Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

Advanced Studies for Resolving Nonlinear Dynamic Systems Involving Complexity Based on Systems Thinking for Non-Physicists

There are many examples of nonlinear dynamics, such as food chains or thermodynamic systems within closed-loop systems. In modern physics, these problems have been resolved based on logical thinking by using the chaos theory in statistical physics, which was arranged by classical physicists in the 17th century. However, this is a significantly erroneous problem because, in engineering science, nonlinear dynamics must be resolved and cleared using systems analysis theory based on systems thinking. It is the main concept in a new solution that is studied through interdisciplinary research;it is needed to introduce control theory into physics. In 2015, on the behalf of physicists, the author successfully resolved and achieved a new solution, which is a significant achievement in modern science. Unfortunately, physicists have not welcomed it because it is disadvantageous to them, similar to the Copernican theory. So, they themselves became outsiders. If so, non-physicists need to follow their chaos theory in physics unless they do not clarify their solution;moreover, non-physicists on behalf of physicists can use their own new solution without risk. Hence, all scientists need to learn the systems analytic method in engineering.

Dissipative-based adaptive neural control for nonlinear systems

A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.

An Adaptive Real-Time Third Order Sliding Mode Control for NonlinearSystems

As most real world systems are significantly nonlinear in nature,developing robust controllers have attracted many researchers for decades.Robust controllers are the controllers that are able to cope with the inherent uncertainties of the nonlinear systems.Many control methods have been developed for this purpose.Sliding mode control(SMC)is one of the most commonly used methods in developing robust controllers.This paper presents a higher order SMC(HOSMC)approach to mitigate the chattering problem of the traditional SMC techniques.The developed approach combines a third order SMC with an adaptive PID(proportional,integral,derivative)sliding surface to overcome the drawbacks of using PID controller alone.Moreover,the presented approach is capable of adaptively tuning the controller parameters online to best fit the real time applications.The Lyapunov theory is used to validate the stability of the presented approach and its feasibility is tested through a comparison with other conventional SMC approaches.

New Systems Solution for Resolving Nonlinear Dynamics Based on Systems Thinking

This study describes a new solution for resolving nonlinear dynamics. Surprisingly, it has been resolved and completed by non-physicists on behalf of physicists in 2021. It is a revolutionary solution like the Copernican Theory, which is perfectly different from the existing chaos theory. In the past, nonlinear dynamics has been analyzed using logical solutions, such as chaos theory, based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings other scientists. It means that the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the future.

Evaluation of the Validity of Chaos Theory Based on Systems Thinking for Non-Physicists

Chaos theory was born in the 18th century, physicists still solve the nonlinear dynamic systematic problems within closed-loop systems such as ecosystems, three-body problems involving complexity, and others. Moreover, it has been resolved these problems based on logical thinking using logical solutions with algebra and statistics such as chaos theory. The reason is determinism. Nevertheless, other scientists do not welcome the old chaos theory because the chaos theory is very imperfect and vague. Amazingly, in 2021, there is emerged, and an advanced and systematic solution based on system thinking;it was resolved by a non-physicist on behalf of physicists through interdisciplinary science and it is more perfect than the old chaos theory. Therefore, it is similar to the New World discovered by Columbus. This paper will prove that the existing chaos theory is invalid as a new solution emerges. Nevertheless, current physicists avoid approaching this study as much as possible. Therefore, other scientists have no reason to follow their invalid chaos theory unless physicists prove the validity of chaos theory.

Multiple Periodic Solutions for Some Classes of First-Order Hamiltonian Systems

Considering a decomposition R2N=A⊕B of R2N , we prove in this work, the existence of at least (1+dimA) geometrically distinct periodic solutions for the first-order Hamiltonian system Jx'(t)+H'(t,x(t))+e(t)=0 when the Hamiltonian H(t,u+v) is periodic in (t,u) and its growth at infinity in v is at most like or faster than |v|a, 0≤ae is a forcing term. For the proof, we use the Least Action Principle and a Generalized Saddle Point Theorem.

Support Vector Machine-Based Nonlinear System Modeling and Control

This paper provides an introduction to a support vector machine, a new kernel-based technique introduced in statistical learning theory and structural risk minimization, then presents a modeling-control framework based on SVM. At last a numerical experiment is taken to demonstrate the proposed approach's correctness and effectiveness.

BIFURCATION IN A NONLINEAR DUFFING SYSTEM WITHMULTI-FREQUENCY EXTERNAL PERIODIC FORCES

By introducing nonlinear frequency, using Floquet theory and referring to the characteristics of the solution when it passes through the transition boundaries, all kinds of bifurcation modes and their transition boundaries of Duffing equation with two periodic excitations as well as the possible ways to chaos are studied in this paper.

Unified Control Theory from PID to ACPID

To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.

The CP^1 nonlinear sigma model with ChernSimons term in the Faddeev-Jachiw quantization formalism

Using the Faddeev-Jackiw （FJ） quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac＇s method.

基于灰色遗传神经网络的建筑工程造价估算预测

投资估算是项目建议书和可行性研究报告的重要组成部分,是项目投资决策的主要依据之一。项目估算准确性直接影响设计概算与施工图预算的编制。估算的影响因素与其结果之间存在复杂的非线性映射关系,传统数学方法用于解决非线性映射问题时具有很大的局限性。为了提高投资估算的准确性,基于遗传BP神经网络,对误差反向传播机理进行深度分析,引入灰色系统理论,得到样本数据之间变化规律以及弱化适应度函数值的波动性,建立了灰色遗传神经网络预测模型。并对已有样本数据进行仿真,结果显示灰色遗传神经网络模型误差均值为1.54%,优于GM(1,1)预测模型、标准BPNN模型、GA-BPNN模型。验证了文中所建立的模型在工程估价中的有效性,对工程建设成本控制具有一定的实际意义。

Koopman原理内嵌MLP神经网络模型驱动的电力系统非线性振荡特征分析方法

针对电力系统非线性动态特性表征与物理机理融合不清晰、精度低的问题,提出了一种Koopman原理内嵌多层感知机(MLP)神经网络模型驱动的电力系统非线性特性表征与分析方法。阐明了Koopman算子的基本原理,分析了Koopman算子在非线性系统时序演化中的作用。采用MLP神经网络构建编码、解码映射,进而形成Koopman原理内嵌的神经网络深度学习模型,通过深度学习实现非线性系统“编码映射-线性演化-解码映射”3种结构的演化逼近。分析了将所提方法应用于电力系统动态特性分析的物理机理,建立了所提方法的求解与应用流程。通过单机与4机系统算例对所提方法进行对比验证,结果表明所提方法可以精确表征平衡点稳定域内的系统动态过程,可用于电力系统非线性振荡动态特性解析。

基于混沌云量子蝙蝠CNN-GRU大坝变形智能预报方法研究

针对大坝变形影响因素复杂、精准预报难度较大问题,为了提高在大坝安全管理过程中大坝变形的预报精度,本文从大坝变形非线性动力系统时间序列的强非线性出发,引入深度卷积神经网络,对大坝变形及其空间影响特性进行挖掘,引入门控循环单元,对大坝变形的时域特性进行挖掘,构建应用于大坝变形预报的深度卷积神经网络-门控循环单元大坝变形组合深度学习网络;同时,为了获取深度卷积神经网络-门控循环单元组合网络的最佳超参,引入了混沌云量子蝙蝠算法,建立了基于混沌云量子蝙蝠算法算法的深度卷积神经网络-门控循环单元组合网络超参优选方法;最后,提出了深度卷积神经网络-门控循环单元-混沌云量子蝙蝠算法大坝变形组合深度学习智能预报方法。基于实测数据开展预报研究,对比结果表明:与对比模型相比,提出的深度卷积神经网络-门控循环单元-混沌云量子蝙蝠算法预报方法取得了更精确的预报结果,混沌云量子蝙蝠算法算法用于超参优选获得了更佳的超参组合。

Coordinated Frequency Control for Isolated Power Systems with High Penetration of DFIG-Based Wind Power

This paper proposes a coordinated frequency control scheme for emergency frequency regulation of isolated power systems with a high penetration of wind power.The proposed frequency control strategy is based on the novel nonlinear regulator theory,which takes advantage of nonlinearity of doubly fed induction generators(DFIGs)and generators to regulate the frequency of the power system.Frequency deviations and power imbalances are used to design nonlinear feedback controllers that achieve the reserve power distribution between generators and DFIGs,in various wind speed scenarios.The effectiveness and dynamic performance of the proposed nonlinear coordinated frequency control method are validated through simulations in an actual isolated power grid.

Reliability analysis of multi-degree-of-freedom nonlinear random structure vibration systems with correlation failure modes

Based on the generalized probabilistic finite element method, this paper presents an approximate solution technique for general multi-degree-of-freedom nonlinear random vibration systems with random parameters. The fourth-moment technique, maximum entropy theory and incomplete probability information theory are employed to systematically develop a reliability analysis method for dynamic random structural systems with correlation failure modes under unavailable joint probability density functions of basic random variables. The first passage problem of multi-degree-of-freedom nonlinear random vibration systems is solved.

Bandwidth Based Stability Analysis of Active Disturbance Rejection Control for Nonlinear Uncertain Systems

This paper focuses on the stability analysis of the active disturbance rejection control (ADRC)for a class of uncertain systems.To overcome the difficulty of defining a reasonable Lyapunov function and setting limitations of system parameters,the converse Lyapunov theorem and the disturbance theory are employed.This paper proves that the estimation error of the extended state observer (ESO)and the tracking error of the closed-loop system using ADRC are uniformly ultimately bounded and monotonously diminishing with the increase of their respective bandwidth,so that the stability of the ADRC system could be performed.In order to further illustrate the relationship between the stability range and bandwidths,it analyzes quantitatively the performance of ESO and ADRC based on the root locus and the step response.Finally,an example based on a typical control system is carried out,and simulation results verify the theoretical analysis proved in this paper.

A Family of Reliable H_∞ State-Feedback Controllers for Nonlinear Systems with Strictly Redundant Actuators: the Full Information Case

The paper is concerned with the reliable H ∞ state feedback control and controller parameterization problem for nonlinear systems with strictly redundant actuators. Based on Hamilton Jacobi inequality, the sufficient condition is presented such that the reliable control problem is resolved, and a family of controllers is given such that the resulting closed loop systems are asymptotically stable and their L 2 gain is limitable not only when all actuators are operational but also when any one,but only one of actuators experiences an outage. The results of this paper provide a deep insight into the synthesis of the reliable nonlinear H ∞ state feedback.

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.

Controllability of Nonlinear Discrete Systems with Degeneracy

This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.