This article first proposes a discrete-time sliding flexible performance preset boundary (DT-SFPPB)-based control algorithm for input saturated discrete-time nonlinear systems (IS-DTNSs). Compared to the existing discrete-time prescribed performance control (DT-PPC) algorithms, the PPB of them present a “trumpet” shape, resulting in fundamental conservation of the transient performance, and whenever the initial error is altered, it is essential to recheck whether the new error meets the original constraint condition, if not, a new PPB with a larger measure has to be reselected. By designing a novel DT-SFPPB associated with the initial error, which can always envelope the initial error with an arbitrarily preset initial measure, indicating that the proposed approach can be utilized for IS-DTNSs with arbitrary initial error without compromising the initial transient performance. Furthermore, the coupling effect between performance preset and input saturation is also considered, by designing a novel equilibrium boundary related to saturation, so that the proposed approach can achieve the synergy between performance preset and input security, i.e., the designed DT-SFPPB can flexibly expand when input saturation occurs to avoid vulnerability, and when the control input is within the safe boundary, it rapidly reverts to the original PPB to guarantee the specified performance metrics. The findings demonstrate that the developed approach guarantees that the system output tracks the desired signal with the specified performance metrics, and all of the tracking errors are always enveloped within their corresponding DT-SFPPBs. The devised approach is exemplified by means of simulation examples.

This article first proposes a sliding flexible prescribed performance boundary-guided reinforcement learning (SFPPB-RL) control approach for input-constrained nonlinear systems (ICNSs). By designing a sliding flexible prescribed performance boundary, which not only can adaptively adjust the initial boundary according to the initial error, but also dynamically adjust the constraint relaxation according to the coupling correlation between the input constraint and the performance constraint, a novel prescribed performance control (PPC) approach is proposed. Compared with the existing "horn" shape performance boundary-based PPC methods, the limitation of having to repeatedly debug design parameters or sacrifice initial transient performance to meet different initial error requirements is eliminated. Meanwhile, the coupling effect between the input constraint and the performance constraint is also considered, and the balance between input safety and control performance is achieved by constructing an auxiliary system. Furthermore, combining identifier-critic-actor structure-based RL strategy and backstepping technique, a sliding flexible PPB-guided reinforcement learning (SFPPB-RL) optimal control algorithm is developed, which minimizes the cost function while ensuring input safety and prescribed performance indicators. The validity of the proposed algorithm is demonstrated via simulations.

This article first presents a dual flexible prescribed performance control (DFPPC) approach of input saturated high-order nonlinear systems (IS-HONSs). Compared to the existing PPC approaches of IS-HONSs, under which the performance constraint boundaries (PCBs) are usually fixed and bounded, resulting in a restriction of the initial error in the algorithm implementation; in addition, the coupling relationship between performance constraints and input saturation is usually ignored, resulting in the methods are very fragile when input saturation occurs. By designing the novel tensile model-based PCBs that depend on output and input constraints, the proposed DFPPC method provides sufficient resilience for both the initial conditions and the input saturation, so that the proposed DFPPC method can not only be suitable for multiple types of initial errors by adjusting the parameters, including , , and , where , and denote the initial PCBs; but also can achieve a good balance between input saturation and performance constraints, i.e., when the control input reaches or exceeds the saturation threshold, the PCBs can adaptively extend to avoid the singularity, and when the control input returns to the saturation threshold range, the PCBs are then adaptively restored to the original PCBs. The results show that the proposed DFPPC algorithm guarantees semi-global boundedness for all closed-loop signals, while ensuring that the system output accurately tracks the desired signal, and it consistently maintains the tracking error within the PCBs. The developed algorithm is illustrated by means of simulation instances.

The issue of sliding flexible prescribed performance control (SFPPC) of input saturated nonlinear systems (ISNSs) is first studied in this article. Compared to the traditional PPC and the finite-time PPC algorithms for ISNSs, under which the performance constraint boundaries (PCBs) present the symmetrical or asymmetric “horn” shape, which leads to a large jitter in the tracking error before the system reaches steady state; and once the parameters are selected, the PCBs are fixed, when the initial state (or reference signal) changes, it is necessary to reverify whether the initial error still satisfies the initial constraint condition. By designing a new pair of sliding flexible PCBs (SFPCBs) associated with the initial error, a novel SFPPC algorithm is presented in this article, which presents two main advantages: 1) the SFPCBs can slide adaptively with the initial tracking error without increasing the measure of the initial PCBs, implying that the proposed SFPPC algorithm can be applied to ISNSs with arbitrary initial errors without sacrificing the initial control performance; 2) the proposed SFPPC algorithm achieves a tradeoff between performance constraint and input saturation, i.e., the SFPCBs can adaptively increase when the control input exceeds the maximum allowable threshold, effectively avoiding singularity, and when the control input is within the saturation threshold range, the SFPCBs can adaptively revert back to the original PCBs. The results demonstrate that the proposed SFPPC approach can guarantee that the system output tracks the desired signal, and the tracking error always kept within the SFPCBs that depend on initial error, input, and output constraints. The developed algorithm is exemplified by means of simulation instances.

This article presents a unified adaptive fuzzy control approach for high-order nonlinear systems (HONSs) with multitype state constraints. Existing methods always require the upper and lower constraint boundaries are strictly positive and negative functions (or constants), respectively, which is often inconsistent with the actual constraints. In this article, "multitype state constraint" means that the upper and lower constraint boundaries include multiple types, such as both being strictly positive (or negative), sometime be positive or negative, and so on (cases ①-⑥). By designing a unified mapping function (UMF), the multitype state constraints are processed under removal the feasibility conditions (FCs). Furthermore, a technical design makes the proposed method also applicable to unconstrained HONSs without changing the control structure. By means of a fuzzy-logic system (FLS) and fixed-time stability theory (FTST), the proposed algorithm can ensure that the tracking error converges to a zero-centered neighborhood within a fixed time, and the singularity which often appears in the existing fixed-time control (FTC) methods of HONSs is effectively avoided. Simulation results demonstrate the scheme developed.

This article presents a prescribed-time output feedback control (PTOFC) algorithm for cyber-physical systems (CPSs) under output constraint occurring in any finite time interval (OC-AFT) and malicious attacks. The OC-AFT meaning that the output constraint only occurs during a finite number of time periods while being absent in others, which is more general and complex than traditional infinite-time/deferred output constraints. A stretch model-based nonlinear mapping function is constructed to handle the OC-AFT, and a salient advantage is that the proposed algorithm is also suit for CPSs with infinite-time/deferred output (or funnel) constraints, as well as those that are constraint-free, without necessitating changes to the control structure. The uncertain terms (including system model uncertainties, malicious attacks, and external disturbances) are compensated by fuzzy logic systems. Furthermore, a novel practical prescribed-time stability criterion is proposed, under which a novel PTOFC scheme is given. The results demonstrate that the proposed scheme can ensure that both tracking error and observation error converge to a neighborhood centered on zero within a prescribed time, while accommodating the OC-AFT and malicious attacks. Additionally, the settling time remains unaffected by control parameters and initial states, and the limitations of excessive initial control inputs and singularity problems in existing prescribed-time control algorithms are eliminated. The developed algorithm is exemplified through simulation instances.

A flexible prescribed performance control (FPPC) approach for input saturated nonlinear systems (ISNSs) with unmeasurable states is first presented in this article. Compared to the standard prescribed performance control (SPPC) or funnel control methods for ISNSs, the “flexibility” of the proposed FPPC algorithm is reflected in two aspects: 1) the proposed FPPC algorithm simultaneously considers multiple key indicators (including the steady state accuracy, convergence time, and overshoot), which are widely demanded in industrial production; 2) the proposed FPPC algorithm achieves a tradeoff between performance constraint and input saturation, i.e., the performance boundary can adaptively increase when the control input exceeds the saturation threshold, effectively avoiding singularity; conversely, when the control input is within the saturation threshold range, the performance constraint boundary can adaptively revert back to the original performance boundary. In addition, the unmeasured states are observed by the state observer, and the unknown nonlinear functions are approximated by fuzzy logic systems. The results demonstrate that the proposed output feedback control algorithm can ensure that all closed-loop signals are semiglobally bounded, the system output can track the desired signal within a prescribed time, and the tracking error is consistently maintained within flexible performance boundaries that depend on input and output constraints. The developed algorithm is exemplified through simulation instances.

A novel practical prescribed-time control (PPTC) approach for high-order nonlinear systems (HONSs) subject to state constraints is studied in this article. Different from the existing methods which always require the constraint boundaries to be continuous functions, the state constraints considered in this article are discontinuous (i.e., the state constraints occur only in some time periods and not in others), which can be found in many practical systems. By designing a novel stretch model-based nonlinear mapping function (NMF), the state constraints are dealt with directly, and the limitations that the virtual control function depends upon the feasibility condition (FC) and the tracking error depends upon the constraint boundaries in the conventional schemes are removed. Meanwhile, the proposed method is a unified one, which is also effective for HONSs with conventional continuous state constraints/ deferred state constraints/ funnel constraints or constraints-free without altering the control structure. Furthermore, by designing a newly time-varying scaling transformation function (STF), a more relaxed criterion for practical prescribed-time stable (PPTS) is given, based on which a newly PPTC algorithm is designed. The result shows that the proposed algorithm can preset the upper bound of the settling time, which does not depend upon the initial state of the system and control parameters, the limitations of singularity problem and excessive initial control input in existing methods are removed. Simulation examples verify the algorithm developed.

Neural networks are increasingly used widely in the solution of partial differential equations (PDEs). This letter proposes 3D-PDE-Net to solve the three-dimensional PDE. We give a mathematical derivation of a three-dimensional convolution kernel that can approximate any order differential operator within the range of expressing ability and then conduct 3D-PDE-Net based on this theory. An optimum network is obtained by minimizing the normalized mean square error (NMSE) of training data, and L-BFGS is the optimized algorithm of second-order precision. Numerical experimental results show that 3D-PDE-Net can achieve the solution with good accuracy using few training samples, and it is of highly significant in solving linear and nonlinear unsteady PDEs.

A unified approach to fixed-time tracking control of stochastic high-order nonlinear systems (HONSs) with or without full-state constraints is studied in this article. By introducing two important universal-constrained functions and using coordinate transformation technology, the stochastic HONS with full-state constraints is transformed into an equivalent one without state constraints. Compared with the existing control schemes, the proposed scheme not only eliminates the feasibility conditions, but also accurately analyzes the scope of tracking error. Moreover, the limitation that the constraint functions need to be bounded is also removed; thus, the proposed scheme is a unified approach that can be applied to stochastic HONSs with or without state constraints. With the help of fixed-time stability theory and adaptive fuzzy control technology, a novel fixed-time fuzzy controller is designed. In addition, an adaptive event-triggering mechanism that the threshold parameters can be adjusted adaptively according to the tracking performance is introduced to reduce the communication burden. Simulation results verify the scheme developed.

Blind image deblurring aims at recovering a clean image from the given blurry image without knowing the blur kernel. Recently proposed dark and extreme channel priors have shown their effectiveness in deblurring various blurry scenarios. However, these two priors fail to help the blur kernel estimation under the particular circumstance that clean images contain neither enough darkest nor brightest pixels. In this paper, we propose a novel and robust non-linear channel (NLC) prior for the blur kernel estimation to fill this gap. It is motivated by a simple idea that the blurring operation will increase the ratio of dark channel to bright channel. This change has been proved to be true both theoretically and empirically. Nonetheless, the presence of the NLC prior introduces a thorny optimization model. To handle it, an efficient algorithm based on projected alternating minimization (PAM) has been established which innovatively combines an approximate strategy, the half-quadratic splitting method, and fast iterative shrinkage-thresholding algorithm (FISTA). Extensive experimental results show that the proposed method achieves state-of-the-art results no matter when it has been applied in synthetic uniform and non-uniform benchmark datasets or in real blurry images.

Image denoising is a common problem during image processing. Salt and pepper noise may contaminate an image by randomly converting some pixel values into 255 or 0. The traditional image denoising algorithm is based on filter design or interpolation algorithm. There exists no work using the convolutional neural network (CNN) to directly remove salt and pepper noise to the authors’ knowledge. In this study, they utilise CNN with the multi‐layer structure for the removal of salt and pepper noise, which contains padding, batch normalisation and rectified linear unit. In training, they divide images into three parts: training set, validation set and test set. Experimental results demonstrate that the architecture can effectively remove salt and pepper noise for the various noisy images. In addition, their model can remove high‐density noise well due to the extensive local receptive fields of the deep neural networks. Finally, extensive experimental results show that their denoiser is effective for those images with a large number of interference pixels which may cause misjudgement. In a word, they generalise the application of CNN to salt and pepper noise removal and obtain competitive results.

The authors propose a terse texture feature, called the dominant centre‐symmetric local binary pattern (DCSLBP), which has similar distinctiveness and half dimension compared against original centre‐symmetric local binary pattern (CS‐LBP). On the basis of DCSLBP histogram and an improved construction, a compact descriptor for local feature is presented. To assess the proposed descriptor with the state‐of‐the‐art in performance and dimension, the authors extend it to two variants with different dimensions using the existing method. These descriptors are compared with scale‐invariant feature transform (SIFT), multisupport region rotation and intensity monotonic invariant descriptor (MRRID), orthagonal combination local binary pattern (OC‐LBP) in interest region matching and in the application of object recognition. The experiments demonstrate the proposed descriptor's compactness and robustness to various image transformations, especially to large illumination change.

This study presents a novel method for automatic detection and removal of high‐density impulse noises. The method consists of two parts: the impulse detection part and the impulse noise removal part. In impulse detection part, an automatic detector based on local mean and variance (LMVD) is presented, which can automatically pick out noisy image from massive images and output corrupted grey levels. The detector utilises LMVD of the neighbourhood of corrupted pixels to simulate the cognitive processes of human observing noisy image. In impulse noise removal part, the Newton–Thiele filter (NTF) instead of median filter is applied to remove impulse noise. The process to construct NTF can be divided into two steps: setting up the grid and constructing the Newton–Thiele's rational interpolation on the grid. First, eight adjacent pixels of the corrupted centre pixel are used to construct the two‐dimensional grid. If a pixel in the grid is corrupted, a four‐direction linear interpolation algorithm will be performed to provide a rough estimate to the corrupted pixel. Second, the corrupted centre pixel value will be updated by Newton–Thiele's rational interpolation on the grid. The NTF has better robustness than existing filters because it does not need to adjust window size or other parameters. Simulations reveal that the proposed detector and filter have perfect performance in terms of both quantitative evaluation and visual quality, especially it can remove the impulse noise effectively even at 90% noise level.

When objects undergo large pose change, illumination variation or partial occlusion, most existed visual tracking algorithms tend to drift away from targets and even fail in tracking them. To address this issue, in this study, the authors propose an online algorithm by combining multiple instance learning (MIL) and local sparse representation for tracking an object in a video system. The key idea in our method is to model the appearance of an object by local sparse codes that can be formed as training data for the MIL framework. First, local image patches of a target object are represented as sparse codes with an overcomplete dictionary, where the adaptive representation can be helpful in overcoming partial occlusion in object tracking. Then MIL learns the sparse codes by a classifier to discriminate the target from the background. Finally, results from the trained classifier are input into a particle filter framework to sequentially estimate the target state over time in visual tracking. In addition, to decrease the visual drift because of the accumulative errors when updating the dictionary and classifier, a two‐step object tracking method combining a static MIL classifier with a dynamical MIL classifier is proposed. Experiments on some publicly available benchmarks of video sequences show that our proposed tracker is more robust and effective than others.

Color transfer between images is one of the most common tasks in image processing. We can borrow one image 's color characteristics from another. In this paper we investigate an advanced algorithm for transferring color. A combined clustering method is introduced to find the match areas between two images. Subtractive clustering is used with FCM clustering to prevent the latter from falling into local optimum solution and minimize the amount of human labor in finding the number of clustering. We show that this technique can be successfully applied to the adaptive color transferring and speed up the process. The experiment results are satisfactory.

A visibility-based image fusion algorithm has been given for multi-focus images. First, through a region with center of the pixel, the definition of one pixel's visibility is given. Then, the fused image is generated by weighted average of corresponding parts of the input images. The weighted function is constructed by using shape preserving rational quartic interpolating splines. The experiments show that the proposed method is superior to the multi-resolution fused algorithm based on wavelet analysis for the strictly registered multi-focus images.