Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This r...Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.展开更多
A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. ...A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.展开更多
The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effe...The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.展开更多
BACKGROUND Othello syndrome(OS)is characterized by delusional beliefs concerning the infidelity of a spouse or sexual partner,which may lead to extreme behaviors.Impulse control disorders refer to behaviors involving ...BACKGROUND Othello syndrome(OS)is characterized by delusional beliefs concerning the infidelity of a spouse or sexual partner,which may lead to extreme behaviors.Impulse control disorders refer to behaviors involving repetitive,excessive,and compulsive activities driven by an intense desire.Both OS and impulse control disorders in Parkinson’s disease(PD)may be side effects of dopamine agonists.At present,there are only a few case reports and studies related to PD with concomitant OS and impulse control disorders.CASE SUMMARY We describe a 70-year-old male patient with PD,OS,and impulse control disorders,who presented with a six-month history of the delusional belief that his wife was having an affair with someone.He began to show an obvious increase in libido presenting as frequent masturbation.He had been diagnosed with PD ten years earlier and had no past psychiatric history.In his fourth year of PD,he engaged in binge eating,which lasted approximately one year.Both OS and hypersexuality were alleviated substantially after a reduction of his pramipexole dosage and a prescription of quetiapine.CONCLUSION Given its potential for severe consequences,OS should be identified early,especially in patients undergoing treatment with dopamine agonists.展开更多
This paper is concerned with periodic optimal control problems governed by semi- linear parabolic differential equations with impulse control. Pontryagin＇s maximum principle is derived. The proofs rely on a unique co...This paper is concerned with periodic optimal control problems governed by semi- linear parabolic differential equations with impulse control. Pontryagin＇s maximum principle is derived. The proofs rely on a unique continuation estimate at one time for a linear parabolic equation.展开更多
A friction model was established for impulse control design in a precision control system. First, the physical characteristics of the impulse in momentum, such as motion and energy, were analyzed and formulated. Then,...A friction model was established for impulse control design in a precision control system. First, the physical characteristics of the impulse in momentum, such as motion and energy, were analyzed and formulated. Then, experimental response to a new pulse with two harmonic expansions was studied. The first harmonic is the main pulse to drive the arm, and the second harmonic has two functions： its first half helps the main pulse eliminate the dead zone, and its second half, a negative pulse, stops the arm motion quickly. Finally, an impulse feedback controller was developed. Comparison between simulation and experiments shows the effectiveness of the proposed controller.展开更多
The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the on...The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.展开更多
Purpose: Rapid eye movement sleep behavior disorder (RBD) and impulse control disorders (ICDs) are common in subjects with Parkinson’s disease. The association between these two conditions has been contradictory. The...Purpose: Rapid eye movement sleep behavior disorder (RBD) and impulse control disorders (ICDs) are common in subjects with Parkinson’s disease. The association between these two conditions has been contradictory. The aim of this study is to analyze the association between these two non-motor symptoms. Methods: Consecutive subjects with Parkinson’s disease attending the Movement Disorders Outpatient Clinic were included. The presence of ICDs was assessed using the Questionnaire for Impulse Control Disorders Rating Scale. RBD was diagnosed by an overnight, single night polysomnography. Results: Fifty-five consecutive subjects with Parkinson’s disease were included. The prevalence of ICDs and related behaviors was 23.6% (ICD in 14.5% and related behaviors in 9.1%). RBD was diagnosed in 47.2% of the patients. No differences were found in the frequency of ICDs and related behaviors when comparing subjects with and without RBD (23% versus 24.1%, p = 0.926, respectively). Conclusion: No association between the presence of RBD and the frequency of ICDs in subjects with Parkinson’s disease was found.展开更多
We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost o...We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.展开更多
Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the...Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.展开更多
Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous sta...Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.展开更多
This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distingui...This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls,which have potential applications in mathematical finance.展开更多
Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the imp...Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.展开更多
This paper focuses on zero-sum stochastic differential games in the framework of forwardbackward stochastic differential equations on a finite time horizon with both players adopting impulse controls.By means of BSDE ...This paper focuses on zero-sum stochastic differential games in the framework of forwardbackward stochastic differential equations on a finite time horizon with both players adopting impulse controls.By means of BSDE methods,in particular that of the notion from Peng’s stochastic backward semigroups,the authors prove a dynamic programming principle for both the upper and the lower value functions of the game.The upper and the lower value functions are then shown to be the unique viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equations with a double-obstacle.As a consequence,the uniqueness implies that the upper and lower value functions coincide and the game admits a value.展开更多
This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems i...This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.展开更多
This paper investigates the secure impulsive consensus of Lipschitz-type nonlinear multi-agent systems(MASs) with input saturation. According to the coupling of input saturation and denial of service(DoS) attacks, imp...This paper investigates the secure impulsive consensus of Lipschitz-type nonlinear multi-agent systems(MASs) with input saturation. According to the coupling of input saturation and denial of service(DoS) attacks, impulsive control for MASs becomes extremely challenging. Considering general DoS attacks,this paper provides the sufficient conditions for the almost sure consensus of the MASs with input saturation, where the error system can achieve almost sure local exponential stability.Through linear matrix inequalities(LMIs), the relation between the trajectory boundary and DoS attacks is characterized, and the trajectory boundary is estimated. Furthermore, an optimization method of the domain of attraction is proposed to maximize the size. And a non-conservative and practical boundary is proposed to characterize the effect of DoS attacks on MASs. Finally, considering a multi-agent system with typical Chua's circuit dynamic model, an example is provided to illustrate the theorems' correctness.展开更多
The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven...The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.展开更多
In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems ...In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.展开更多
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From th...This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.展开更多
In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impu...In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.展开更多
文摘Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.
基金Project supported by the Center for Nonlinear Systems,Chennai Institute of Technology,India (Grant No. CIT/CNS/2020/RD/061)。
文摘A fractional-order difference equation model of a third-order discrete phase-locked loop(FODPLL) is discussed and the dynamical behavior of the model is demonstrated using bifurcation plots and a basin of attraction. We show a narrow region of loop gain where the FODPLL exhibits quasi-periodic oscillations, which were not identified in the integer-order model. We propose a simple impulse control algorithm to suppress chaos and discuss the effect of the control step. A network of FODPLL oscillators is constructed and investigated for synchronization behavior. We show the existence of chimera states while transiting from an asynchronous to a synchronous state. The same impulse control method is applied to a lattice array of FODPLL, and the chimera states are then synchronized using the impulse control algorithm. We show that the lower control steps can achieve better control over the higher control steps.
基金partially supported by the Project for the National Natural Science Foundation of China(Grant Nos.72174121 and 71774111)the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning+1 种基金the Project for the Natural Science Foundation of Shanghai(Grant No.21ZR1444100)Project Soft Science Research of Shanghai(Grant No.22692112600)。
文摘The Internet era has brought great convenience to our life and communication.Meanwhile,it also makes a bunch of rumors propagate faster and causes even more harm to human life.Therefore,it is necessary to perform effective control mechanisms to minimize the negative social impact from rumors.Thereout,firstly,we formulate a rumor spreading model considering psychological factors and thinking time,then,we add white noise(i.e.,stochastic interference)and two pulse control strategies which denote education mechanism and refutation mechanism into the model.Secondly,we obtain the global positive solutions and demonstrate the global exponential stability of the unique positive periodic rumor-free solution.Thirdly,we discuss the extinction and persistence of rumor.Moreover,we use Pontriagin’s minimum principle to explore the optimal impulse control.Finally,several numerical simulations are carried out to verify the effectiveness and availability of the theoretical analysis.We conclude that the pulse control strategies have a great influence on controlling rumor spreading,and different control strategies should be adopted under different transmission scenarios.
基金Supported by Zhejiang Province Medical Science and Technology Project,No.2018KY872Yiwu Science and Technology Bureau Project,No.20-3-074.
文摘BACKGROUND Othello syndrome(OS)is characterized by delusional beliefs concerning the infidelity of a spouse or sexual partner,which may lead to extreme behaviors.Impulse control disorders refer to behaviors involving repetitive,excessive,and compulsive activities driven by an intense desire.Both OS and impulse control disorders in Parkinson’s disease(PD)may be side effects of dopamine agonists.At present,there are only a few case reports and studies related to PD with concomitant OS and impulse control disorders.CASE SUMMARY We describe a 70-year-old male patient with PD,OS,and impulse control disorders,who presented with a six-month history of the delusional belief that his wife was having an affair with someone.He began to show an obvious increase in libido presenting as frequent masturbation.He had been diagnosed with PD ten years earlier and had no past psychiatric history.In his fourth year of PD,he engaged in binge eating,which lasted approximately one year.Both OS and hypersexuality were alleviated substantially after a reduction of his pramipexole dosage and a prescription of quetiapine.CONCLUSION Given its potential for severe consequences,OS should be identified early,especially in patients undergoing treatment with dopamine agonists.
基金partially supported by the National Science Foundation of China(11371285)
文摘This paper is concerned with periodic optimal control problems governed by semi- linear parabolic differential equations with impulse control. Pontryagin＇s maximum principle is derived. The proofs rely on a unique continuation estimate at one time for a linear parabolic equation.
基金The Foundation of Sichuan Education Department (No.09ZC24)
文摘A friction model was established for impulse control design in a precision control system. First, the physical characteristics of the impulse in momentum, such as motion and energy, were analyzed and formulated. Then, experimental response to a new pulse with two harmonic expansions was studied. The first harmonic is the main pulse to drive the arm, and the second harmonic has two functions： its first half helps the main pulse eliminate the dead zone, and its second half, a negative pulse, stops the arm motion quickly. Finally, an impulse feedback controller was developed. Comparison between simulation and experiments shows the effectiveness of the proposed controller.
文摘The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.
文摘Purpose: Rapid eye movement sleep behavior disorder (RBD) and impulse control disorders (ICDs) are common in subjects with Parkinson’s disease. The association between these two conditions has been contradictory. The aim of this study is to analyze the association between these two non-motor symptoms. Methods: Consecutive subjects with Parkinson’s disease attending the Movement Disorders Outpatient Clinic were included. The presence of ICDs was assessed using the Questionnaire for Impulse Control Disorders Rating Scale. RBD was diagnosed by an overnight, single night polysomnography. Results: Fifty-five consecutive subjects with Parkinson’s disease were included. The prevalence of ICDs and related behaviors was 23.6% (ICD in 14.5% and related behaviors in 9.1%). RBD was diagnosed in 47.2% of the patients. No differences were found in the frequency of ICDs and related behaviors when comparing subjects with and without RBD (23% versus 24.1%, p = 0.926, respectively). Conclusion: No association between the presence of RBD and the frequency of ICDs in subjects with Parkinson’s disease was found.
基金supported by the National Center for Scientific and Technical Research CNRST,Rabat,Morocco[grant number 17 UIZ 19].
文摘We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.
基金the financial support from the National Natural Science Foundation of China(12171405 and 11661074)the Program for New Century Excellent Talents in Fujian Province University+2 种基金the financial support from the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)Collaborative Innovation Center of Statistical Data Engineering Technology&ApplicationDigital+Discipline Construction Project(SZJ2022B004)。
文摘Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.
基金supported by the National Natural Science Foundation of China(62403393,12202058,62103118)the China Postdoctoral Science Foundation(2021T140160,2023 T160051)the Natural Science Foundation of Chongqing(CSTB 2023NSCQ-MSX0152)
文摘Dear Editor,This letter deals with the stabilization problem of nonlinear stochastic systems via self-triggered impulsive control(STIC), where the timing of impulsive control actions is not dependent on continuous state monitoring. In contrast to the existing self-triggered control method, novel self-triggered mechanism(STM) is proposed by incorporating a waiting time for stabilizing impulses. This allows for direct prediction of the next impulsive instant.
基金supported by the Natural Science Foundation of China under Grant No.61573217,111 Project(B12023)the National High-Level Personnel of Special Support Programthe Chang Jiang Scholar Program of Chinese Education Ministry
文摘This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls,which have potential applications in mathematical finance.
基金supported by the National Natural Science Foundation of China under Grant No.61174081
文摘Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.
基金supported by the National Nature Science Foundation of China under Grant Nos.11701040,11871010,61871058the Fundamental Research Funds for the Central Universities under Grant No.2019XDA11。
文摘This paper focuses on zero-sum stochastic differential games in the framework of forwardbackward stochastic differential equations on a finite time horizon with both players adopting impulse controls.By means of BSDE methods,in particular that of the notion from Peng’s stochastic backward semigroups,the authors prove a dynamic programming principle for both the upper and the lower value functions of the game.The upper and the lower value functions are then shown to be the unique viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equations with a double-obstacle.As a consequence,the uniqueness implies that the upper and lower value functions coincide and the game admits a value.
基金supported by the National Natural Science Foundation of China under Grant Nos.11926402and 61973338。
文摘This paper discusses the impulse controllability and impulse observability of stochastic singular systems.Firstly,the condition for the existence and uniqueness of the impulse solution to stochastic singular systems is given by Laplace transform.Secondly,the necessary and sufficient conditions for the impulse controllability and impulse observability of systems considered are derived in terms of matrix theory.Finally,an example is given to illustrate the effectiveness of the obtained theoretical results.
基金supported by the National Natural Science Foundation of China(62373302,62333009)
文摘This paper investigates the secure impulsive consensus of Lipschitz-type nonlinear multi-agent systems(MASs) with input saturation. According to the coupling of input saturation and denial of service(DoS) attacks, impulsive control for MASs becomes extremely challenging. Considering general DoS attacks,this paper provides the sufficient conditions for the almost sure consensus of the MASs with input saturation, where the error system can achieve almost sure local exponential stability.Through linear matrix inequalities(LMIs), the relation between the trajectory boundary and DoS attacks is characterized, and the trajectory boundary is estimated. Furthermore, an optimization method of the domain of attraction is proposed to maximize the size. And a non-conservative and practical boundary is proposed to characterize the effect of DoS attacks on MASs. Finally, considering a multi-agent system with typical Chua's circuit dynamic model, an example is provided to illustrate the theorems' correctness.
基金supported by the National Natural Science Foundation of China (Grant No 60604007)
文摘The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10926066 and 11026182)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6100007)+3 种基金the Zhejiang Educational Committee,China(Grant No.Y200805720)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010408)the Innovation Fund of Basic Scientific Research Operating Expenses,China(Grant No.3207010501)the Alexander von Humboldt Foundation of Germany
文摘In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10902085)
文摘This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations, and establishes a comparison theory to ensure the trivial solution＇s stochastic asymptotical stability. From the comparison theory, it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterministic comparison system. As a general application of this theory, it controls the chaos of stochastic Lii system using impulsive control method, and numerical simulations are employed to verify the feasibility of this method.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+2 种基金Liaoning Provincial Natural Science Foundation of China (Grant No 20062018)State Key Development Program for Basic research of China (Grant No 2009CB320601)111 Project,China (Grant No B08015)
文摘In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.
