Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardseq...Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.展开更多
Optimizing the efficiency of traffic flow while minimizing fuel consumption is of significant importance in the context of resource scarcity and environmental preservation.Currently,the two-layer optimization strategy...Optimizing the efficiency of traffic flow while minimizing fuel consumption is of significant importance in the context of resource scarcity and environmental preservation.Currently,the two-layer optimization strategy has been employed in autonomous intersection cooperation problems.The traffic efficiency is optimized on the first layer and energy consumption is optimized on the second layer based on an optimal timetable gained in the first layer.This operation prioritizes traffic efficiency over energy consumption,which may present a limitation in terms of equilibrating them.This paper develops an equilibrium control strategy for autonomous intersection.This control strategy includes vehicle schedule and equilibrium control.A schedule algorithm is initially proposed for platoons,in which the most passing sequence is gained when considering platoon formation.Then,a game deep reinforcement learning model is designed,and an equilibrating control algorithm is proposed,in which equilibrium state can be gained between traffic efficiency and energy consumption.Simulation results demonstrate that the proposed method can equilibrate traffic efficiency and energy consumption to an equilibrium state,as well as reducing trip cost compared with existing methods.展开更多
Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this t...Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this theory, a perfect control method should not only guarantee stability of the system, but also ensure the control-equilibrium of the system. To achieve the control-equilibrium, feed-forward control is required.展开更多
The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analy...The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.展开更多
This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. T...This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.展开更多
By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from ...By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.展开更多
The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if so...The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.展开更多
Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system...Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.展开更多
Steel plate cold common （SPCC） is a Al-killed steel with Ca-treatment. The control of Al2O3 inclusion into low melting point liquid region is beneficial for inclusion removal, cast-ability promotion and defects redu...Steel plate cold common （SPCC） is a Al-killed steel with Ca-treatment. The control of Al2O3 inclusion into low melting point liquid region is beneficial for inclusion removal, cast-ability promotion and defects reduction during rolling. Thus it is essential to understand steel-inclusion equilibrium since inclusion composition is determined by composition of liquid steel directly through steel-inclusion reaction. Thermodynamic calculation software FactSage is performed to understand how to control inclusion composition during ladle furnace （LF） refining, and industrial trials are carried out to verify calculated results. Firstly, target region for controlling CaO-Al2O3-MgO ternary inclusion is analyzed on the basis of the ternary phase diagram and the relationship between activities related to pure solid and activities related to pure liquid was fixed by thermodynamic analysis in order to obtain reliable activities for components of inclusions in the target region by FactSage. In addition, inclusions in steel samples are detected by scanning electron microscopy （SEM） combined with energy dispersive spectroscopy （EDS）. It is found that most of Al2O3 inclusions are modified into lower melting point region but a number of them are still located in high melting point region at the end of LF refining after Ca-treatment. Moreover, the composition of liquid steel equilibrating with liquid CaO-Al2O3-MgO inclusion is obtained by steel-inclusion equilibrium calculation when w[Al]s is approximating 0.03% as： a[O] is 1.0×10-6 to 4.0×10-6, w[Ca] is 20×10-6 to 50×10-6 and w[Mg] is 0.1×10-6 to 3.0×10-6. At last, stability diagrams of various calcium aluminates and CaS are established and they show that liquid calcium aluminate inclusions form when w[Ca] is more than 20×10-6, but CaS precipitation is difficult to prevent because sufficiently low w[S] （〈0.003%） is required.展开更多
Controlling the poloidal field (PF) in the HT-7U superconducting tokamak is critical to the realization of the mission of advanced tokamak research. Plasma start-up, plasma position, shape, current control and plasma ...Controlling the poloidal field (PF) in the HT-7U superconducting tokamak is critical to the realization of the mission of advanced tokamak research. Plasma start-up, plasma position, shape, current control and plasma shape reconstruction have been performed as a part of its design process. The PF coils have been designed to produce a wide range of plasmas. Plasma start-up can be achieved for multiple conditions. Fast controlling coils for plasma position inside the vacuum vessel are used for controlling the plasma vertical position on a short timescale. The PF coils control the plasma current and shape on a slower timescale. VXI (VME bus extensions for Instrumentation) Bus system and DSP (Digital Signal Processor is a basic unit of the feedback control system), the response time of which is about (2-4) ms. The basic unit of this system, the shape-controlling algorithms of a few critical points on plasma boundary and real-time equilibrium fitting (RTEFIT) will be described in this paper.展开更多
This paper focuses on how to determine the instantaneous damping of the semi-active tuned mass damper (SATMD) with continuously variable damping.An off-and-towards-equilibrium (OTE) algorithm is employed to examine th...This paper focuses on how to determine the instantaneous damping of the semi-active tuned mass damper (SATMD) with continuously variable damping.An off-and-towards-equilibrium (OTE) algorithm is employed to examine the control performance of the structure/SATMD system by considering the damping as an assumptive control action.The damping modification of the SATMD is carried out according to the proposed OTE algorithm,which is formulated based on analysis of the structural movement under external excitations,and the measured responses of the structure at every time instant. As examples two numerical simulations of a five-storey and a ten-storey shear structures with a SATMD on the roof are conducted.The effectiveness on vibration reduction of MDOF systems subjected to seismic excitations is discussed.Analysis results show that the behavior of the structure with a SATMD is significantly improved and the feasibility of applying the OTE algorithm to the structural control design of SATMD is also verified.展开更多
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively...This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.展开更多
The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned ana...The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.展开更多
This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generati...This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.展开更多
<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is t...<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction number </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;">R</span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub><span style="font-family:Verdana;">0</span></sub></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> can go down from 3 to 1.7. The pressures on the economic and social situation are rather viable. It is the most suitable for the Malagasy health system. The results proposed are a way to control the spread of the disease and limit its devastation in a country like Madagascar.</span></span></span>展开更多
基金National Natural Science Foundation of China Under Grants No. 50508003 and No.50478042, and A Municipal New Star Plan Program Approved by Beijing Municipal Science & Technology Commission
文摘Traditional control strategies have difficulty handling nonlinear behavior of structures, time variable features and parameter uncertainties of structural control systems under seismic excitation. An off-and-towardsequilibrium （OTE） strategy combined with fuzzy control is presented in this paper to overcome these difficulties. According to the OTE strategy, the control force is designed from the viewpoint of a mechanical relationship between the motions of the structure, the exciting force and the control force. The advantage of the OTE strategy is that it can be used for a variety of control systems. In order to evaluate the performance of the proposed strategy, the seismic performance of a three-story shear building with an Active Tendon System （ATS） using a Fuzzy Logic Controller （FLC） is studied. The main advantage of the fuzzy controller is its inherent robustness and ability to handle any nonlinear behavior of structures. However, there are no design guidelines to set up the corresponding control rule table for a FLC. Based on the proposed strategy for the FLC, a control rule table associated with the building under study is developed, which then allows formation of a detailed algorithm. The results obtained in this study show that the proposed strategy performs slightly better than the linear quadratic regulator （LQR） strategy, while possessing several advantages over the LQR controller. Consequently, the feasibility and validity of the proposed strategy are verified.
基金supported in part by the National Key R&D Program of China(2022YFB2502904)the Natural Science Foundation of Hubei Province for Distinguished Young Scholars(2022CFA091)+2 种基金the Key R&D Program of Hubei Province(2021BAA0202021BAA181)Wuhan Science and Technology Major Project(2022013702025184)the Natural Science Foundation of Chongqing,China(CSTB2023NSCQ-MSX0932).
文摘Optimizing the efficiency of traffic flow while minimizing fuel consumption is of significant importance in the context of resource scarcity and environmental preservation.Currently,the two-layer optimization strategy has been employed in autonomous intersection cooperation problems.The traffic efficiency is optimized on the first layer and energy consumption is optimized on the second layer based on an optimal timetable gained in the first layer.This operation prioritizes traffic efficiency over energy consumption,which may present a limitation in terms of equilibrating them.This paper develops an equilibrium control strategy for autonomous intersection.This control strategy includes vehicle schedule and equilibrium control.A schedule algorithm is initially proposed for platoons,in which the most passing sequence is gained when considering platoon formation.Then,a game deep reinforcement learning model is designed,and an equilibrating control algorithm is proposed,in which equilibrium state can be gained between traffic efficiency and energy consumption.Simulation results demonstrate that the proposed method can equilibrate traffic efficiency and energy consumption to an equilibrium state,as well as reducing trip cost compared with existing methods.
文摘Not so much had been talked about equilibrium in control area. On the basis of the phenomenon of balance, the concept of control-equilibrium and control-equilibrium of a control system is proposed. According to this theory, a perfect control method should not only guarantee stability of the system, but also ensure the control-equilibrium of the system. To achieve the control-equilibrium, feed-forward control is required.
基金Hie-Tch Research and Development Program of China (2002AA723011)
文摘The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.
文摘This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.
基金This work was supported by the National Natural Science Foundation of China under grant No.50075053the Emphasized Item of Development Funds of Science and Technology of Shanghai City,China(No.03H201).
文摘By combining the α/γ interface migration and the carbon diffusion at the interface in Fe-C alloys, a mathematical model is constructed to describe the mixed-control mechanism for proeutectoid ferrite formation from austenite. In this model, the α/γ interface is treated as non-equilibrium interface, i.e., the carbon concentration of austenite at γ/α interface is obtained through theoretical calculation, instead of that assumed as the local equilibrium concentration. For isothermal precipitation of ferrite in Fe-C alloys, the calculated results show that the rate of interface migration decreases monotonically during the whole process, while the rate of carbon diffusion from γ/α interface into austenite increases to a peak value and then decreases. The process of ferrite growth may be considered as composed of three stages: the period of rapid growth, slow growth and finishing stage. The results also show that the carbon concentration of austenite at γ/α interface could not reach the thermodynamic equilibrium value even at the last stage of ferrite growth.
文摘The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
基金supported by the National High Technology Research and Development Program of China (Grant No. 2007AA041401)Tianjin Natural Science Foundation,China (Grant Nos. 08JCZDJC18600 and 09JCZDJC23900)the University Science and Technology Development Foundation of Tianjin City,China (Grant No. 2006ZD32)
文摘Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.
基金Item Sponsored by National Natural Science Foundation of China(61271303)
文摘Steel plate cold common （SPCC） is a Al-killed steel with Ca-treatment. The control of Al2O3 inclusion into low melting point liquid region is beneficial for inclusion removal, cast-ability promotion and defects reduction during rolling. Thus it is essential to understand steel-inclusion equilibrium since inclusion composition is determined by composition of liquid steel directly through steel-inclusion reaction. Thermodynamic calculation software FactSage is performed to understand how to control inclusion composition during ladle furnace （LF） refining, and industrial trials are carried out to verify calculated results. Firstly, target region for controlling CaO-Al2O3-MgO ternary inclusion is analyzed on the basis of the ternary phase diagram and the relationship between activities related to pure solid and activities related to pure liquid was fixed by thermodynamic analysis in order to obtain reliable activities for components of inclusions in the target region by FactSage. In addition, inclusions in steel samples are detected by scanning electron microscopy （SEM） combined with energy dispersive spectroscopy （EDS）. It is found that most of Al2O3 inclusions are modified into lower melting point region but a number of them are still located in high melting point region at the end of LF refining after Ca-treatment. Moreover, the composition of liquid steel equilibrating with liquid CaO-Al2O3-MgO inclusion is obtained by steel-inclusion equilibrium calculation when w[Al]s is approximating 0.03% as： a[O] is 1.0×10-6 to 4.0×10-6, w[Ca] is 20×10-6 to 50×10-6 and w[Mg] is 0.1×10-6 to 3.0×10-6. At last, stability diagrams of various calcium aluminates and CaS are established and they show that liquid calcium aluminate inclusions form when w[Ca] is more than 20×10-6, but CaS precipitation is difficult to prevent because sufficiently low w[S] （〈0.003%） is required.
基金This work was supported by the National Meg-science Engineering Project of the Chinese Government
文摘Controlling the poloidal field (PF) in the HT-7U superconducting tokamak is critical to the realization of the mission of advanced tokamak research. Plasma start-up, plasma position, shape, current control and plasma shape reconstruction have been performed as a part of its design process. The PF coils have been designed to produce a wide range of plasmas. Plasma start-up can be achieved for multiple conditions. Fast controlling coils for plasma position inside the vacuum vessel are used for controlling the plasma vertical position on a short timescale. The PF coils control the plasma current and shape on a slower timescale. VXI (VME bus extensions for Instrumentation) Bus system and DSP (Digital Signal Processor is a basic unit of the feedback control system), the response time of which is about (2-4) ms. The basic unit of this system, the shape-controlling algorithms of a few critical points on plasma boundary and real-time equilibrium fitting (RTEFIT) will be described in this paper.
文摘This paper focuses on how to determine the instantaneous damping of the semi-active tuned mass damper (SATMD) with continuously variable damping.An off-and-towards-equilibrium (OTE) algorithm is employed to examine the control performance of the structure/SATMD system by considering the damping as an assumptive control action.The damping modification of the SATMD is carried out according to the proposed OTE algorithm,which is formulated based on analysis of the structural movement under external excitations,and the measured responses of the structure at every time instant. As examples two numerical simulations of a five-storey and a ten-storey shear structures with a SATMD on the roof are conducted.The effectiveness on vibration reduction of MDOF systems subjected to seismic excitations is discussed.Analysis results show that the behavior of the structure with a SATMD is significantly improved and the feasibility of applying the OTE algorithm to the structural control design of SATMD is also verified.
基金Project supported by the National Natural Science Foundation of China(Grant No.61403143)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030313739)+1 种基金the Science and Technology Foundation Program of Guangzhou City,China(Grant No.201510010124)the Excellent Doctorial Dissertation Foundation of Guangdong Province,China(Grant No.XM080054)
文摘This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.
文摘The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.
基金supported by the National Natural Science Foundation of China (11072002,10832006)
文摘This paper studies the problem of coordinated motion generation for a group of rigid bodies. Two classes of coordinated motion primitives, relative equilibria and ma- neuvers, are given as building blocks for generating coordi- nated motions. In a motion-primitive based planning frame- work, a control method is proposed for the robust execution of a coordinated motion plan in the presence of perturba- tions. The control method combines the relative equilibria stabilization with maneuver design, and results in a close- loop motion planning framework. The performance of the control method has been illustrated through a numerical sim- ulation.
文摘<span style="font-family:Verdana;">For Madagascar, with the uncertainty over vaccines against the novel coronavirus 2019 and its variants, non-pharmaceutical approach is widely used. Our objective is to propose a mathematical control model which will serve as a tool to help decision-makers in the strategy to be implemented to better face the pandemic</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> By separating asymptomatic cases which are often not reported and symptomatic who are hospitalized after tests;we develop a mathematical model of the propagation of covid-19 in Madagascar, by integrating control strategies. We study the stability of the model by expressing the basic reproduction number using the next-generation matrix. Simulation with different parameters shows the effects of non-pharmaceutical measures on the speed of the disease spread. By integrating a control parameter linked to compliance with barrier measures in the virus propagation equation, we were able to show the impacts of the implementation of social distancing measures on the basic reproduction number. The strict application of social distancing measures and total confinement </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> unfavorable for economic situation even if they allow the contamination to be reduced quickly. Without any restrictions, the disease spreads at high speed and the peak is reached fairly quickly. In this condition, hospitals are overwhelmed and the death rate increases rapidly. With 50% respect for non-pharmaceutical strategies such as rapid detection and isolation of positive cases and barrier gestures;the basic reproduction number </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;">R</span></i></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub><span style="font-family:Verdana;">0</span></sub></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> can go down from 3 to 1.7. The pressures on the economic and social situation are rather viable. It is the most suitable for the Malagasy health system. The results proposed are a way to control the spread of the disease and limit its devastation in a country like Madagascar.</span></span></span>
