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stability analysis.of a fractional-order cancer model with chaotic dynamics

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International Journal of Biomathematics 2021年第6期14卷 239-261页

作者： Parvaiz Ahmad Naik Jian Zu Mehraj-ud-din Naikt School of Mathematics and Statistics Xi’an Jiaotong University Xi’anShaanxi 710049P.R.China Department of Chemical Engineering College of Engineering Jazan UniversityJazan 45142Saudi Arabia

In this paper,we develop a three-dimensional fractional-order cancer *** proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector *** detailed analysis.of the equilibrium points is ***,the existence and uniqueness of the solution are *** fractional derivative is considered in the Caputo *** simulations are performed to illustrate the effectiveness of the obtained theoretical *** outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic ***,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed ***,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.

关键词： Cancer model Caputo fractional derivative chaos stability analysis.

Invariant subspaces,exact solutions and stability analysis.of nonlinear water wave equations

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Journal of Ocean Engineering and Science 2020年第1期5卷 35-40页

作者： K.Hosseini M.Inc M.Shafiee M.Ilie A.Shafaroody A.Yusuf M.Bayram Department of Mathematics Rasht BranchIslamic Azad UniversityRashtIran Department of Mathematics Science FacultyFirat University23119 ElazigTurkey Young Researchers and Elite Club Rasht BranchIslamic Azad UniversityRashtIran Department of Mathematics Federal University Dutse7156 JigawaNigeria Department of Computer Engineering Istanbul Gelisim UniversityIstanbulTurkey

The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra *** an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally *** the end,the stability analysis.for the NLWWE is investigated through the linear stability scheme.

关键词： Nonlinear water wave equations Invariant subspace scheme Exact solutions stability analysis.

Experimental and Numerical analysis.of Rock Block stability Using a Remotely Positioned Laser Doppler Vibrometer

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Journal of Civil Engineering and Architecture 2014年第5期8卷 624-632页

作者： Guichen Ma Kazuhide Sawada Atsushi Yashima Fumiaki Uehan Osamu Murata Hideki Saito Yasunori Ootsuka Engineering Headquarters O YO Corporation Saitama 331-8688 Japan Department of Civil Engineering Gifu University Gifu 501-1193 Japan Structural Mechanics Laboratory Railway Technical Research Institute Tokyo 185-8540 Japan

This paper examines a new method of evaluating the stability of a rock slope using a remotely positioned LDV （laser Doppler vibrometer）. We conducted an experiment using physical models and performed a numerical analysis.to evaluate the new method. The physical model included：（l） concrete blocks on an artificial soil slope with two block sizes and three slopes; （2） concrete blocks bonded to the concrete base with different contact area. The LDV measurements agreed with conventional seismometer measurements. The dominant frequency of the blocks varied with the stability and dominant frequency and the amplitude varied with the block size. The numerical model was used to examine a concrete block adhered to a concrete base with different contact areas. The dominant frequency of the blocks determined using the numerical model agreed with those obtained from the physical experiments. We analyzed different sized blocks to examine the scaling effects. The dominant frequency of the blocks was inversely related to the block size. These results demonstrated the effectiveness of LDV for evaluating the stability of rock slopes and cleared the block size scaling effects.

关键词： Field measurements risks and hazards rock failure rock mass stability analysis.

Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems

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Journal of Systems Engineering and Electronics 2008年第6期19卷 1203-1207页

作者： Shi Wuxi School of Computer Technology and Automation Tianjin Polytechnic Univ. Tianjin 300160 P. R. China

An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.

关键词： nonlinear discrete-time systems adaptive fuzzy control stability analysis.

State Observer Based Dynamic Fuzzy Logic System for a Class of SISO Nonlinear Systems

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International Journal of Automation and computing 2013年第2期10卷 118-124页

作者： Mohamed Hamdy Department of Industrial Electronics and Control Engineering Faculty of Electronic Engineering Menofia University

This paper presents an observer based dynamic fuzzy logic system （DFLS） scheme for a class of unknown single-input single-output （SISO） nonlinear dynamic systems with external disturbances. The proposed approach does not need the availability of the state variables. Within this scheme, the DFLS is employed to identify the unknown nonlinear dynamic system. The control law and parameter adaptation laws of the DFLS are derived based on Lyapunov synthesis approach. The control law is robustfied in H∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions, it guarantees the boundedness of all the signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. The proposed method is applied to an inverted pendulum system to verify the effectiveness of the proposed algorithms.

关键词： Single-input single-output (SISO) nonlinear system dynamic fuzzy logic system (DFLS) observer Lyapunov synthesis approach stability analysis.

Nonlinear observer-controller design for dynamic positioning of ships

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Journal of Systems Engineering and Electronics 2004年第3期15卷 359-363页

作者：何黎明田作华施颂椒 AutomationDepartment ShanghaiJiaotongUniversityShanghai200030P.R.China

The main focus is nonlinear model-based dynamic positioning (DP) control system design. A nonlinear uniform global exponential stability (UGES) observer produces noise-free estimates of the position, the slowly varying environmental disturbances and the velocity, which are used in a proportional-derivative (PD) + feedforward control law. The stability of this observer-controller system is proved by introducing a specific nonlinear cascaded system. The simulation results have successfully demonstrated the performance of designed DP control system.

关键词： dynamic positioning nonlinear observer nonlinear PD + feedforward control stability analysis.

Adaptive Neural Network Dynamic Surface Control for Perturbed Nonlinear Time-delay Systems

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International Journal of Automation and computing 2012年第2期9卷 135-141页

作者： Geng Ji School of Mathematics and Information Engineering Taizhou University Linhai 317000 PRC

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of ＂explosion of complexity＂ in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of ＂curse of dimensionality＂ and ＂explosion of complexity＂ are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.

关键词： Adaptive control dynamic surface control neural network nonlinear time delay system stability analysis.

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

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International Journal of Automation and computing 2010年第2期7卷 236-246页

作者： Shao-Cheng Tong Ning Sheng Department of Mathematics Liaoning University of Technology Jinzhou 121000 PRC

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

关键词： Fuzzy logic systems nonlinear time-delay systems adaptive backstepping control state observer stability analysis.

Fast adaptive principal component extraction based on a generalized energy function

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Science in China(Series F) 2003年第4期46卷 250-261页

作者：欧阳缮保铮廖桂生 National Key Laboratory of Radar Signal Processing Xidian University Xi'an 710071 China Department of Communication and Information Engineering Guilin University of Electronic Technology Guilin 541004 China

By introducing an arbitrary diagonal matrix, a generalized energy function (GEF) is proposed for searching for the optimum weights of a two layer linear neural network. From the GEF, we derive a recur- sive least squares (RLS) algorithm to extract in parallel multiple principal components of the input covari- ance matrix without designing an asymmetrical circuit. The local stability of the GEF algorithm at the equilibrium is analytically verified. Simulation results show that the GEF algorithm for parallel multiple principal components extraction exhibits the fast convergence and has the improved robustness resis- tance to the eigenvalue spread of the input covariance matrix as compared to the well-known lateral inhi- bition model (APEX) and least mean square error reconstruction (LMSER) algorithms.

关键词： linear neural networks principal component analysis generalized energy function recursive least squares (RLS) algorithm stability analysis.