This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
We consider an H∞ synchronization problem in nonlinear Bloch systems. Based on Lyapunov stability theory and linear matrix inequality formulation, a dynamic feedback controller is designed to guarantee asymptotic sta...We consider an H∞ synchronization problem in nonlinear Bloch systems. Based on Lyapunov stability theory and linear matrix inequality formulation, a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization. Moreover, this controller reduces the effect of an external disturbance to the H∞ norm constraint. A numerical example is given to validate the proposed synchronization scheme.展开更多
In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogen...In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-Jacobi-Isaacs equations or inequalities, we solve regular H∞ of nonlinear systems with homogeneous properties. To overcome the H∞ problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts： regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞ control, we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties.展开更多
The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for cancelin...The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for canceling the effect of backlash. Adaptive nonlinear PID controller together with rule? based backlash compensator was developed and a satisfactory tracking performance was achieved. Simulation results demonstrated the effectiveness of the proposed method.展开更多
This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of...This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.展开更多
This anticle gives a design method of the economical nonlinear controller. The controller is composed of an expert intelligent coordination controller, a fuzzy prediction controller, a fuzzy feedforward controller, a ...This anticle gives a design method of the economical nonlinear controller. The controller is composed of an expert intelligent coordination controller, a fuzzy prediction controller, a fuzzy feedforward controller, a nonlinear controller and so on. The consistence of a distributed control system based on this controller is also shown briefly.展开更多
A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller desig...A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.展开更多
In this paper,an integrated guidance and control method based on an adaptive path-following controller is proposed to control a spin-stabilized projectile with only translational motion information under the constrain...In this paper,an integrated guidance and control method based on an adaptive path-following controller is proposed to control a spin-stabilized projectile with only translational motion information under the constraint of an actuator,uncertainties in aerodynamic parameters and measurements,and control system complexity.Owing to the fairly high rotation speed,the dynamic model of this missile is strongly nonlinear,uncertain and coupled in pitch,yaw and roll channels.A theoretical equivalent resultant force and uncertainty compensation method are comprehensively used to realize decoupling of pitch and yaw.In response to the strong nonlinear and time-varying characteristics of the dynamic system,the quasi-linear model whose parameters are obtained by interpolation of points selected as the segmentation points in the trajectory envelope,is used for calculation in each step.To cope with the system uncertainty caused by model approximation,parameter uncertainty and ballistic interference,an extended state estimator is used to compensate the output feedback according to the test ballistic angle.In order to improve the tracking efficiency and ensure the tracking error convergence with only translational motion information,the virtual guide point,whose derivative is deduced according to the Lyapunov principle,is calculated in real time according to the projection relationship between the real-time position and the reference trajectory,and a virtual line-of-sight angle and the backstepping method are used for the design of the guidance and control system.In order to avoid the influence of control input saturation on the guidance and control performance due to the actuator limitation and improve the robustness of the system,an anti-saturation compensator is designed according to the two-step method.The feasibility and effectiveness of the path-following controller is verified through closed-loop flight simulations with measurement,control,and condition uncertainties.The results indicate that the designed controller can converge to the reference path and evidently decrease the distance between the impact point and target under different uncertainties.展开更多
In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally c...In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.展开更多
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapun...This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.展开更多
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
This paper studies the distributed H∞control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communica...This paper studies the distributed H∞control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞controllers are proposed. The concept of an H∞performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.展开更多
A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J2 perturbation and atmospheric dra...A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J2 perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation（SDRE）, a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode（IM） control law is added to eliminate disturbances.These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method.Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.展开更多
A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC...A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC)and the nonlinear disturbance observer(NDO).DSC technique provides the ability to overcome the″explosion of complexity″problem in backstepping control.NDO is adopted to observe the uncertainties in nonlinear flight dynamic system.It has been proved that the proposed design method can guarantee uniformly ultimately boundedness of all the signals in the closed-loop system by Lyapunov stability theorem.Finally,simulation results show that the proposed controller provides better performance than the traditional nonlinear controller.展开更多
This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer fu...This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.展开更多
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee t...This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feas.ibility of the proposed technique.展开更多
In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variation...In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.展开更多
In order to improve the security and reliability for autonomous underwater vehicle （AUV） navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain Operating c...In order to improve the security and reliability for autonomous underwater vehicle （AUV） navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities （LMI） to solve for the Hv controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.展开更多
On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in m...On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation.In this paper,considering the multilingual environment and intervention mechanism in the rumor-spreading process,an improved ignorants–spreaders-1–spreaders-2–removers(I2SR)rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks.Firstly,based on the mean-field equations corresponding to the model,the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium.Secondly,by applying Lyapunov stability theory and graph theory,the global stability of rumor-spreading equilibrium is analyzed in detail.In particular,aiming at the lowest control cost,the optimal control scheme is designed to optimize the intervention mechanism,and the optimal control conditions are derived using the Pontryagin's minimum principle.Finally,some illustrative examples are provided to verify the effectiveness of the theoretical results.The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time,which provides guiding insights for public opinion managers to control rumors.展开更多
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金Project supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology (Grant No.2010-0009373)
文摘We consider an H∞ synchronization problem in nonlinear Bloch systems. Based on Lyapunov stability theory and linear matrix inequality formulation, a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization. Moreover, this controller reduces the effect of an external disturbance to the H∞ norm constraint. A numerical example is given to validate the proposed synchronization scheme.
基金Supported by the Education Department of Henan Province(200511517007)
文摘In this paper, the nonlinear singular stabilization, H∞ control problem of systems with ordinary homogeneous properties is considered. At first, we discuss the stabilization problems of nonlinear systems with homogeneous. Secondly, by vitue of Hamilton-Jacobi-Isaacs equations or inequalities, we solve regular H∞ of nonlinear systems with homogeneous properties. To overcome the H∞ problem of singular nonlinear system, we try to transform inputs of the singular nonlinear system into two parts： regular part input and singular part input. Following the previous results, we solve the singular nonlinear system H∞ control, we give the Lyapunov function and the state feedback controller of the singular nonlinear systems with homogeneous properties.
文摘The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for canceling the effect of backlash. Adaptive nonlinear PID controller together with rule? based backlash compensator was developed and a satisfactory tracking performance was achieved. Simulation results demonstrated the effectiveness of the proposed method.
文摘This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.
文摘This anticle gives a design method of the economical nonlinear controller. The controller is composed of an expert intelligent coordination controller, a fuzzy prediction controller, a fuzzy feedforward controller, a nonlinear controller and so on. The consistence of a distributed control system based on this controller is also shown briefly.
文摘A class of triangular non li near system with disturbances which has unknown multiplicative time varying par ametric uncertainties in each virtual control is treated by a backstepping techn ique. The controller designed for all admissible uncertainties can guarantee tha t all states of its closed loop system are uniformly bounded. The robust contro ller design algorithm and a sufficient condition of the system stability are giv en. In addition, the closed loop system has an ISS property when the multiplica tive time varying parametric uncertainties are viewed as inputs to the system. Thus, this design provides a way to prevent a destabilizing effect of the multip licative time varying parametric uncertainties. Finally, simulational example i s given and simulational result shows that the controller exhibits effectiveness and excellent robustness.
文摘In this paper,an integrated guidance and control method based on an adaptive path-following controller is proposed to control a spin-stabilized projectile with only translational motion information under the constraint of an actuator,uncertainties in aerodynamic parameters and measurements,and control system complexity.Owing to the fairly high rotation speed,the dynamic model of this missile is strongly nonlinear,uncertain and coupled in pitch,yaw and roll channels.A theoretical equivalent resultant force and uncertainty compensation method are comprehensively used to realize decoupling of pitch and yaw.In response to the strong nonlinear and time-varying characteristics of the dynamic system,the quasi-linear model whose parameters are obtained by interpolation of points selected as the segmentation points in the trajectory envelope,is used for calculation in each step.To cope with the system uncertainty caused by model approximation,parameter uncertainty and ballistic interference,an extended state estimator is used to compensate the output feedback according to the test ballistic angle.In order to improve the tracking efficiency and ensure the tracking error convergence with only translational motion information,the virtual guide point,whose derivative is deduced according to the Lyapunov principle,is calculated in real time according to the projection relationship between the real-time position and the reference trajectory,and a virtual line-of-sight angle and the backstepping method are used for the design of the guidance and control system.In order to avoid the influence of control input saturation on the guidance and control performance due to the actuator limitation and improve the robustness of the system,an anti-saturation compensator is designed according to the two-step method.The feasibility and effectiveness of the path-following controller is verified through closed-loop flight simulations with measurement,control,and condition uncertainties.The results indicate that the designed controller can converge to the reference path and evidently decrease the distance between the impact point and target under different uncertainties.
文摘In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.
基金Project supported by the National Natural Science Foundations of China (Grant Nos. 70571030 and 90610031)the Society Science Foundation from Ministry of Education of China (Grant No. 08JA790057)the Advanced Talents’ Foundation and Student’s Foundation of Jiangsu University (Grant Nos. 07JDG054 and 07A075)
文摘This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov expo- nents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench （EWB）. Numerical simulations are presented to show these results.
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
文摘This paper studies the distributed H∞control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞controllers are proposed. The concept of an H∞performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.
基金supported by the National Natural Science Foundation of China(Grant No.11404404)
文摘A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying.The formation flying is described by a nonlinear model with the J2 perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation（SDRE）, a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode（IM） control law is added to eliminate disturbances.These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method.Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.
基金supported by the Open Research Project of the State Key Laboratory of Industrial Control Technology Zhejiang University China(No.ICT1401)Shanghai Leading Academic Discipline Project(No.J50103)
文摘A new robust control method of a nonlinear flight dynamic system with aerodynamic coefficients and external disturbance has been proposed.The proposed control system is a combination of the dynamic surface control(DSC)and the nonlinear disturbance observer(NDO).DSC technique provides the ability to overcome the″explosion of complexity″problem in backstepping control.NDO is adopted to observe the uncertainties in nonlinear flight dynamic system.It has been proved that the proposed design method can guarantee uniformly ultimately boundedness of all the signals in the closed-loop system by Lyapunov stability theorem.Finally,simulation results show that the proposed controller provides better performance than the traditional nonlinear controller.
基金Project supported by the National Natural Science Foundation of China (Grant No 10832006)the Key Projects of Educational Ministry of China (Grant No 107110)
文摘This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.
基金Project supported by the National Natural Science Foundation of China (Grant No 60674026)the Key Project of Chinese Ministry of Education (Grant No 107058)+1 种基金the Jiangsu Provincial Natural Science Foundation of China (Grant No BK2007016)the Jiangsu Provincial Program for Postgraduate Scientific Innovative Research of Jiangnan University (Grant No CX07B_116z)and PIRT Jiangnan
文摘This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feas.ibility of the proposed technique.
基金supported financially by the National Natural Science Foundation of China(10971019)supported financially by the Scientific Research Fund of Hunan Provincial Educational Department(09C852)
文摘In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN.The results are established by using the variational methods, the related duality theory and Kakutani Fixed-point Theorem.
基金Supported by the Heilongjiang Postdoctoral Foundation under Grant No. LH-04010
文摘In order to improve the security and reliability for autonomous underwater vehicle （AUV） navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities （LMI） to solve for the Hv controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.
基金the National Natural Science Foundation of People’s Republic of China(Grant Nos.U1703262 and 62163035)the Special Project for Local Science and Technology Development Guided by the Central Government(Grant No.ZYYD2022A05)Xinjiang Key Laboratory of Applied Mathematics(Grant No.XJDX1401)。
文摘On the multilingual online social networks of global information sharing,the wanton spread of rumors has an enormous negative impact on people's lives.Thus,it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation.In this paper,considering the multilingual environment and intervention mechanism in the rumor-spreading process,an improved ignorants–spreaders-1–spreaders-2–removers(I2SR)rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks.Firstly,based on the mean-field equations corresponding to the model,the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium.Secondly,by applying Lyapunov stability theory and graph theory,the global stability of rumor-spreading equilibrium is analyzed in detail.In particular,aiming at the lowest control cost,the optimal control scheme is designed to optimize the intervention mechanism,and the optimal control conditions are derived using the Pontryagin's minimum principle.Finally,some illustrative examples are provided to verify the effectiveness of the theoretical results.The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time,which provides guiding insights for public opinion managers to control rumors.
