This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to tr...This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle＇s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov＇s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.展开更多
Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value,...Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value, a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory. For discrete-time multi-agent systems with desired trajectory, trajectory tracking and formation control problems were studied. The main idea of trajectory tracking problems was to design trajectory controller such that each agent tracked desired trajectory. For a type of formation problem with fixed formation structure, the formation structure set was introduced. According to the formation structure set, each agent can track its individual desired trajectory. Finally, simulations were provided to demonstrate the effectiveness of the theoretical results. The mlmerical results show that the states of agents converge to zero with consensus protocol, which is said to achieve a consensus asymptotically. In addition, through designing appropriate trajectory controllers, the simulation results show that agents converge to the desired trajectory asymptotically and can form different formations.展开更多
This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol i...This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.展开更多
The non linear dynamic model is set up of one type of high speed painting automizor with gas supporting system. The stability of motion and dynamic response of the gas painting automizor system are studied over a rela...The non linear dynamic model is set up of one type of high speed painting automizor with gas supporting system. The stability of motion and dynamic response of the gas painting automizor system are studied over a relatively wide range of rotating speed by numerical analytic method, the critical velocity under working condition is found, and rotate stability and critical condition are discussed in theory. Furthermore, the range of the critical parameter of the system when Hopf bifurcation occurs and the law between axis trace and bearing clearance are acquired, too.展开更多
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th...Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.展开更多
A novel wheel-track hybrid mobile robot with many movement patterns is designed.According to different environments,it can switch between the pure wheel pattern and the pure track one.According to a homogeneous coordi...A novel wheel-track hybrid mobile robot with many movement patterns is designed.According to different environments,it can switch between the pure wheel pattern and the pure track one.According to a homogeneous coordinate transformation matrix,gravity stability and its obstacle performance are analyzed.Its gravity equation and climbing obstacle conditions are established.Experimental results show that this hybrid mobile robot could fully possess the advantages of both the wheel and the track mechanisms and achieve a good obstacle climbing capability.展开更多
As the modern railway construction continues to mature, now the laying of the continuously welded rail track has become an important part of the construction and development of the modern industry of the railway. The ...As the modern railway construction continues to mature, now the laying of the continuously welded rail track has become an important part of the construction and development of the modern industry of the railway. The study and evaluation of the stability of the continuously welded rail track will better play the values and roles of the continuously welded rail track. At the same time, through the analysis of the specific factors affecting the stability of the CWR track, especially with the combination of the data simulation, we can thus carry out the more accurate the application of the continuously welded rail track. This paper will explore the construction and application background of the continuously welded rail track, and combine the cognition of the specific factors that affect the stability of the continuously welded rail track, so as to accurately analyze and evaluate the stability of the continuously welded rail track.展开更多
The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed b...The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments.展开更多
In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differentia...In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincare＇s Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that： （1） the pest population can be controlled below some threshold; （2） compared to single measure, it is more efficient to take two measures for reducing the level of the pests.展开更多
Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.I...Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.In this paper,these reported orbits are checked stringently by means of a reliable numerical approach(namely the"Clean Numerical Simulation",CNS),which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification.It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time,and are thus most possibly unstable at least.It is suggested to carefully check whether or not these seven unstable orbits are the so-called"computational periodicity"mentioned by Lorenz in 2006.This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.展开更多
The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,...The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.展开更多
The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf ...The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.展开更多
A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-fr...A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.展开更多
基金Supported in Part by the Australian Research Council under Grant DP0988424
文摘This paper presents a design of optimal controllers with respect to a meaningful cost function to force an underactuated omni-directional intelligent navigator （ODIN） under unknown constant environmental loads to track a reference trajectory in two-dimensional space. Motivated by the vehicle＇s steering practice, the yaw angle regarded as a virtual control plus the surge thrust force are used to force the position of the vehicle to globally track its reference trajectory. The control design is based on several recent results developed for inverse optimal control and stability analysis of nonlinear systems, a new design of bounded disturbance observers, and backstepping and Lyapunov＇s direct methods. Both state- and output-feedback control designs are addressed. Simulations are included to illustrate the effectiveness of the proposed results.
基金Projects(60474029,60774045,60604005) supported by the National Natural Science Foundation of ChinaProject supported by the Graduate Degree Thesis Innovation Foundation of Central South University,China
文摘Consensus problems for discrete-time multi-agent systems were focused on. In order to design effective consensus protocols, which were aimed at ensuring that the concerned states of agents converged to a common value, a new consensus protocol for general discrete-time multi-agent system was proposed based on Lyapunov stability theory. For discrete-time multi-agent systems with desired trajectory, trajectory tracking and formation control problems were studied. The main idea of trajectory tracking problems was to design trajectory controller such that each agent tracked desired trajectory. For a type of formation problem with fixed formation structure, the formation structure set was introduced. According to the formation structure set, each agent can track its individual desired trajectory. Finally, simulations were provided to demonstrate the effectiveness of the theoretical results. The mlmerical results show that the states of agents converge to zero with consensus protocol, which is said to achieve a consensus asymptotically. In addition, through designing appropriate trajectory controllers, the simulation results show that agents converge to the desired trajectory asymptotically and can form different formations.
基金Supported by the National Natural Science Foundation of China （No. 61075065,60774045, U1134108） and the Ph. D Programs Foundation of Ministry of Education of China （ No. 20110162110041 ）.
文摘This paper discusses consensus problems for high-dimensional networked multi-agent systems with fixed topology. The communication topology of multi-agent systems is represented by a digraph. A new consensus protocol is proposed, and consensus convergence of multigent systems is analyzed based on the Lyapunov stability theory. The consensus problem can be formulated into solving a feasible problem with bilinear matrix inequality （BMI） constrains. Furthermore, the consensus protocol is extended to achieving tracking and formation control. By introducing the formation structure set, each agent can gain its individual desired trajectory. Finally, numerical simulations are provided to show the effectiveness of our strategies. The results show that agents from arbitrary initial states can asymptotically reach a consensus. In addition, agents with high-dimensional can track any target trajectory, and maintain desired formation during movement by selecting appropriate structure set.
文摘The non linear dynamic model is set up of one type of high speed painting automizor with gas supporting system. The stability of motion and dynamic response of the gas painting automizor system are studied over a relatively wide range of rotating speed by numerical analytic method, the critical velocity under working condition is found, and rotate stability and critical condition are discussed in theory. Furthermore, the range of the critical parameter of the system when Hopf bifurcation occurs and the law between axis trace and bearing clearance are acquired, too.
文摘Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.
基金Supported by the National Natural Science Foundation of China(No.61175069,51075272,51475300)
文摘A novel wheel-track hybrid mobile robot with many movement patterns is designed.According to different environments,it can switch between the pure wheel pattern and the pure track one.According to a homogeneous coordinate transformation matrix,gravity stability and its obstacle performance are analyzed.Its gravity equation and climbing obstacle conditions are established.Experimental results show that this hybrid mobile robot could fully possess the advantages of both the wheel and the track mechanisms and achieve a good obstacle climbing capability.
文摘As the modern railway construction continues to mature, now the laying of the continuously welded rail track has become an important part of the construction and development of the modern industry of the railway. The study and evaluation of the stability of the continuously welded rail track will better play the values and roles of the continuously welded rail track. At the same time, through the analysis of the specific factors affecting the stability of the CWR track, especially with the combination of the data simulation, we can thus carry out the more accurate the application of the continuously welded rail track. This paper will explore the construction and application background of the continuously welded rail track, and combine the cognition of the specific factors that affect the stability of the continuously welded rail track, so as to accurately analyze and evaluate the stability of the continuously welded rail track.
基金supported by the Doctoral Fund of Ministry of Education of China under Grant No.20103402110044the National Key Basic Research Program under Grant No.2011CBA00200
文摘The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments.
基金Research is supported by the National Natural Science Foundation of China （11271260）, Shanghai Leading Academic Discipline Project （No. XTKX2012）, the Hujiang Foundation of China （B14005） and the Innovation Program of Shanghai Municipal Education Committee （13ZZ116）.
文摘In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincare＇s Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that： （1） the pest population can be controlled below some threshold; （2） compared to single measure, it is more efficient to take two measures for reducing the level of the pests.
基金supported by the National Natural Science Foundation of China (Grant No.11272209)the Deanship of Scientific Research (DSR),King Abdulaziz University (KAU) (Grant No.37-130-35-HiCi)
文摘Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.In this paper,these reported orbits are checked stringently by means of a reliable numerical approach(namely the"Clean Numerical Simulation",CNS),which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification.It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time,and are thus most possibly unstable at least.It is suggested to carefully check whether or not these seven unstable orbits are the so-called"computational periodicity"mentioned by Lorenz in 2006.This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.
基金supported by National Natural Science Foundation of China (Grant No.11131004)
文摘The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.
基金Acknowledgments This work was supported by the Science Foundation of Liaoning Province （20092179） and by the National Natural Science Foundation （60974004/F030101）.
文摘The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows： one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.
文摘A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.
