Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter 7 as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate 7, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.

Sign-invariant and Explicit Solutions of Nonlinear Reaction-Diffusion Systems

用症状不变的理论，我们学习非线性的反应散开系统。我们也获得一些新明确的解决方案到非线性的产生系统。

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.

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.

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.

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。

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。

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.

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.

互联网运营商与内容商数据补贴策略优化设计

移动运营商设计并推出数据补贴策略,允许内容提供商为消费者消耗的流量付费,消费者可以免流量费用上网.针对运营商和内容提供商在何种市场条件下应该达成数据补贴策略,建立了一个移动运营商和一个内容提供商或两个内容提供商情境下的经济学分析模型,并考虑了单位流量价格的非线性特征(单位流量价格的折扣率)以及市场规模的动态变化(数据补贴策略对消费者的吸引效果:消费者消耗平均流量的增长率以及消费者数量的增长率).研究表明,为了达成数据补贴策略,运营商给予内容提供商的折扣率不宜过高,内容提供商给予广告商的折扣率同样不宜过高.在数据补贴策略的效果较弱的条件下,内容提供商不采纳数据补贴策略;在数据补贴策略的效果适中的条件下,只有一个内容提供商采纳数据补贴策略;在数据补贴策略的效果较强的条件下,两个内容提供商都会采纳数据补贴策略,并且运营商以及两个内容提供商实现三赢.考虑了数据补贴策略的效果、定价中存在的二级价格歧视现象以及运营商和内容提供商组成的系统的情况,为运营商和内容提供商的策略治理、价格治理以及生态治理提供新视角.

基于学习及演算子理论的非线性系统控制方法综述

基于演算子理论的鲁棒右互质分解(operator-based robust right coprime factorization,ORRCF)方法可以有效地处理非线性系统的鲁棒镇定和跟踪问题。首先,简述本方法相关的概念和定义。其次,基于利普希茨范数、同构思想和无源性控制方法讨论了此方法在非线性系统的鲁棒稳定、鲁棒分解和无源性方面的主要结果。再次,基于指数迭代定理、内模控制方法和滑模控制方法分别讨论了非线性的跟踪、鲁棒容错跟踪和自适应跟踪问题。最后,介绍此方法的实际应用,从而进一步证明其有效性。

突发公共卫生事件情境下基于群体恐慌情绪的应急防护物资管理演化分析

针对突发公共卫生事件下民众对应急防护物资疯狂抢购的问题,以及衍生的供求失衡、价格暴涨、质量良莠不齐等问题,基于演化博弈理论构建政府、企业和民众三方参与的博弈模型。考虑到恐慌情绪对抢购行为的影响,首先刻画了民众在恐慌情绪下的防护物资购买价值;然后结合模型特征,运用非线性系统理论探讨了不同参与主体间的演化机制,得出不同情境下的博弈均衡点和稳定性;最后通过仿真模拟进一步分析不同恐慌强度对参与主体行为演化的影响。研究结果对识别突发公共卫生事件下应急防护物资管理的演化机理具有一定理论价值。

卫星电源控制设备的非线性控制研究

近年来,卫星供配电系统中全调节母线方式供电系统的功率等级不断提升,负载规模和多样性也变得复杂,平台中电源控制设备的控制方法已成为研究热点。首先建立控制设备中双向DC/DC变换器的非线性模型,利用大信号建模分析,结合二阶经典控制系统理论,分析电路参数对系统性能影响;最后,利用Matlab/Simulink仿真平台和搭建试验平台进行验证,所提的控制方法可以准确、快速地实现蓄电池组充放电功率指令跟踪功能,在平台母线电压扰动、负载突变及系统参数偏移等情况下体现出强鲁棒性。

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.