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 t...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.展开更多
The<span>re are many examples of nonlinear dynamics, such as food chains o</span>r thermodynamic systems within closed-loop systems. In modern physics, these problems have been resolved based on logical th...The<span>re are many examples of nonlinear dynamics, such as food chains o</span>r 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 17<sup>th</sup> 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 <span><span><span style="font-family:;" "="">the</span></span></span><span><span><span style="font-family:;" "=""> main concept in </span></span></span><span><span><span style="font-family:;" "="">a </span></span></span><span><span><span style="font-family:;" "="">new solution that</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span><span><span style="font-family:;" "="">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.</span></span></span>展开更多
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...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.展开更多
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 propose...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.展开更多
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...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.展开更多
This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a re...This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> 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 <span>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</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.展开更多
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...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.展开更多
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...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.展开更多
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 base...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.展开更多
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 bound...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.展开更多
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,s...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.展开更多
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 ...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.展开更多
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...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。展开更多
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 fo...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.展开更多
基金Supported by National Natural Science Foundation of China under Grant No. 61078011
文摘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.
基金National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘The<span>re are many examples of nonlinear dynamics, such as food chains o</span>r 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 17<sup>th</sup> 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 <span><span><span style="font-family:;" "="">the</span></span></span><span><span><span style="font-family:;" "=""> main concept in </span></span></span><span><span><span style="font-family:;" "="">a </span></span></span><span><span><span style="font-family:;" "="">new solution that</span></span></span><span><span><span style="font-family:;" "=""> </span></span></span><span><span><span style="font-family:;" "="">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.</span></span></span>
文摘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.
文摘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.
基金This work is funded by the Deputyship for Research&Innovation,Ministry of Education in Saudi Arabia through the project number(IF-PSAU-2021/01/17796).
文摘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.
文摘This study describes a new solution for resolving nonlinear dynamics. Surpri<span>singly, it has been resolved and completed by non-physicists on behalf of</span> phy<span>sicists in 2021. It is a revolutionary solution like the Copernican Theory,</span> which is perfectly different from the existing chaos theory. In the past, nonlinear <span>dynamics has been analyzed using logical solutions, such as chaos theory,</span> 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 <span>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</span></span><span style="font-family:""> </span><span style="font-family:"">other</span><span style="font-family:""> </span><span style="font-family:"">scientists. It means that</span><span style="font-family:""> <span>the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the fu</span>ture.
文摘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.
文摘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.
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (grant No.41874132)supported by National Natural Science Foundation of China (grant No.11201173)+3 种基金National Natural Science Foundation of China (grant No.11171132,grant No.11571065)Science and Technology Developing Plan of Jilin Province (grant No.20180101220JC)supported by National Basic Research Program of China (grant No.2013CB834100)Jilin DRC (grant No.2017C028-1)。
文摘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.
文摘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.
文摘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。
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.50175043,19990510)the 973 Project Foundation of China(1998020320)the Foundation for University Key Teacher by Ministry of Education of China.
文摘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.