The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential...The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.展开更多
For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we prese...For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network(RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error,which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function,which can guarantee the uniform ultimate boundedness(UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.展开更多
A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ulti...A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.展开更多
The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances,with bounded moving average,is solved using a Lyapunov-like design.The analysis and design approache...The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances,with bounded moving average,is solved using a Lyapunov-like design.The analysis and design approaches are introduced in the case in which the underlying system is an integrator and are then applied to the satellite attitude regulation problem.The performance of the resulting closed-loop systems are studied in detail and it is shown that trajectories are ultimately bounded despite the effect of the persistent disturbance.Simulation results on a model of a small satellite subject to large,but bounded in moving average,disturbances are presented.展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.展开更多
A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a uni...A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.展开更多
The model of uonlinear differential systems with impulsive effect on random moments is brought forward in this paper. Then, sufficient conditions for (uniform, uniform and ultimate, and uniform and uniformly ultimate)...The model of uonlinear differential systems with impulsive effect on random moments is brought forward in this paper. Then, sufficient conditions for (uniform, uniform and ultimate, and uniform and uniformly ultimate) p-moment boundedness of the systems are presented. Finally, an example is discussed to show applications of two obtained results.展开更多
Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive soluti...Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive solution and the property of stochastically ultimate boundedness of model(1.1)are proved.Moreover,the extinction and the persistence of the disease are established.The results are verified by numerical simulations.展开更多
This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov...This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.展开更多
In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linea...In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.展开更多
The tracking control of linear differential inclusion is discussed. First, the definition of uniformly ultimate boundedness for linear differential inclusion is given. Then, a feedback law is constructed by using the ...The tracking control of linear differential inclusion is discussed. First, the definition of uniformly ultimate boundedness for linear differential inclusion is given. Then, a feedback law is constructed by using the convex hull Lyapunov function. The sufficient condition is given to guarantee the tracking error system uniformly ultimately bounded. Finally, a numerical example is simulated to illustrate the effectiveness of this control design.展开更多
In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded m...In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded mean of solution is obtained by using the Liyapunov function and Chebyshev inequality. Lastly,stochastic global asymptotic stability of zero equilibriums is analyzed.展开更多
基金the National Natural Science Foundation of China (Grant No. 11971055)the Beijing Natural Science Foundation, China (Grant No. 1202019)。
文摘The use of flocculants to collect/extract microorganisms is of great practical significance for the development of the application of microorganisms. In this paper, a high-dimensional nonlinear stochastic differential equation model is constructed to describe the continuous culture of microorganisms with multiple nutrients and the flocculation process of microorganisms. The study of the dynamics of this model can provide feasible control strategies for the collection/extraction of microorganisms. The main theoretical results are sufficient conditions for the permanence and extinction of the stochastic differential equation model, which are also extensions of some results in the existing literatures. In addition, through numerical simulations, we vividly demonstrate the statistical characteristics of the stochastic differential equation model.
基金supported in part by the National Natural Science Foundation of China(61433004,61703289)
文摘For a single machine infinite power system with thyristor controlled series compensation(TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network(RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error,which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function,which can guarantee the uniform ultimate boundedness(UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.
基金National Natural Science Foundations of China(No.11071259,No.11371374)Research Fund for the Doctoral Program of Higher Education of China(No.20110162110060)
文摘A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.
基金supported in part by the China Scholarship Council (201906120101)in part by the European Union’s Horizon 2020 Research and Innovation Program (739551)(KIOS Centre of Excellence)+3 种基金in part by the Italian Ministry for Research in the framework of the 2017Program for Research Projects of National Interest (PRIN)(2017YKXYXJ)in part by the Science Center Program of National Natural Science Foundation of China (62188101)in part by the National Natural Science Foundation of China (61833009, 61690212)in part by Heilongjiang Touyan Team
文摘The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances,with bounded moving average,is solved using a Lyapunov-like design.The analysis and design approaches are introduced in the case in which the underlying system is an integrator and are then applied to the satellite attitude regulation problem.The performance of the resulting closed-loop systems are studied in detail and it is shown that trajectories are ultimately bounded despite the effect of the persistent disturbance.Simulation results on a model of a small satellite subject to large,but bounded in moving average,disturbances are presented.
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
基金Natural Science Foundation of Hunan University of Technology,China(No.2012HZX08)the Special Foundation of National Independent Innovation Demonstration Area Construction of Zhuzhou(Applied Basic Research),China
文摘A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.
基金Partially supported by the NNSF of China(No.19831030,No.10371074)
文摘The model of uonlinear differential systems with impulsive effect on random moments is brought forward in this paper. Then, sufficient conditions for (uniform, uniform and ultimate, and uniform and uniformly ultimate) p-moment boundedness of the systems are presented. Finally, an example is discussed to show applications of two obtained results.
基金This work is supported by the National Natural Science Foundation of China(No.11701495)Scientific and Technological Key Projects of Henan Province(No.192102310193)Nanhu Scholars Program for Young Scholars of XYNU.
文摘Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive solution and the property of stochastically ultimate boundedness of model(1.1)are proved.Moreover,the extinction and the persistence of the disease are established.The results are verified by numerical simulations.
基金supported by the National Natural Science Foundation of China(Nos.11901398,11671149,11871225 and 11771102)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515011350)the Fundamental Research Funds for the Central Universities(No.2018MS58).
文摘This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.
基金supported by the National Natural Science Foundation of China(Nos.11771044 and 11871007).
文摘In this paper,stochastic properties of solution for a chemostat model with a distributed delay and random disturbance are studied,and we use distribution delay to simulate the delay in nutrient conversion.By the linear chain technique,we transform the stochastic chemostat model with weak kernel into an equivalent degenerate system which contains three equations.First,we state that this model has a unique global positive solution for any initial value,which is helpful to explore its stochastic properties.Furthermore,we prove the stochastic ultimate boundness of the solution of system.Then sufficient conditions for solution of the system tending toward the boundary equilibrium point at exponential rate are established,which means the microorganism will be extinct.Moreover,we also obtain some sufficient conditions for ergodicity of solution of this system by constructing some suitable stochastic Lyapunov functions.Finally,we provide some numerical examples to illustrate theoretical results,and some conclusions and analysis are given.
基金Project (No. 61074003) supported by the National Natural Science Foundation of China
文摘The tracking control of linear differential inclusion is discussed. First, the definition of uniformly ultimate boundedness for linear differential inclusion is given. Then, a feedback law is constructed by using the convex hull Lyapunov function. The sufficient condition is given to guarantee the tracking error system uniformly ultimately bounded. Finally, a numerical example is simulated to illustrate the effectiveness of this control design.
基金supported by the National Natural Sciences Foundation of China(11371313)the Sciences Foundation of Yuncheng University(XK2012003)
文摘In this paper, we formulate a single-species model of contraception control with white noise on the death rate. Firstly, the uniqueness of global positive solution of the model is proved. Secondly, uniformly bounded mean of solution is obtained by using the Liyapunov function and Chebyshev inequality. Lastly,stochastic global asymptotic stability of zero equilibriums is analyzed.