In this paper, an adaptive dynamic control scheme based on a fuzzy neural network is presented, that presents utilizes both feed-forward and feedback controller elements. The former of the two elements comprises a neu...In this paper, an adaptive dynamic control scheme based on a fuzzy neural network is presented, that presents utilizes both feed-forward and feedback controller elements. The former of the two elements comprises a neural network with both identification and control role, and the latter is a fuzzy neural algorithm, which is introduced to provide additional control enhancement. The feedforward controller provides only coarse control, whereas the feedback controller can generate on-line conditional proposition rule automatically to improve the overall control action. These properties make the design very versatile and applicable to a range of industrial applications.展开更多
System Identification becomes very crucial in the field of nonlinear and dynamic systems or practical systems.As most practical systems don’t have prior information about the system behaviour thus,mathematical modell...System Identification becomes very crucial in the field of nonlinear and dynamic systems or practical systems.As most practical systems don’t have prior information about the system behaviour thus,mathematical modelling is required.The authors have proposed a stacked Bidirectional Long-Short Term Memory(Bi-LSTM)model to handle the problem of nonlinear dynamic system identification in this paper.The proposed model has the ability of faster learning and accurate modelling as it can be trained in both forward and backward directions.The main advantage of Bi-LSTM over other algorithms is that it processes inputs in two ways:one from the past to the future,and the other from the future to the past.In this proposed model a backward-running Long-Short Term Memory(LSTM)can store information from the future along with application of two hidden states together allows for storing information from the past and future at any moment in time.The proposed model is tested with a recorded speech signal to prove its superiority with the performance being evaluated through Mean Square Error(MSE)and Root Means Square Error(RMSE).The RMSE and MSE performances obtained by the proposed model are found to be 0.0218 and 0.0162 respectively for 500 Epochs.The comparison of results and further analysis illustrates that the proposed model achieves better performance over other models and can obtain higher prediction accuracy along with faster convergence speed.展开更多
The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is define...The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.展开更多
The mechanism and the course of two_dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically. By extending the Lotka_Volterra model from the viewpoint of biomechanics, it develo...The mechanism and the course of two_dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically. By extending the Lotka_Volterra model from the viewpoint of biomechanics, it developed new models of two_dimensional nonlinear autonomous and nonautonomous dynamic systems, with its equilibrium point's stability and the existence and stability of its periodical solutions analyzed, and did numerical simulation experiments on its dynamics course. The results show that efficiency of interaction between two populations, time_varying effort, and change direction of action coefficient and reaction coefficient have important influences on the stability of dynamic system, that too large or too small interspecific interaction efficiency and contrary change direction of action coefficient and reaction coefficient may result in the nonstability of the system, and thus it is difficult for two populations to coexist, and that time_varying active force contributes to system stability.展开更多
A computation algorithm based on the Poincaré Mapping in combination with Pseudo_Arc Length Continuation Method is presented for calculating the unstable response with saddle_node bifurcation, and the singularity...A computation algorithm based on the Poincaré Mapping in combination with Pseudo_Arc Length Continuation Method is presented for calculating the unstable response with saddle_node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that this method is effective in analysis of nonlinear dynamic system with saddle_node bifurcations.展开更多
The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is estab...The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.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 mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the a...A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.展开更多
Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dam...Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers(SFDs),and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied.Effects of the translational accelerative motions,the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated.The results show that,due to the nonlinear coupled effects among the rotor,ball bearings and SFDs,within the first bending resonance region,responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon,amplitude jumping phenomenon and non-synchronous vibration.Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region.The pitching angular motion mainly affects rotational vibration of the rotor system,and thus further induces their transverse vibrations.For the pitching flight with combined translational and angular motions,a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system,in which one response displays small amplitude and synchronous vibration,and the other shows large amplitude and non-synchronous vibration.展开更多
The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into considera...The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.展开更多
This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topol...This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.展开更多
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital ...The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.展开更多
Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based c...Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.展开更多
Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coup...Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.展开更多
This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The pap...This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.展开更多
An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this pa...An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.展开更多
Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The fin...Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.展开更多
Combining the field monitoring results of a deep-buried tunnel in Chongqing,the dynamic characteristics of the surrounding rock system under high in situ stress wasanalyzed by phase space reconstruction, calculating c...Combining the field monitoring results of a deep-buried tunnel in Chongqing,the dynamic characteristics of the surrounding rock system under high in situ stress wasanalyzed by phase space reconstruction, calculating correlation dimension, Kolmogoroventropy and largest Lyapunov exponents.Both the Kolmogorov entropy and largestLyapunov exponents show that the surrounding rock system is a chaotic one.Based onthis, a local model was applied to predict surrounding rock displacement, and a nonlineardynamic model was derived to forecast the interaction of the surrounding rock and supportstructure.The local method was found to have an extremely small total error.Also, thenonlinear dynamic model forecasting curves agree with the monitoring ones very well.It isproved that the nonlinear dynamic characteristic study is very important in analyzing rockstability and predicting the evolution of rock systems.展开更多
Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite e...Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.展开更多
This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under par...This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.展开更多
基金China Postdoctoral Science Foundation and Natural Science of Heibei Province!698004
文摘In this paper, an adaptive dynamic control scheme based on a fuzzy neural network is presented, that presents utilizes both feed-forward and feedback controller elements. The former of the two elements comprises a neural network with both identification and control role, and the latter is a fuzzy neural algorithm, which is introduced to provide additional control enhancement. The feedforward controller provides only coarse control, whereas the feedback controller can generate on-line conditional proposition rule automatically to improve the overall control action. These properties make the design very versatile and applicable to a range of industrial applications.
文摘System Identification becomes very crucial in the field of nonlinear and dynamic systems or practical systems.As most practical systems don’t have prior information about the system behaviour thus,mathematical modelling is required.The authors have proposed a stacked Bidirectional Long-Short Term Memory(Bi-LSTM)model to handle the problem of nonlinear dynamic system identification in this paper.The proposed model has the ability of faster learning and accurate modelling as it can be trained in both forward and backward directions.The main advantage of Bi-LSTM over other algorithms is that it processes inputs in two ways:one from the past to the future,and the other from the future to the past.In this proposed model a backward-running Long-Short Term Memory(LSTM)can store information from the future along with application of two hidden states together allows for storing information from the past and future at any moment in time.The proposed model is tested with a recorded speech signal to prove its superiority with the performance being evaluated through Mean Square Error(MSE)and Root Means Square Error(RMSE).The RMSE and MSE performances obtained by the proposed model are found to be 0.0218 and 0.0162 respectively for 500 Epochs.The comparison of results and further analysis illustrates that the proposed model achieves better performance over other models and can obtain higher prediction accuracy along with faster convergence speed.
文摘The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.
文摘The mechanism and the course of two_dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically. By extending the Lotka_Volterra model from the viewpoint of biomechanics, it developed new models of two_dimensional nonlinear autonomous and nonautonomous dynamic systems, with its equilibrium point's stability and the existence and stability of its periodical solutions analyzed, and did numerical simulation experiments on its dynamics course. The results show that efficiency of interaction between two populations, time_varying effort, and change direction of action coefficient and reaction coefficient have important influences on the stability of dynamic system, that too large or too small interspecific interaction efficiency and contrary change direction of action coefficient and reaction coefficient may result in the nonstability of the system, and thus it is difficult for two populations to coexist, and that time_varying active force contributes to system stability.
文摘A computation algorithm based on the Poincaré Mapping in combination with Pseudo_Arc Length Continuation Method is presented for calculating the unstable response with saddle_node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that this method is effective in analysis of nonlinear dynamic system with saddle_node bifurcations.
文摘The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.
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>
基金supported in part by the Open Research Funds of BACC-STAFDL of China under Grant No.2015afdl010the National Natural Science Foundation of China under Grant No.61673282the PCSIRT16R53
文摘A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramér-Rao inequality. The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously. Moreover, the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems. Finally, the lower bound is evaluated by a typical example in target tracking. It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques, and the colored noise has a significantly effect on the lower bound and the performance of filters.
基金the National Key Basic Research Program of China(No.2015CB057400)the National Natural Science Foundation of China(Nos.11672201 and 11872045)the Major Special Basic Research Projects for Aeroengines and Gas Turbines(No.2017-IV-0008-0045)。
文摘Aero-engine rotor systems installed in aircraft are considered to have a base motion.In this paper,a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers(SFDs),and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied.Effects of the translational accelerative motions,the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated.The results show that,due to the nonlinear coupled effects among the rotor,ball bearings and SFDs,within the first bending resonance region,responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon,amplitude jumping phenomenon and non-synchronous vibration.Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region.The pitching angular motion mainly affects rotational vibration of the rotor system,and thus further induces their transverse vibrations.For the pitching flight with combined translational and angular motions,a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system,in which one response displays small amplitude and synchronous vibration,and the other shows large amplitude and non-synchronous vibration.
基金This project is supported by National Natural Science Foundation of China (No.50275116) National 863 of China(No.2002AA414060, No.2002AA-503020).
文摘The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.
基金co-supported by the Key-area Research and Development Program of Guangdong ProvinceChina(No.2019B090915001)+2 种基金National Key R&D Program of China(No.2018YFB1308000),National Natural Science Funds of China(Nos.61772508,U1913202,U1813205,U1713213)CAS Key Technology Talent Program,Shenzhen Technology ProjectChina(Nos.JCYJ20180507182610734,JSGG20191129094012321).
文摘This paper tackles the robust leaderless Time-Varying Formation(TVF)control problem for the Unmanned Aerial Vehicle(UAV)swarm system with Lipschitz nonlinear dynamics,external disturbances and directed switching topologies.In comparison with the previous achievements on formation control problems,the UAV swarm system with Lipschitz nonlinear dynamics can accomplish the pre-designed TVF while tracking a pre-given trajectory which is produced by a virtual leader UAV in the presence of external disturbances.Firstly,by applying the consensus theory,a TVF controller is developed with the local neighborhood status information,the errors of real time status of all UAVs,the expected formation configuration and the pre-given trajectory under directed switching topologies.Secondly,through a certain matrix variable substitution,the UAV swarm system formation control issue is transformed into a lower dimensional asymptotically stable control issue.Thirdly,by introducing the minimum dwell time,the design steps of formation control algorithm are further acquired.In the meantime,the stability of the UAV swarm system is analyzed through the construction of a piecewise continuous Lyapunov functional and via the Linear Matrix Inequalities(LMIs)method.Finally,the comparison results of a numerical simulation are elaborated to verify the validity of the proposed approach.
基金supported by the National Natural Science Foundation of China(Nos.11002068 and11202094)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(No.0113Y01)the Priority Academic Program of Jiangsu Higher Education Institutions
文摘The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.
文摘Incremental Nonlinear Dynamic Inversion(INDI)is a control approach that has gained popularity in flight control over the past decade.Besides the INDI law,several common additional components complement an INDI-based controller.This paper,the second part of a two-part series of surveys on INDI,aims to summarize the modern trends in INDI and its related components.Besides a comprehensive components specification,it addresses their most common challenges,compares different variants,and discusses proposed advances.Further important aspects of INDI are gain design,stability,and robustness.This paper also provides an overview of research conducted concerning these aspects.This paper is written in a tutorial style to familiarize researchers with the essential specifics and pitfalls of INDI and its components.At the same time,it can also serve as a reference for readers already familiar with INDI.
基金supported by the National Key Research and Development Program of China(No.2022YFB3203600)the National Natural Science Foundation of China(Nos.12202355,12132013,and 12172323)the Zhejiang Provincial Natural Science Foundation of China(No.LZ22A020003)。
文摘Due to scale effects,micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications.This review focuses on mode-coupled micromechanical resonators,highlighting the latest advancements in four key areas:internal resonance,synchronization,frequency combs,and mode localization.The origin,development,and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated,with the goal of inspiring new ideas and directions for researchers in this field.
基金This study was supported by the National Key Basic Research and Development Project of China 2004CB418303 the National Natural Science foundation of China under Grant Nos. 40305012 and 40475027Jiangsu Key Laboratory of Meteorological Disaster KLME0601.
文摘This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.
基金the National Natural Science Foundation of China(Nos.11772293 and12072312)Zhejiang Science and Technology Project(No.2019C03129)。
文摘An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.
文摘Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.
基金Supported by the New Century Excellent Talent Foundation from MOE of China(NCET-09-0844)the National Natural Science Foundation of China(50804060,50621403)
文摘Combining the field monitoring results of a deep-buried tunnel in Chongqing,the dynamic characteristics of the surrounding rock system under high in situ stress wasanalyzed by phase space reconstruction, calculating correlation dimension, Kolmogoroventropy and largest Lyapunov exponents.Both the Kolmogorov entropy and largestLyapunov exponents show that the surrounding rock system is a chaotic one.Based onthis, a local model was applied to predict surrounding rock displacement, and a nonlineardynamic model was derived to forecast the interaction of the surrounding rock and supportstructure.The local method was found to have an extremely small total error.Also, thenonlinear dynamic model forecasting curves agree with the monitoring ones very well.It isproved that the nonlinear dynamic characteristic study is very important in analyzing rockstability and predicting the evolution of rock systems.
基金Project supported by National Natural Science Foundation of China （Grant No. 50275116）, and National High-Technology Research and Development Program of China （ Nos. 2002AA414060, 2002AA503020）
文摘Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.
基金supported by the National Natural Science Foundation of China (Grant No.60704037)the Natural Science Foundation of Hebei Province,China (Grant No.F2010001317)the Doctor Foundation of Yanshan University of China (Grant No.B451)
文摘This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.
