Recursive Idea Research Articles

Adaptive tracking control for constrained nonlinear nonstrict-feedback switched stochastic systems with unknown control directions

This brief proposes a novel tracking control strategy to cope with the asymmetric state constraints for nonstrict-feedback and nonlinear switched stochastic systems with unknown control directions. Firstly, without requiring piecewise Barrier Lyapunov functions (BLFs), the asymmetric constraint restrictions are unfastened well in the recursive idea according to a series of new-style coordinate transformations. Then, a novel error compensation mechanism based on the state constraint conditions is incorporated into the tracking differentiator (TD) technology to tackle the “differential explosion” problem in the backstepping design, and a low-cost adaptive control strategy under single adaptive law is built to simplify the computation, meanwhile, the control objective is achieved. Followed by the rigorous theoretical proof, the applicability is presented by a practical example.

An Adaptive Threshold Line Segment Feature Extraction Algorithm for Laser Radar Scanning Environments

An accurate map is needed for the autonomous navigation of mobile robots in unknown environments. The application of laser radars has the advantages of high ranging accuracy and long ranging distances. Due to the small amount of data on laser radars and the influence of noise on the sensor itself, these amount to causing problems such as low accuracies of map construction and large positioning errors. Currently, the feature extraction of environmental line segments based on radar scanning data generally adopts the idea of recursion. However, the amount of calculations for applying recursion is large, and the threshold of extracted feature points needs to be set manually. Moreover, the fixed segmentation threshold will cause under-segmentation or over-segmentation. In this paper, an adaptive threshold-based feature extraction method for environmental line segments is proposed. The method denoises the original data first, and then an adaptive threshold of the nearest neighbor algorithm is provided to improve the accuracy of breakpoint judgment; next, the slope difference between adjacent line segments is evaluated according to the line segment fitting error in order to obtain the optimal corner feature. Finally, the point set is segmented to fit line-segment features. Based on actual environment tests, the environmental similarity of the line segment features extracted by the new algorithm in this paper increases by 8.3% compared with the IEPF (Iterative End Point Fit) algorithm. The algorithm avoids recursive operations, improves the efficiency by four times, and meets the real-time requirements of line segment fitting.

Recursive-YOLOv5 Network for Edible Mushroom Detection in Scenes With Vertical Stick Placement

In many rural edible mushroom growing sites, due to their growing environments and economic factors, growers are often unable to use industrial automation to pick edible mushrooms, resulting in losses of hundreds of millions of dollars each year due to missing the optimal picking cycles of edible mushrooms. For this reason, this project aimed to find an object detection algorithm that can be used with industrial cameras to help detect the growth statuses of edible mushrooms in real time and can be applied to future automatic picking machines. In this paper, based on the You Only Look Once version 5 (YOLOv5) network, by introducing the idea of recursion, remerging the first output with the convolutional layer of the backbone part of the network, introducing atrous spatial pyramid pooling (ASPP) instead of SPP (as in the original algorithm), utilizing the complete intersection over union (CIOU) and distance IOU (DIOU) instead of the generalized IOU (GIOU), and employing DIOU_nonmaximum suppression (NMS) instead of the original NMS algorithm, we propose a new deep learning network called Recursive-YOLOv5. This network can effectively identify 98% of edible mushrooms when dealing with large-resolution, small-target situations; this is a 12.87% improvement over the accuracy of YOLOv5X. Although the algorithm proposed in this paper utilizes almost double the parameters of the original network, with today’s computing power and the rapid development of cloud computing, this sacrifice of computing power for accuracy is very cost-effective.

A switching-based state-scaling design for prescribed-time stabilization of nonholonomic systems with actuator dead-zones

Nonholonomic constraint is widespread in many aerospace applications such as space robots, artificial satellites, aircrafts etc. In this paper, the problem of global prescribed-time stabilization is addressed for a category of uncertain nonholonomic constraint systems (namely, nonholonomic systems for short) with actuator dead-zones. To deal with the obstacle that the presence of input dead-zone nonlinearities renders the traditional discontinuous feedback control technique inapplicable to nonholonomic systems, a novel switching-based state-scaling transformation (switching-based-SST) is introduced. This transformation can change the original predefined-time stabilization into the asymptotic stabilization of the transformed one. Under such new framework, a state feedback controller that achieves the prescribed-time convergence performance is developed by using the recursive idea. Finally, a practical application to a unicycle-type mobile robot is presented to confirm the validity of the proposed method.

Global Prescribed-Time Controller Design for p-Normal Switched Nonlinear Systems With Dead-Zone Inputs

The global stabilization controller design is addressed in this paper for a kind of uncertain switched nonlinear systems (SNSs) in p-normal form. Notably, the study possess two significant features: the system under investigation is subject to the dead-zone inputs, and the system states are expected to be driven to zero in prescribed finite time. To do this, a novel time-varying scaling transformation (TVST), which can be used to change the original prescribed-time stabilization into the asymptotic stabilization of transformed one, is first recommended. Then, with the aid of the common Lyapunov function (CLF) technique, the state feedback stabilization within prescribed-time of SNSs is established by using the recursive idea. Finally, the effectiveness of given control method is confirmed by simulation results of a liquid-level system.

Design and Simulation of Two Elements Fractal Tree Antenna Arrays

Fractal reception apparatuses have been appeared to exhibit monotonous multi-band or log-intermittent conduct that has been ascribed to the self-comparable scale factor of the recieving wire's geometry. This geometry, which has been utilized to display complex articles found in nature, for example, mists and coastlines, has space filling properties that can be used to scale down reception apparatuses. These exceptional properties of fractals have been abused to build up another class of recieving wire component plans to have a few profoundly attractive properties, including multiband execution, low side flap levels, and its capacity to create quick shaft framing calculations dependent on the recursive idea of fractals. There are a few focal points of these fractal gadgets including decrease of full frequencies, littler size and broadband width. In this paper, another structure of fractal tree recieving wire Arrays dependent on ternary fractal tree geometry for meet the addition or radiation design prerequisites is proposed.Farctal tree radio wire exhibits are plan with two for gain improvement and radiation pattern.Fractal tree reception apparatus clusters upgrade the increase upto 10 dB.

A Compact Recursive Dense Convolutional Network for image classification

In general, the deeper the convolutional network is, the higher the accuracy will be. However, when the depth of the network increases, the number of parameters (weights and bias) will increase quickly, which requires a lot of storage space when it is applied in real life. Considering the parameters’ efficiency for the deep network, we propose an improved deep convolutional network, named Recursive Dense Convolutional Network (RDenseNet), inspired by the recursive idea. The proposed RDenseNet still utilizes the dense block in Dense Convolutional Network (DenseNet) as a basic structure, but different from the cascade structure of DenseNet, our proposed RDenseNet uses the output of the dense block as input for the current block again. That is, our proposed RDenseNet turns the cascade structure in DenseNet into a recursive structure, which can reduce the number of parameters that actually need to be stored. Experiments illustrate that our proposed RDenseNet can still keep or exceed the accuracy of some state-of-the-art deep networks with much less parameters.

Hyperspectral image super-resolution using recursive densely convolutional neural network with spatial constraint strategy

Hyperspectral images (HSIs) have been widely applied in real life, such as remote sensing, geological exploration, and so on. Many deep networks have been proposed to raise the resolution of HSIs for their better applications. But training their huge number of model parameters (weights and biases) needs more memory for storage and computation, which may bring some difficulties when they are applied in mobile terminal devices. In order to condense the deep networks and still keep the reconstruction effect, this paper proposes a compact deep network for HSI super-resolution (SR) by fusing the idea of recursion, dense connection, and spatial constraint (SCT) strategy. We name this method as recursive densely convolutional neural network with a spatial constraint strategy (SCT-RDCNN). The proposed method uses a novel designed recursive densely convolutional neural network (RDCNN) to learn the mapping relation between the low-resolution (LR) HSI and the high-resolution (HR) HSI and then adopts the SCT to improve the determined HR HSI. Compared with some existing deep-network-based HSI SR methods, the proposed method can use much less parameters (weight and bias) to attain or exceed the performance of methods with similar convolution layers because of the recursive structure and dense connection. It is significant and meaningful for the practical applications of the network in HSI SR due to the limitations of hardware devices. Some experiments on three HSI databases illustrate that our proposed SCT-RDCNN method outperforms several state-of-the-art HSI SR methods.

Research on settlement particle recognition based on fuzzy comprehensive evaluation method

In order to solve the problems of the laser scattering rate of settlement particles during sedimentation, such as polymerization, coverage, and disappearance, the grayscale characteristics, morphological features, and motion characteristics of the settlement particles are analyzed and studied in this paper. On the basis of these, the recursive idea is applied to the multi-threshold segmentation algorithm with fuzzy 3-partition entropy algorithm, and then, the fuzzy comprehensive evaluation method is used to identify the settlement particles. Finally, the proposed method is implemented in MATLAB 9 and compared with the traditional Kalman filtering and Otsu segmentation algorithm. The experimental results show that the proposed algorithm is better than other algorithms on the ROC curve, and the recognition rate of the settling particles is higher.

Image Segmentation Method for Rail Track Obstacle Based on Improved Fast Binarization

The idea of recursion and limited range is introduced in the traditional fast binarization algorithm. Firstly, according to the characteristics of the fast binarization algorithm, the recursion formulas of four parameters are deduced, and the complexity of the image is calculated . Then fast threshold segmentation of image is finished within the reduced gray level range. Because of considering the four parameters formula of recursive and fully aware of the images complexity, the gray value of the image to be traversed is greatly reduced, and the redundancy of the algorithm is reduced. Finally, the improved algorithm is applied to extraction of railway track obstacle. The experimental results show that this algorithm complexity is lower than traditional algorithm and Otsu, and the computation speed can be improved by about 60%. It can meet the real-time requirement for railway track obstacle image segmentation, and the segmentation effect is almost the same as the traditional one.

GF(3<sup>n</sup>)椭圆曲线密码体制中标量乘快速算法研究

本文研究了特征为3的椭圆曲线密码体制中标量乘的快速算法，并针对底层运算和上层运算分别进行改进。在底层运算中，采用递推归纳、乘法代替求逆、立方代替乘法的思想提出在仿射坐标下直接计算3kP的算法，将求逆运算降至1次；在上层运算中，采用滑动窗口标量乘的方法，既有效减少了非零窗口的长度又减少了算法中3倍点总的运算量。 In this paper we investigate the fast algorithm of scalar multiplication based on Elliptic Curve Cryptography (ECC) over fields of characteristic three, and make improvements both in underlying operations and upper operations respectively. In the underlying operations, we deduce a formula of calculating 3kP directly under the affine coordinates based upon the idea of recursion, trading inversion for multiplication and trading multiplication for cube, which reduces the inversion to once; in the upper operations, we adopt the sliding window scalar multiplication method, which reduces the length of the non-zero windows and the total computations of 3P effectively.

The far side of recursion

Recursion is somewhat of an enigma, and examples used to illustrate the idea of recursion often emphasize three algorithms: Towers of Hanoi, Factorial, and Fibonacci, often sacrificing the exploration of recursive behavior for the notion that a "function calls itself". Very little effort is spent on more interesting recursive algorithms. This paper looks at how three lesser known algorithms of recursion can be used in teaching behavioral aspects of recursion: The Josephus Problem, the Hailstone Sequence and Ackermann's Function.

Elucidating the stop bands of structurally colored systems through recursion

Interference is the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics: specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer structure and solve it using recursion relations. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursion. We compare to experimental data for various beetles, whose optical structure resembles the proposed model. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concept of band structure in the context of the experimentally observed high reflectance and iridescent appearance of structurally colored beetles.

Unifying Section of Chord Member of Transmission Tower Based on Recursion Method

A unifying section problem of a double circuit power transmissions tower (DCPT)’s chord member was studied in this paper. The collision between the theoretic analysis and practical process in optimization of unifying section was proposed. The bourn of each chord member’s broken position was taken into consideration. The concept of dynamic programming was cited, and a procedure to get all the feasible combination patterns for unifying section was put forward by recursion. The object function which is the combination of the decision making and the state in every phase was set up. The object function value of whole structure can be obtained based on the previous decision of every phase. The optimization value in a decision of the weight of the tower’s chord member was set up though above object function value in a certain combination. At last, the optimization solution is designed via selecting a series of self calling functions on the basis of recursive idea.

Recursion—or, Better Computational Thinking Through Laughter

One of the predictable side effects of writing this column is that on a regular basis—at least several times a year—I am compelled to come up with a topic, a computational diversion. I would like to pretend that this process is structured, impeccably organized, planned months in advance; but as anyone who knows me could attest, things just do not work out that way. The result is that I am periodically on the lookout for some subject matter that could make for a column—and more especially, a subject that has not already been done to death in recreational math circles. Last weekend, I was in this sort of quietly panicked condition when I took my 7-yearold son to see the animated movie Kung Fu Panda. (We both enjoyed it.) At one point during the cartoon, the title creature is excitedly taking an introductory tour of his martial arts school, marveling at all the ancient kung fu-related artifacts; and he comes upon a beautifully rendered Chinese painting. The panda exclaims, ‘‘I’ve only seen paintings of that painting!’’ The line brought an appreciative laugh from the audience (including, interestingly, the children as well); and it occurred to me that there might be a relatively unexplored subject for discussion in this. After all, there is currently a push in computer science circles to promote ‘‘computational thinking’’ (a notion whose definition is itself energetically debated). At the same time, one of the purportedly difficult topics in computational thinking is mastery of the idea of recursion. The panda’s line—and the laugh that it received—suggests that people already have an aesthetic sense of the oddness or appeal of recursive thinking. And the panda’s line is, undeniably, recursive: once you have seen a painting of a painting, you could see a painting of a painting of a painting, and so forth. Recursion is funny, in many senses of the word. I am not entirely sure why this is so: after all, conditionals, and while loops, and compound data structures, and variables are not especially funny. But recursion is. Since arriving at this insight, I have been trying to collect a variety of instances in literature, plays, movies, to illustrate this sort of enjoyably emotionally charged computational thinking. I ask readers to help me in adding to this collection, and will print

Recursive and Fast Recursive Capon Spectral Estimators

The Capon algorithm, which was originally proposed for wavenumber estimation in array signal processing, has become a powerful tool for spectral analysis. Over several decades, a significant amount of research attention has been devoted to the estimation of the Capon spectrum. Most of the developed algorithms thus far, however, rely on the direct computation of the inverse of the input correlation (or covariance) matrix, which can be computationally very expensive particularly when the dimension of the matrix is large. This paper deals with fast and efficient algorithms in computing the Capon spectrum. Inspired from the recursive idea established in adaptive signal processing theory, we first derive a recursive Capon algorithm. This new algorithm does not require an explicit matrix inversion, and hence it is more efficient to implement than the direct-inverse approach. We then develop a fast version of the recursive algorithm based on techniques used in fast recursive least-squares adaptive algorithms. This new fast algorithm can further reduce the complexity of the recursive Capon algorithm by an order of magnitude. Although our focus is on the Capon spectral estimation, the ideas shown in this paper can also be generalized and applied to other applications. To illustrate this, we will show how to apply the recursive idea to the estimation of the magnitude squared coherence function, which plays an important role for problems like time-delay estimation, signal-to-noise ratio estimation, and doubletalk detection in echo cancellation.

A brief comparison between two programs that compute the static conductance of a disordered two-dimensional tight-binding system

There are two programs in the CPC program library that compute the static conductance of a disordered two-dimensional cluster described by a tight-binding Hamiltonian. The older program uses the Landauer scheme to get the conductance from the transmittance of a cluster attached to two semi-infinite chains that play the role of physical leads. The second program directly uses the Kubo formula to get the conductance of a similar cluster connected to leads of arbitrary width. In both cases, the local Green function should be calculated, but while the first method uses the idea of recursion and implements a set of subroutines to get the desired matrix elements of the resolvent, the second method employs LAPACK subroutines to propagate the self-energy matrix from one side of the cluster to the other. At the end both methods deliver the same numerical answer, with a comparable high precision but at quite different computing speeds. The newer method is typically one order of magnitude quicker thanks to modern methods in linear algebra when just one system is solved, but recursion is advantageous for solving the same systems for several Fermi energies because in this case the slow part of the calculation is done only once.

Induction, recursion, and the Towers of Hanoi

We introduce the idea of recursion through simple examples of Pascal subroutines; and, discounting cases of ‘tail’ recursion (which can be easily recoded as iterative loops, that are generally more efficient), we demonstrate how ‘stacking’ can permit elegant and intellectually satisfying recursive solutions. We also emphasize the equivalence between recursive programming and mathematical induction. We complete our paper with an inductive and recursive discussion of the famous Bramah Temple puzzle, ‘The Towers of Hanoi’.