This paper addresses a class of sliding mode control (SMC) strategies for high-frequency sampled systems with uncertainties, utilizing a generalized Delta operator reaching law. First, Delta operator sampled systems are regarded as a bridge in the unified research framework of discrete-time systems and continuous-time systems. With the increase of sampling frequency, Delta operator sampled systems can maintain consistent stability with their corresponding continuous models. Then, a generalized reaching law by Delta operator is presented, which can degenerate into multiple existed reaching laws under certain conditions. And then, the reaching condition, quasi-sliding mode (QSM) band, and finite time reachability of the proposed generalized Delta operator reaching law are analyzed. Next, sliding mode controllers are designed separately for both matched uncertainty and unmatched uncertainty cases. With the effect of these controllers, Delta operator SMC systems exhibit desirable dynamic characteristics. Finally, two examples on truck-trailer system and ball-beam system demonstrate the effectiveness of Delta operator sliding mode controllers, and show efficient performance in stabilizing high-frequency sampled systems with uncertainties. These scenarios illustrate the potential of the proposed strategies for practical applications. Note to Practitioners—This work aims to develop sliding mode control strategy for Delta operator sampled systems, which is of fundamental significance in the fields of high-frequency sampled control. We propose a generalized Delta operator reaching law and provide a unified framework for high-frequency sampled discrete-time systems and their corresponding continuous-time systems, addressing practical challenges in areas, such as high-speed motors, supercomputing, and network transmission. The reaching condition, quasi-sliding mode bandwidth, and finite time reachability of the proposed generalized Delta operator reaching law are fully considered. Given that the effects of unknown matched or unmatched uncertainties, sliding mode controllers based on Delta operator are designed, which are applied to truck-trailer system and ball-beam system.

The fractional-order (FO) nonlinear differential system with state-dependent (SD) delayed impulses (DI) is considered in this brief. The considered impulses are related to the delayed state of the system and the delays are SD. A novel lemma for the monotonicity of the solution of Caputo's FO derivative equation is given. By means of linear matrix inequality (LMI) and several comparative arguments, criteria of uniform stability, uniform asymptotical stability, and Mittag-Leffler stability are obtained. Compared with other works on integer-order (IO) impulsive delayed systems with SD delays or fixed delays, how to impose constraints on parameters and impulses is explored, without imposing the boundedness on the state delays. Two examples are implemented to examine the practicality and sharpness of our theoretical analysis.

Images captured in hazy or foggy weather conditions are seriously degraded by the scattering of atmospheric particles, which directly influences the performance of outdoor computer vision systems. In this paper, a fast algorithm for single image dehazing is proposed based on linear transformation by assuming that a linear relationship exists in the minimum channel between the hazy image and the haze-free image. First, the principle of linear transformation is analyzed. Accordingly, the method of estimating a medium transmission map is detailed and the weakening strategies are introduced to solve the problem of the brightest areas of distortion. To accurately estimate the atmospheric light, an additional channel method is proposed based on quad-tree subdivision. In this method, average grays and gradients in the region are employed as assessment criteria. Finally, the haze-free image is obtained using the atmospheric scattering model. Numerous experimental results show that this algorithm can clearly and naturally recover the image, especially at the edges of sudden changes in the depth of field. It can, thus, achieve a good effect for single image dehazing. Furthermore, the algorithmic time complexity is a linear function of the image size. This has obvious advantages in running time by guaranteeing a balance between the running speed and the processing effect.

Hazy images hinder image understanding in many applications such as autonomous vehicle. In this paper, we propose an efficient method to improve image quality of hazy images. Our method estimates the transmission function based on a linear model that allows efficient computation and employs quadtree to search for a region that best represents the scatter of airlight. Experiments were conducted using publicly available images. It is demonstrated that our proposed method achieved comparable results to the state-of-the-art ones. In the estimation of sunlight radiance, the quadtree that integrates local brightness and gradient as well as spatial constraint provide a robust means to identify region of sky. Most significantly, our proposed method greatly improved the efficiency. When dealing with moderate and large size image, the improvement could be more than thirty-fold.

For constrained three-link manipulation robots it is shown how the complexity of controlling anthropomorphic arm-like manipulators can be considerable ameliorated by designing a sliding-mode control. First, a representation singular system model of three-link manipulators is established by employing constrained equations and corresponding descriptions of force restriction. Then sliding-mode control with constrained control inputs for three-link manipulator is expatiated as appropriate. Based on quadratic performance index, the optimal sliding mode switching function for three-link manipulator system is derived and a modified reaching law on the grounds of the singular model is constructed using a power function. Then the sliding mode controller for three-link constrained manipulator is designed using the proposed reaching law. Using PUMA-560 the efficiency of the proposed method is demonstrated via the obtained simulation results.