With the continuous breakthrough in information technology and its integration into practical applications, industrial digital twins are expected to accelerate their development in the near future. This paper studies ...With the continuous breakthrough in information technology and its integration into practical applications, industrial digital twins are expected to accelerate their development in the near future. This paper studies various control strategies for digital twin systems from the viewpoint of practical applications.To make full use of advantages of digital twins for control systems, an architecture of digital twin control systems, adaptive model tracking scheme, performance prediction scheme, performance retention scheme, and fault tolerant control scheme are proposed. Those schemes are detailed to deal with different issues on model tracking, performance prediction, performance retention, and fault tolerant control of digital twin systems. Also, the stability of digital twin control systems is analysed. The proposed schemes for digital twin control systems are illustrated by examples.展开更多
Dear Editor,In this letter,a novel data-driven adaptive predictive control method is proposed using the triangular dynamic linearization technique.The proposed method only contains one time-varying parameter with expl...Dear Editor,In this letter,a novel data-driven adaptive predictive control method is proposed using the triangular dynamic linearization technique.The proposed method only contains one time-varying parameter with explicit physical meaning,which can prevent severe deviation in parameter estimation.Specifically,a triangular dynamic linearization(TDL)data model is employed to predict future system outputs,and then to correct inaccurate predictive outputs,a feedback regulator is designed.An autotuned weighing factor is introduced to alleviate the computational burden in practical applications and further improve output tracking performance.Closed-loop stability conditions are derived by rigorous analysis.Simulation results are provided to demonstrate the efficacy of the proposed method.展开更多
Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety o...Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety of study results in last over two decades,fully incorporating control requirements and actuator characteristics of space missions.This paper presents a novel and comprehensive survey to the coupled position and attitude motions of spacecraft from the perspective of dynamics and control.To this end,a systematic analysis is firstly conducted in details to show the position and attitude mutual couplings of spacecraft.Particularly,in terms of the time discrepancy between spacecraft position and attitude motions,space missions can be categorized into two types:space proximity operation and space orbital maneuver.Based on this classification,the studies on the coupled dynamic modeling and the integrated control design for position and attitude motions of spacecraft are sequentially summarized and analyzed.On the one hand,various coupled position and dynamic formulations of spacecraft based on various mathematical tools are reviewed and compared from five aspects,including mission applicability,modeling simplicity,physical clearance,information matching and expansibility.On the other hand,the development of the integrated position and attitude control of spacecraft is analyzed for two space missions,and especially,five distinctive development trends are captured for space operation missions.Finally,insightful prospects on future development of the integrated position and attitude control technology of spacecraft are proposed,pointing out current primary technical issues and possible feasible solutions.展开更多
Dear Editor,In this letter,in order to deal with random network delays and packet losses in a class of networked nonlinear systems,three data-driven networked predictive control methods are designed.Their closed-loop ...Dear Editor,In this letter,in order to deal with random network delays and packet losses in a class of networked nonlinear systems,three data-driven networked predictive control methods are designed.Their closed-loop systems and control increments are derived,respectively.展开更多
Dear Editor,In this letter,an output tracking control problem of uncertain cyber-physical systems(CPSs)is considered in the perspective of high-order fully actuated(HOFA)system theory,where a lumped disturbance is use...Dear Editor,In this letter,an output tracking control problem of uncertain cyber-physical systems(CPSs)is considered in the perspective of high-order fully actuated(HOFA)system theory,where a lumped disturbance is used to denote the total uncertainties containing parameters perturbations and external disturbances.展开更多
This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external disturbance.Unlike the existing approaches,we transform the considered system into a fully actuated system(FAS)m...This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external disturbance.Unlike the existing approaches,we transform the considered system into a fully actuated system(FAS)model,simplifying the stabilizing controller design.We implement a separate controller design and propose exponential stabilization controller and finite-time stabilization controller under finite-time disturbance observer(FTDO)for the two system inputs.In addition,we discuss the specifics of global stabilization control design.Our approach demonstrates that two system states exponentially or asymptotically converge to zero under the provided switching stabilization control strategy,while all other system states converge to zero within a finite time.展开更多
With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper stu...With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper studies the tracking control problem of networked multi-agent systems with communication constraints,where each agent has no information on the dynamics of other agents except their outputs.A networked predictive proportional integral derivative(PPID)tracking scheme is proposed to achieve the desired tracking performance,compensate actively for communication delays,and simplify implementation in a distributed manner.This scheme combines the past,present and predictive information of neighbour agents to form a tracking error signal for each agent,and applies the proportional,integral,and derivative of the agent tracking error signal to control each individual agent.The criteria of the stability and output tracking consensus of multi-agent systems with the networked PPID tracking scheme are derived through detailed analysis on the closed-loop systems.The effectiveness of the networked PPID tracking scheme is illustrated via an example.展开更多
This paper studies the privacy-preserving distributed economic dispatch(DED)problem of smart grids.An autonomous consensus-based algorithm is developed via local data exchange with neighboring nodes,which covers both ...This paper studies the privacy-preserving distributed economic dispatch(DED)problem of smart grids.An autonomous consensus-based algorithm is developed via local data exchange with neighboring nodes,which covers both the islanded mode and the grid-connected mode of smart grids.To prevent power-sensitive information from being disclosed,a privacy-preserving mechanism is integrated into the proposed DED algorithm by randomly decomposing the state into two parts,where only partial data is transmitted.Our objective is to develop a privacy-preserving DED algorithm to achieve optimal power dispatch with the lowest generation cost under physical constraints while preventing sensitive information from being eavesdropped.To this end,a comprehensive analysis framework is established to ensure that the proposed algorithm can converge to the optimal solution of the concerned optimization problem by means of the consensus theory and the eigenvalue perturbation approach.In particular,the proposed autonomous algorithm can achieve a smooth transition between the islanded mode and the grid-connected mode.Furthermore,rigorous analysis is given to show privacy-preserving performance against internal and external eavesdroppers.Finally,case studies illustrate the feasibility and validity of the developed algorithm.展开更多
This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state...This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable elimination.Considering the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total disturbance.Then,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure.The solution to the parameter matrices of the observer and controller is given subsequently.It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin.Finally,numerical simulation demonstrates the effectiveness of the proposed controller.展开更多
This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factoriz...This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.展开更多
The issue of stability and group consensus tracking is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints(e.g.,time delays and data loss)in this paper.Firstly...The issue of stability and group consensus tracking is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints(e.g.,time delays and data loss)in this paper.Firstly,the couple-group consensus tracking control is analyzed theoretically,the communication constraints are compensated by the prediction method,and the factor of leaders is introduced to make the system not lose generality.Secondly,the necessary and sufficient condition is given to ensure the stability of the system and achieve the couple-group consensus tracking control,and relax the topology constraint of in-degrees balance by cooperative-competitive interactions.In addition,the result of couple groups is extended to multiple groups based on the predictive control protocol.Numerical simulations with Matlab show that the proposed networked predictive control can effectively overcome the network constraints,the dynamic performance and control effect are better than the general control without the prediction.展开更多
In this paper,a fully actuated system approach(FASA)-based control scheme is proposed for the trajectory tracking of a quadrotor unmanned aerial vehicle(UAV).System uncertainty,external disturbance and actuator constr...In this paper,a fully actuated system approach(FASA)-based control scheme is proposed for the trajectory tracking of a quadrotor unmanned aerial vehicle(UAV).System uncertainty,external disturbance and actuator constraint are all considered,which make the problem challenging.Inspired by the active disturbance rejection control(ADRC),tracking di®erentiator(TD)and extended state observer(ESO)are introduced for handling the uncertainties and generating the feedback signals.With the proposed feedback control law,the performance of the resulted closed loop system is related to its eigenstructure-eigenvalue and eigenvectors.Based on a type of control parametrization method,the parametrized eigenstructure of the closed loop system are optimized.A better performance is observed by comparative numerical simulation.展开更多
In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the ...In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero exponentially.Secondly,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the origin.The idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.展开更多
In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drive...In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially.Such a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential sub-stability.The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin.This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially.Based on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.展开更多
It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state feedback.This brief points out that for a scalar high-order fully actuated linear syste...It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state feedback.This brief points out that for a scalar high-order fully actuated linear system,the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account,that is,controllability cannot guarantee arbitrary pole assignment by state feedback.展开更多
This paper considers the leaderless consensus problem of linear time-invariant multi-agent systems with infinite distributed communication delays.A novel distributed low gain controller is proposed based on the soluti...This paper considers the leaderless consensus problem of linear time-invariant multi-agent systems with infinite distributed communication delays.A novel distributed low gain controller is proposed based on the solution to a parametric algebraic Riccati equation.It is shown via the newly developed Lyapunov-like method that not only the consensus of linear time-invariant multi-agent systems can be achieved exponentially under some mild assumptions but also an estimate of the exponential convergence rate of consensus is given in this work.The Lyapunovlike method is also extended to handle a special case of linear time-varying multi-agent systems.In addition,the obtained results include the results on the leaderless consensus of linear multiagent systems with bounded distributed communication delays as special cases.To the best of our knowledge,this is thefirst work that develops the Lyapunov-like method for the leaderless consensus problems of both time-invariant and time-varying linear multi-agent systems with infinite distributed communication delays.Finally,a numerical example is presented to illustrate the effectiveness of the proposed controller.展开更多
基金supported in part by Shenzhen Key Laboratory of Control Theory and Intelligent Systems (ZDSYS20220330161800001)the National Natural Science Foundation of China (62173255, 62188101)。
文摘With the continuous breakthrough in information technology and its integration into practical applications, industrial digital twins are expected to accelerate their development in the near future. This paper studies various control strategies for digital twin systems from the viewpoint of practical applications.To make full use of advantages of digital twins for control systems, an architecture of digital twin control systems, adaptive model tracking scheme, performance prediction scheme, performance retention scheme, and fault tolerant control scheme are proposed. Those schemes are detailed to deal with different issues on model tracking, performance prediction, performance retention, and fault tolerant control of digital twin systems. Also, the stability of digital twin control systems is analysed. The proposed schemes for digital twin control systems are illustrated by examples.
基金supported in part by the National Natural Science Foundation of China(62173002,52301408,62173255)the Beijing Natural Science Foundation(4222045).
文摘Dear Editor,In this letter,a novel data-driven adaptive predictive control method is proposed using the triangular dynamic linearization technique.The proposed method only contains one time-varying parameter with explicit physical meaning,which can prevent severe deviation in parameter estimation.Specifically,a triangular dynamic linearization(TDL)data model is employed to predict future system outputs,and then to correct inaccurate predictive outputs,a feedback regulator is designed.An autotuned weighing factor is introduced to alleviate the computational burden in practical applications and further improve output tracking performance.Closed-loop stability conditions are derived by rigorous analysis.Simulation results are provided to demonstrate the efficacy of the proposed method.
基金supported by the National Science Foundation of China(61703437,52232014,61690210,61690212)。
文摘Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety of study results in last over two decades,fully incorporating control requirements and actuator characteristics of space missions.This paper presents a novel and comprehensive survey to the coupled position and attitude motions of spacecraft from the perspective of dynamics and control.To this end,a systematic analysis is firstly conducted in details to show the position and attitude mutual couplings of spacecraft.Particularly,in terms of the time discrepancy between spacecraft position and attitude motions,space missions can be categorized into two types:space proximity operation and space orbital maneuver.Based on this classification,the studies on the coupled dynamic modeling and the integrated control design for position and attitude motions of spacecraft are sequentially summarized and analyzed.On the one hand,various coupled position and dynamic formulations of spacecraft based on various mathematical tools are reviewed and compared from five aspects,including mission applicability,modeling simplicity,physical clearance,information matching and expansibility.On the other hand,the development of the integrated position and attitude control of spacecraft is analyzed for two space missions,and especially,five distinctive development trends are captured for space operation missions.Finally,insightful prospects on future development of the integrated position and attitude control technology of spacecraft are proposed,pointing out current primary technical issues and possible feasible solutions.
基金the National Natural Science Foundation of China(62173002,61925303,62088101,U20B2073,61720106011,62173255)the National Key R&D Program of China(2018YFC0809700)the Beijing Natural Science Foundation(4222045)。
文摘Dear Editor,In this letter,in order to deal with random network delays and packet losses in a class of networked nonlinear systems,three data-driven networked predictive control methods are designed.Their closed-loop systems and control increments are derived,respectively.
基金supported in part by the National Natural Science Foundation of China(621732556218,8101)the Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)。
文摘Dear Editor,In this letter,an output tracking control problem of uncertain cyber-physical systems(CPSs)is considered in the perspective of high-order fully actuated(HOFA)system theory,where a lumped disturbance is used to denote the total uncertainties containing parameters perturbations and external disturbances.
基金partially supported by the National Natural Science Foundation of China(62173207,62073187)the Science Center Program of the National Natural Science Foundation of China(62188101)+1 种基金the China Postdoctoral Science Special Foundation(2023T160334)the Youth Innovation Team Project of Colleges and Universities in Shandong Province(2022KJ176)。
文摘This study examines the stabilization issue of extended chained nonholonomic systems(ECNSs)with external disturbance.Unlike the existing approaches,we transform the considered system into a fully actuated system(FAS)model,simplifying the stabilizing controller design.We implement a separate controller design and propose exponential stabilization controller and finite-time stabilization controller under finite-time disturbance observer(FTDO)for the two system inputs.In addition,we discuss the specifics of global stabilization control design.Our approach demonstrates that two system states exponentially or asymptotically converge to zero under the provided switching stabilization control strategy,while all other system states converge to zero within a finite time.
文摘With the rapid development of network technology and control technology,a networked multi-agent control system is a key direction of modern industrial control systems,such as industrial Internet systems.This paper studies the tracking control problem of networked multi-agent systems with communication constraints,where each agent has no information on the dynamics of other agents except their outputs.A networked predictive proportional integral derivative(PPID)tracking scheme is proposed to achieve the desired tracking performance,compensate actively for communication delays,and simplify implementation in a distributed manner.This scheme combines the past,present and predictive information of neighbour agents to form a tracking error signal for each agent,and applies the proportional,integral,and derivative of the agent tracking error signal to control each individual agent.The criteria of the stability and output tracking consensus of multi-agent systems with the networked PPID tracking scheme are derived through detailed analysis on the closed-loop systems.The effectiveness of the networked PPID tracking scheme is illustrated via an example.
基金supported in part by Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)the National Natural Science Foundation of China(62303210,62173255,62188101)+1 种基金the Guangdong Basic and Applied Basic Research Foundation of China(2022A1515110459)the Shenzhen Science and Technology Program of China(RCBS20221008093348109)。
文摘This paper studies the privacy-preserving distributed economic dispatch(DED)problem of smart grids.An autonomous consensus-based algorithm is developed via local data exchange with neighboring nodes,which covers both the islanded mode and the grid-connected mode of smart grids.To prevent power-sensitive information from being disclosed,a privacy-preserving mechanism is integrated into the proposed DED algorithm by randomly decomposing the state into two parts,where only partial data is transmitted.Our objective is to develop a privacy-preserving DED algorithm to achieve optimal power dispatch with the lowest generation cost under physical constraints while preventing sensitive information from being eavesdropped.To this end,a comprehensive analysis framework is established to ensure that the proposed algorithm can converge to the optimal solution of the concerned optimization problem by means of the consensus theory and the eigenvalue perturbation approach.In particular,the proposed autonomous algorithm can achieve a smooth transition between the islanded mode and the grid-connected mode.Furthermore,rigorous analysis is given to show privacy-preserving performance against internal and external eavesdroppers.Finally,case studies illustrate the feasibility and validity of the developed algorithm.
基金This research was partially supported by the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101the Major Program of the National Natural Science Foundation of China under Grant Nos.61690210 and 61690212the National Natural Science Foundation of China under Grant Nos.62103164 and 61703437.
文摘This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable elimination.Considering the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total disturbance.Then,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable eigenstructure.The solution to the parameter matrices of the observer and controller is given subsequently.It is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the origin.Finally,numerical simulation demonstrates the effectiveness of the proposed controller.
基金the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101the Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212+1 种基金the National Natural Science Foundation of China under Grant No.61333003the Self-Planned Task of State Key Laboratory of Robotics and System(HIT)under Grant No.SKLRS201716A。
文摘This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.
基金supported by Natural Science Foundation of Heilongjiang Province of China under Grant No.LH2022F033the National Natural Science Foundation of China under Grant Nos.61903104,61773144 and 12071102Heilongjiang Postdoctoral Scientific Research Developmental Fund under Grant Nos.LBHQ20099 and LBH-Q20168。
文摘The issue of stability and group consensus tracking is investigated for the discrete-time heterogeneous networked multi-agent systems with communication constraints(e.g.,time delays and data loss)in this paper.Firstly,the couple-group consensus tracking control is analyzed theoretically,the communication constraints are compensated by the prediction method,and the factor of leaders is introduced to make the system not lose generality.Secondly,the necessary and sufficient condition is given to ensure the stability of the system and achieve the couple-group consensus tracking control,and relax the topology constraint of in-degrees balance by cooperative-competitive interactions.In addition,the result of couple groups is extended to multiple groups based on the predictive control protocol.Numerical simulations with Matlab show that the proposed networked predictive control can effectively overcome the network constraints,the dynamic performance and control effect are better than the general control without the prediction.
基金supported by the National Defense Basic Scientific Research Program of China (Grant No.JCKY2021204B051).
文摘In this paper,a fully actuated system approach(FASA)-based control scheme is proposed for the trajectory tracking of a quadrotor unmanned aerial vehicle(UAV).System uncertainty,external disturbance and actuator constraint are all considered,which make the problem challenging.Inspired by the active disturbance rejection control(ADRC),tracking di®erentiator(TD)and extended state observer(ESO)are introduced for handling the uncertainties and generating the feedback signals.With the proposed feedback control law,the performance of the resulted closed loop system is related to its eigenstructure-eigenvalue and eigenvectors.Based on a type of control parametrization method,the parametrized eigenstructure of the closed loop system are optimized.A better performance is observed by comparative numerical simulation.
基金This paper has been partially supported by the Major Program of National Natural Science Foundation of China under Grant Nos.61690210,61690212National Natural Science Foundation of China under Grant No.61333003also by the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101.
文摘In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)approach.Firstly,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero exponentially.Secondly,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the origin.The idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.
基金partially supported by the Major Program of National Natural Science Foundation of China under Grant Nos.61690210 and 61690212the National Natural Science Foundation of China under Grant No.61333003the Science Center Program of the National Natural Science Foundation of China under Grant No.62188101。
文摘In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)approach.It is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin exponentially.Such a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential sub-stability.The region of attraction is allowed to be an unbounded open set of the initial values with closure containing the origin.This sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin exponentially.Based on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.
基金This paper was supported by the National Science Fund for Distinguished Young Scholars under Grant No.62125303the Science Center Program of National Natural Science Foundation of China under Grant No.62188101.
文摘It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state feedback.This brief points out that for a scalar high-order fully actuated linear system,the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account,that is,controllability cannot guarantee arbitrary pole assignment by state feedback.
基金supported by the Research Grants Council of the Hong Kong Special Administrative Region of China(CityU/11201120).
文摘This paper considers the leaderless consensus problem of linear time-invariant multi-agent systems with infinite distributed communication delays.A novel distributed low gain controller is proposed based on the solution to a parametric algebraic Riccati equation.It is shown via the newly developed Lyapunov-like method that not only the consensus of linear time-invariant multi-agent systems can be achieved exponentially under some mild assumptions but also an estimate of the exponential convergence rate of consensus is given in this work.The Lyapunovlike method is also extended to handle a special case of linear time-varying multi-agent systems.In addition,the obtained results include the results on the leaderless consensus of linear multiagent systems with bounded distributed communication delays as special cases.To the best of our knowledge,this is thefirst work that develops the Lyapunov-like method for the leaderless consensus problems of both time-invariant and time-varying linear multi-agent systems with infinite distributed communication delays.Finally,a numerical example is presented to illustrate the effectiveness of the proposed controller.
