processing. We construct the multilevel 2-D QWT's general theory. Explicitly, we built multilevel 2-D Haar QWT and the multilevel Daubechies D4 QWT, respectively. We have given the complete quantum circuits for these wavelet transforms, using both noniterative and iterative methods. Compared to the 1-D QWT and wavelet packet transform, the multilevel 2-D QWT involves the entanglement between components in different degrees. Complexity analysis reveals that the proposed transforms offer exponential speedup over their classical counterparts. Also, the proposed wavelet transforms are used to realize quantum image compression. Simulation results demonstrate that the proposed wavelet transforms are significant and obtain the same results as their classical counterparts with an exponential speedup.This article studies fault-tolerant resilient control (FTRC) problems for uncertain Takagi-Sugeno fuzzy systems when subjected to additive actuator faults and/or malicious injections on control input signals. The effects of faults and malicious injections are modeled by unknown bounded signals. buy Cryptotanshinone The signals are produced by any finite-L₂-gain dynamical system and a Lipschitz and derivable function with respect to states, so that the considered fault model contains some reported ones as special cases. By employing the available state and input data, a function, which is equivalent to a fictitious dynamical system comprising the information about compensation errors for unknown actuator faults, is presented. Then, based on the virtual system, a novel actuator failure compensator (AFC) with the structure of dynamic feedbacks is proposed, so that the compensation capability is improved via cooperative interaction designs between the virtual dynamical systems and closed-loop systems. Furthermore, through the equivalence class and Lyapunov theories, it is proved that the presented robust dynamic AFC-based fuzzy controller ensures the asymptotic convergence of system states to zero. Different from the existing FTRCs, good transient performance is guaranteed, even in the presence of unforeseen actuator faults. Two illustrative examples verify the effectiveness of the presented method.In this article, the data-driven optimal formation control problem is addressed for a heterogeneous quadrotor team with a virtual leader. Each quadrotor is considered as a highly nonlinear system with six degrees of freedom and the accurate dynamic information of the quadrotor is difficult to obtain in practical applications. An optimal cascade formation controller, including a position controller and an attitude controller, is proposed to track a virtual leader and form a predesigned formation. By using the reinforcement learning (RL) approach, the optimal formation controller is learned from the quadrotor system data without any knowledge of dynamic information of the quadrotors. Simulation results of a heterogeneous multiquadrotor system in a formation flight are given to show the effectiveness of the proposed controllers.This work is concerned with the issue of finite-time filter design for a type of Takagi-Sugeno (T-S) fuzzy Markov switching system (MSSs) with deception attacks (DAs). In view of communication network security, the randomly occurring DAs are considered in the measurement output (MO), in which the malicious unknown but bounded signals are launched by the adversary. Notably, to characterize the fallibility of the communication links between the MO and the filter, the packet dropouts, DAs, and quantization effects are taken into account simultaneously, which signifies that the resulting system is much more applicable than the existing results. Meanwhile, to deal with the phenomenon of asynchronous switching, a hierarchical structure approach is adopted, which involves the existing nonsynchronous/synchronous strategy as special cases. By means of a fuzzy-basis-dependent Lyapunov strategy, sufficient criteria are formulated such that the resulting system is stochastic finite-time boundedness under randomly occurring DAs.

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