The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly un...The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.展开更多
In this paper, the existence of periodic solution to nonlinear integro-differential equations with infinite delay is studied in the phase space (Cg,|·|g). We prove that the g-uniformly ultimately bounded solution...In this paper, the existence of periodic solution to nonlinear integro-differential equations with infinite delay is studied in the phase space (Cg,|·|g). We prove that the g-uniformly ultimately bounded solutions implies the existence of periodic solutions using Horn’s fixed point theorem. Some known results are generalized, including the famous Yoshizawa’s theorem.展开更多
In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is co...In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.展开更多
There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
This paper addresses an integrated relative position and attitude control strategy for a pursuer spacecraft flying to a space target in proximity operation missions. Relative translation and rotation dynamics are both...This paper addresses an integrated relative position and attitude control strategy for a pursuer spacecraft flying to a space target in proximity operation missions. Relative translation and rotation dynamics are both presented, and further integratedly considered due to mutual couplings, which results in a six degrees-of-freedom (6-DOF) control system. In order to simultaneously achieve relative position and attitude requirements, an adaptive backstepping control law is designed, where a command filter is introduced to overcome 'explosion of terms'. Within the Lyapunov framework, the proposed controller is proved to ensure the ultimate boundedness of relative position and attitude signals, in the presence of external disturbances and unknown system parameters. Numerical simulation demonstrates the effect of the designed control law.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 stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated...The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.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
This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bound...This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.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 novel adaptive fault-tolerant control scheme in the differential algebraic framework was proposed for attitude control of a heavy lift launch vehicle （HLLV）. By using purely mathematical transformations, the decou...A novel adaptive fault-tolerant control scheme in the differential algebraic framework was proposed for attitude control of a heavy lift launch vehicle （HLLV）. By using purely mathematical transformations, the decoupled input-output representations of HLLV were derived, rendering three decoupled second-order systems, i.e., pitch, yaw and roll channels. Based on a new type of numerical differentiator, a differential algebraic observer （DAO） was proposed for estimating the system states and the generalized disturbances, including various disturbances and additive fault torques. Driven by DAOs, three improved proportional-integral- differential （PID） controllers with disturbance compensation were designed for pitch, yaw and roll control. All signals in the closed-loop system were guaranteed to be ultimately uniformly bounded by utilization of Lyapunov＇s indirect method. The convincing numerical simulations indicate that the proposed control scheme is successful in achieving high performance in the presence of parametric perturbations, external disturbances, noisy corruptions, and actuator faults.展开更多
This paper is mainly devoted to the flocking of a class of swarm with fixed topology in a changing environment. Firstly, the controller for each agent is proposed by employing the error terms between the state of the ...This paper is mainly devoted to the flocking of a class of swarm with fixed topology in a changing environment. Firstly, the controller for each agent is proposed by employing the error terms between the state of the agent and the average state of its neighbors. Secondly, a sufficient condition for the swarm to achieve flocking is presented under assumptions that the gradient of the environment is bounded and the initial position graph is connected. Thirdly, as the environment is a plane, it is further proved that the velocity of each agent finally converges to the velocity of the swarm center although not one agent knows where the center of the group is. Finally, numerical examples are included to illustrate the obtained results.展开更多
In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating qu...In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.展开更多
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
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
This paper addresses the leader-following consensus problem in multi-agent systems(MASs)with limited communication rates,while also considering sensor and actuator false data injection(FDI)attacks.A distributed event-...This paper addresses the leader-following consensus problem in multi-agent systems(MASs)with limited communication rates,while also considering sensor and actuator false data injection(FDI)attacks.A distributed event-triggered adaptive control protocol is developed to achieve cooperative uniform ultimate boundedness(UUB)in consensus tracking for compromised networked MASs.To implement this protocol,a distributed estimator is first designed to allow followers to estimate the leader's state.Then,adaptive internal controllers are constructed for each follower to mitigate the impact of FDI attack signals.Additionally,an event-triggered transmission logic is introduced to handle the constraints imposed by finite communication rates.Simulation results demonstrate the effectiveness of the proposed approach.展开更多
This paper addresses the ultimate boundedness control problem for a class of networked nonlinear systems with the round-robin(RR)protocol and uniform quantisation.The communication between sensor nodes and the control...This paper addresses the ultimate boundedness control problem for a class of networked nonlinear systems with the round-robin(RR)protocol and uniform quantisation.The communication between sensor nodes and the controller is implemented via a constrained communication channel.The quantised output of the system is transmitted to the remote controller through a communication channel subject to a transmission delay.For the purpose of alleviating possible data collision,the well-known RR communication protocol is deployed to schedule the data transmissions.On the other hand,the uniform quantisation effects of the network are characterised by a round function(i.e.the nearest integer function).The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that,in the presence of RR protocol and uniform quantisation effects,the closed-loop system is ultimately bounded.The controller is designed based on mean square stability analysis and Lyapunov-like method.A set of sufficient conditions for the ultimate boundedness of the closed-loop system are established and,on the basis of which,the desired controller gains are obtained by solving a set of linear matrix inequalities.The effectiveness of the proposed method is verified by numerical examples.展开更多
In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analy...In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analytic method of Liapunov Function, we established the sufficient conditions of the existence of the uniformly ultimately bounded solutions and periodic solutions of the system(1).展开更多
基金supported by the National Natural Science Foundation of China (No. 60874006)
文摘The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.
基金supported by National Natural Sciences Foundations of China (10771107)
文摘In this paper, the existence of periodic solution to nonlinear integro-differential equations with infinite delay is studied in the phase space (Cg,|·|g). We prove that the g-uniformly ultimately bounded solutions implies the existence of periodic solutions using Horn’s fixed point theorem. Some known results are generalized, including the famous Yoshizawa’s theorem.
基金supported in part by the National Natural Science Foundation of China(62222301,62373012,62473012,62021003)the National Science and Technology Major Project(2021ZD0112302,2021ZD0112301)the Beijing Natural Science Foundation(JQ19013)
文摘In this paper, a fault-tolerant-based online critic learning algorithm is developed to solve the optimal tracking control issue for nonaffine nonlinear systems with actuator faults.First, a novel augmented plant is constructed by fusing the system state and the reference trajectory, which aims to transform the optimal fault-tolerant tracking control design with actuator faults into the optimal regulation problem of the conventional nonlinear error system. Subsequently, in order to ensure the normal execution of the online learning algorithm, a stability criterion condition is created to obtain an initial admissible tracking policy. Then, the constructed model neural network(NN) is pretrained to recognize the system dynamics and calculate trajectory control. The critic and action NNs are constructed to output the approximate cost function and approximate tracking control,respectively. The Hamilton-Jacobi-Bellman equation of the error system is solved online through the action-critic framework. In theoretical analysis, it is proved that all concerned signals are uniformly ultimately bounded according to the Lyapunov principle.The tracking control law can approach the optimal tracking control within a finite approximation error. Finally, two experimental examples are conducted to indicate the effectiveness and superiority of the developed fault-tolerant tracking control scheme.
文摘There are given sufficient conditions for the ultimate boundedness of solutions and for the existence of periodic solutions of a certain vector differential equation of third-order.
文摘We consider a system of neutral equations with unbounded delay, and derive conditions on Liapunov functionals to ensure that the solutions are uniformly bounded and uniformly ultimately bounded.
基金supported by Innovative Team Program of the National Natural Science Foundation of China (No.61021002)
文摘This paper addresses an integrated relative position and attitude control strategy for a pursuer spacecraft flying to a space target in proximity operation missions. Relative translation and rotation dynamics are both presented, and further integratedly considered due to mutual couplings, which results in a six degrees-of-freedom (6-DOF) control system. In order to simultaneously achieve relative position and attitude requirements, an adaptive backstepping control law is designed, where a command filter is introduced to overcome 'explosion of terms'. Within the Lyapunov framework, the proposed controller is proved to ensure the ultimate boundedness of relative position and attitude signals, in the presence of external disturbances and unknown system parameters. Numerical simulation demonstrates the effect of the designed control law.
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 by the National Natural Science Foundation of China (10672007)
文摘The stability and boundedness of mechanical system have been one of important research topics. In this paper ultimate boundedness of a dry friction oscillator, belonging to nonsmooth mechanical system, is investigated by proposing a controller design method. Firstly a sufficient condition of the stability for the nominal system with delayed state feedback is derived by constructing a Lyapunov-Krasovskii function. The delayed feedback gain matrix is calculated by applying linear matrix inequality method. Secondly on the basis of the delayed state feedback, a continuous function is designed by Lyapunov redesign to ensure that the solutions of the friction oscillator system are ultimately bounded under the overall control. Moreover, the ultimate bound can be adjusted in practice by choosing appropriate parameter. Accordingly friction-induced vibration or instability can be controlled effectively. Numerical results show that the pro- posed method is valid.
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.
基金This work was supported by the National Natural Science Foundation of China (No. 60325311, 60274017).
文摘This paper focuses on the robust adaptive control problems for a class of interval time-delay systems and a class of large-scale interconnected systems. The nonlinear uncertainties of the systems under study are bounded by high- order polynomial functions with unknown gains. Firstly, the adaptive feedback controller which can guarantee the stability of the closed-loop system in the sense of uniform ultimate boundedness is proposed. Then the proposed adaptive idea is extended to robust stabilizing designing method for a class of large-scale interconnected systems. Here, another problem we address is to design a decentralized feedback adaptive controller such that the closed-loop system is stable in the sense of uniform ultimate boundedness for all admissible uncertainties and time-delay. Finally, an illustrative example is given to show the validity of the proposed approach.
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Foundation item： Project（2012M521538） supported by China Postdoctoral Science Foundation Project suppolted by Postdoctoral Science Foundation of Central South University
文摘A novel adaptive fault-tolerant control scheme in the differential algebraic framework was proposed for attitude control of a heavy lift launch vehicle （HLLV）. By using purely mathematical transformations, the decoupled input-output representations of HLLV were derived, rendering three decoupled second-order systems, i.e., pitch, yaw and roll channels. Based on a new type of numerical differentiator, a differential algebraic observer （DAO） was proposed for estimating the system states and the generalized disturbances, including various disturbances and additive fault torques. Driven by DAOs, three improved proportional-integral- differential （PID） controllers with disturbance compensation were designed for pitch, yaw and roll control. All signals in the closed-loop system were guaranteed to be ultimately uniformly bounded by utilization of Lyapunov＇s indirect method. The convincing numerical simulations indicate that the proposed control scheme is successful in achieving high performance in the presence of parametric perturbations, external disturbances, noisy corruptions, and actuator faults.
基金the National Natural Science Foundation of China (No.60374001,60334030)the Doctoral Fund of Ministry of Education of China (No.20030006003)the Commission of Science,Technology and Industry for National Defence (No.A2120061303)
文摘This paper is mainly devoted to the flocking of a class of swarm with fixed topology in a changing environment. Firstly, the controller for each agent is proposed by employing the error terms between the state of the agent and the average state of its neighbors. Secondly, a sufficient condition for the swarm to achieve flocking is presented under assumptions that the gradient of the environment is bounded and the initial position graph is connected. Thirdly, as the environment is a plane, it is further proved that the velocity of each agent finally converges to the velocity of the swarm center although not one agent knows where the center of the group is. Finally, numerical examples are included to illustrate the obtained results.
基金Supported by National Natural Science Foundation of China(10671069) the program of Shanghai Priority Academic Discipline
文摘In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.
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.
文摘This paper addresses the leader-following consensus problem in multi-agent systems(MASs)with limited communication rates,while also considering sensor and actuator false data injection(FDI)attacks.A distributed event-triggered adaptive control protocol is developed to achieve cooperative uniform ultimate boundedness(UUB)in consensus tracking for compromised networked MASs.To implement this protocol,a distributed estimator is first designed to allow followers to estimate the leader's state.Then,adaptive internal controllers are constructed for each follower to mitigate the impact of FDI attack signals.Additionally,an event-triggered transmission logic is introduced to handle the constraints imposed by finite communication rates.Simulation results demonstrate the effectiveness of the proposed approach.
基金supported in part by the National Natural Science Foundation of China under Grants 62173079 and U1808205the Science and Technology Program of Gansu Province under Grant 21ZD4GA028.
文摘This paper addresses the ultimate boundedness control problem for a class of networked nonlinear systems with the round-robin(RR)protocol and uniform quantisation.The communication between sensor nodes and the controller is implemented via a constrained communication channel.The quantised output of the system is transmitted to the remote controller through a communication channel subject to a transmission delay.For the purpose of alleviating possible data collision,the well-known RR communication protocol is deployed to schedule the data transmissions.On the other hand,the uniform quantisation effects of the network are characterised by a round function(i.e.the nearest integer function).The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that,in the presence of RR protocol and uniform quantisation effects,the closed-loop system is ultimately bounded.The controller is designed based on mean square stability analysis and Lyapunov-like method.A set of sufficient conditions for the ultimate boundedness of the closed-loop system are established and,on the basis of which,the desired controller gains are obtained by solving a set of linear matrix inequalities.The effectiveness of the proposed method is verified by numerical examples.
文摘In this paper, we study the existence of the uniformly ultimately bounded solutions and periodic solutions for a class of third order nonlinear control systemx …+F(r)x ¨+G(r)x ·+H(r)x=e(t).(1)Using analytic method of Liapunov Function, we established the sufficient conditions of the existence of the uniformly ultimately bounded solutions and periodic solutions of the system(1).
