Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping

Peng, Xiaoming; Zheng, Xiaoxiao; Shang, Yadong

doi:10.3934/math.2018.4.514

Cited by 12 publications

(13 citation statements)

References 19 publications

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“…As is well known, most physical systems usually suffer from system uncertainty, for example, parametric uncertainty, modeling error, or external disturbance, which will decrease the control performance or even leads to instability of the controlled system [9][10][11][12][13][14][15][16][17][18][19][20][21]. Thus, the ABC method usually requires cancelation of the nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Adaptive dynamic surface control of parametric uncertain and disturbed strict-feedback nonlinear systems

Wang

2019

Adv Differ Equ

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The construction of backstepping control input needs the derivative of the virtual controller to be available. However, this requirement usually makes the implementation of the controller very difficult and complicated. To overcome this problem, in this paper, an adaptive dynamic surface control (ADSC) is proposed for a class of strict-feedback nonlinear systems with parametric uncertainty and external disturbance. In each step of the backstepping control design, the virtual control input is estimated by an auxiliary signal which is generated by a proposed dynamic surface. This signal's derivative is easy to obtain, so it is not necessary to achieve the derivative of the virtual control input. By using the Lyapunov stability theorem, an ADSC has been established to guarantee the boundedness of all signals and the convergence of the tracking errors. Finally, a simulation example is given to indicate the effectiveness of our control approach.

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Section: Introductionmentioning

confidence: 99%

Adaptive dynamic surface control of parametric uncertain and disturbed strict-feedback nonlinear systems

Wang

2019

Adv Differ Equ

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“…Chaos phenomenon is very common in physical systems (also biology, economics, etc. ), and chaotic systems have become one of the hot topics in the nonlinear systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Since Lorenz discovered the first chaotic attractor, the research on the control and synchronization of chaotic systems has been widely used in many fields.…”

Section: Introductionmentioning

confidence: 99%

Robust adaptive control for fractional-order chaotic systems with system uncertainties and external disturbances

Zhang

Liu

2018

Adv Differ Equ

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This paper studies the robust adaptive control of fractional-order chaotic systems with system uncertainties and bounded external disturbances. Based on a proposed lemma, quadratic Lyapunov functions are used in the stability analysis and fractional-order adaptation laws are designed to update the controller parameters. By employing the fractional-order expansion of classical Lyapunov stability method, a robust controller is designed for fractional-order chaotic systems. The system states asymptotically converge to the origin and all signals in the closed-loop system remain bounded. A counterexample is constructed to show that the fractional-order derivative of a function is less than zero does not mean that the function monotonically decreases (this property appears in many references). Finally, simulation results are presented to confirm our theoretical results.

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“…Websites such as Kaggle plays a great role in promoting the semantic segmentation of images in practical applications and they are good at semantic editing or based on a more realistic scenario, such as MIT and satellite images, etc, for semantic segmentation in the context of deep learning. There are also a large number of valuable research results, which a large number of researchers have done semantic segmentation and realistic applications based on deep learning. Besides, the deep learning techniques have been applied to various fields of image processing such as other works, making a great breakthrough in traditional image processing.…”

Section: Introductionmentioning

confidence: 99%

Research of animals image semantic segmentation based on deep learning

Liu

et al. 2018

Concurrency and Computation

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It is imperative for us to develop the technology of image semantic segmentation with the increasing demand in the image processing. Nowadays, the development of deep learning is of great significance to the improvement of image segmentation. Furthermore, the paper discussed the relationship between image semantic segmentation and animal image research based on the actual situation, and found that animal image processing technology plays a more important role in the field of protecting precious animals. The end-to-end network training of this paper is consisted of Fully Convolutional Network (FCN) for the front end and Conditional Random Fields as Recurrent Neural Networks (CRF-RNN) for the back end via comparing a variety of research methods. The experiments achieved desired outcome for the semantic segmentation of animal images by utilizing Caffe deep learning framework and explained the implementation details from the aspects of training and testing. KEYWORDS Caffe, CRF-RNN, FCN, image semantic segmentation INTRODUCTIONTraditionally, the segmentation of the image is only directly on the surface layer, such as the appearance features based on texture, color, and shape, and they are separated after aggregating the similar features. Among them, the segmentation method based on regions, because the selection of seed points will lead to low efficiency of the algorithm, the segmented results have a certain flaw and can not reach the expected effect. However, the histogram-based threshold segmentation method ignores certain image space information, and it is very likely to segment a discontinuous and meaningless regions, making the segmentation result less satisfying. Therefore, with the demand for image segmentation technology, the semantic segmentation is indispensable.In semantic segmentation, the method of deep learning can be well escaped from the traditional processing methods, and the limitation of using only the underlying features is eliminated, making process in the level of understanding for image. The deep learning framework of Caffe 1 can handle semantic segmentation well. As the number of treasured animals continues to decline, the application of science and technology to protect them is imminent. In particular, it is necessary to collect a set of quality and distinctive animal image data for a specific animal, and the collection of a large number of data sets depends not only on human resources but also requires the support of the relevant sensors, cameras, and other hardware in the wild places it can automatically detect in the field or other places. One solution is to establish a corresponding index for the existing animal picture database. For the protected animal, it can use image processing technology to quickly identify for these animals, and then semantic segmentation is exploited to make a good recognition of animal images. This will not only increase the efficiency of the staff, but reduce the situation in which Concurrency Computat Pract Exper. 2020;32:e4892. wileyonlinelibrary.com/journal/cp...

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Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping

Cited by 12 publications

References 19 publications

Adaptive dynamic surface control of parametric uncertain and disturbed strict-feedback nonlinear systems

Adaptive dynamic surface control of parametric uncertain and disturbed strict-feedback nonlinear systems

Robust adaptive control for fractional-order chaotic systems with system uncertainties and external disturbances

Research of animals image semantic segmentation based on deep learning

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