The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order...The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.展开更多
This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-...This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-square stability of the networked control system are derived subject that the sequence of transmission interval is driven by an identically independently distributed sequence and by a finite state Markov chain, respectively. Stabilization controllers are constructed in terms of linear matrix inequalities correspondingly. An example is provided to illustrate our results.展开更多
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generali...The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.展开更多
Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expr...Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.展开更多
This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth...This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth rate. A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities. To demonstrate the efficiency of the proposed scheme, the well-known chaotic system namely Chua's circuit is considered as an illustrative example.展开更多
In this paper, we study the robust leader-following consensus problem for a class of multi-agent systems with unknown nonlinear dynamics and unknown but bounded disturbances. The control input of the leader agent is n...In this paper, we study the robust leader-following consensus problem for a class of multi-agent systems with unknown nonlinear dynamics and unknown but bounded disturbances. The control input of the leader agent is nonzero and not available to any follower agent. We first consider a class of high order chain integrator-type multi-agent systems.By employing the robust integral of the sign of the error technique, a continuous distributed control law is constructed using local information obtained from neighboring agents. Using Lyapunov analysis theory, we show that under a connected undirected information communication topology, the proposed protocol achieves semiglobal leader-following consensus. We then extend the approach to a class of more general uncertain multiagent systems. A numerical example is given to verify our proposed protocol.展开更多
This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno (T-S) fuzzy model is employed to ...This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.展开更多
Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial s...Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.展开更多
This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be...This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality (LMI) feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.展开更多
In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear si...In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.展开更多
A new method that stabilizes network-based systems with both bounded delay and packet disordering is discussed under the state feedback controller. A novel model, fully describing the dynamic characteristic of network...A new method that stabilizes network-based systems with both bounded delay and packet disordering is discussed under the state feedback controller. A novel model, fully describing the dynamic characteristic of network-based systems with packet disordering, is constructed. Different from the existing models of network-based systems, the number of delay items is time-varying in the model proposed. Further, this model is converted into a parameter-uncertain discrete-time system with time-varying delay item numbers in terms of matrix theory. Moreover, the less conservative stability condition is obtained by avoiding utilisation of Moon et al.’ inequality and bounding inequalities for quadratic functional terms. By solving a minization problem based on linear matrix inequalities, the state feedback controller is presented. A numerical example is given to illustrate the effectiveness of the proposed method.展开更多
Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed.The novelty of the proposed method is a combined use of the st...Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed.The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.展开更多
This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic out...This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator,which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.展开更多
Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators des...Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.展开更多
Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we st...Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.展开更多
In this paper, a Ritt-Wu's characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithm...In this paper, a Ritt-Wu's characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.展开更多
基金Project supported by the National Natural Science Foundation of China (Grants Nos.12375031 and 11905068)the Natural Science Foundation of Fujian Province, China (Grant No.2023J01113)the Scientific Research Funds of Huaqiao University (Grant No.ZQN-810)。
文摘The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.
基金National Natural Science Foundation of China (No.60874021, 60674046)Natural Science Foundation from JiangsuProvince (No.BK2007061)+1 种基金Natural Science Foundation from Jiangsu Provincial Department for Education (No.06KJB120088)Research Fundfor Doctoral Program of Nantong University (No.07B14).
文摘This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-square stability of the networked control system are derived subject that the sequence of transmission interval is driven by an identically independently distributed sequence and by a finite state Markov chain, respectively. Stabilization controllers are constructed in terms of linear matrix inequalities correspondingly. An example is provided to illustrate our results.
基金This work is partly supported by the National Natural Science Foundation of China (No. 60274010, 60221301, 60334040, 60228003).
文摘The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.
文摘Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60974004)
文摘This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth rate. A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities. To demonstrate the efficiency of the proposed scheme, the well-known chaotic system namely Chua's circuit is considered as an illustrative example.
文摘In this paper, we study the robust leader-following consensus problem for a class of multi-agent systems with unknown nonlinear dynamics and unknown but bounded disturbances. The control input of the leader agent is nonzero and not available to any follower agent. We first consider a class of high order chain integrator-type multi-agent systems.By employing the robust integral of the sign of the error technique, a continuous distributed control law is constructed using local information obtained from neighboring agents. Using Lyapunov analysis theory, we show that under a connected undirected information communication topology, the proposed protocol achieves semiglobal leader-following consensus. We then extend the approach to a class of more general uncertain multiagent systems. A numerical example is given to verify our proposed protocol.
基金Project supported by the National Natural Science Foundation of China(Grant No.60974004)
文摘This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
文摘Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.
基金National Natural Science Foundation of China(No.60574011).
文摘This paper considers the problems of practical stability analysis and synthesis of linear descriptor systems subject to timevarying and norm-bounded exogenous disturbances. A sufficient condition for the systems to be regular, impulsive-free and practically stable is derived. Then the synthesis problem is addressed and a state feedback controller is designed. To deal with the computational issue, the conditions of the main results are converted into linear matrix inequality (LMI) feasibility problems. Furthermore, two optimization algorithms are formulated to improve the system performances. Finally, numerical examples are given to illustrate the obtained results.
基金This work was supported by the Science Technical Foundation of Liaoning of China (No. 2001401041)
文摘In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.
基金supported by the National Natural Science Foundation of China (60874057 60725312+3 种基金 61074029)the Liaoning Provincal Foundation of Science and Technology (20082023)the Natural Science Foundation of Liaoning Province (20092083)China Postdoctoral Science Foundation Project (20100471488)
文摘A new method that stabilizes network-based systems with both bounded delay and packet disordering is discussed under the state feedback controller. A novel model, fully describing the dynamic characteristic of network-based systems with packet disordering, is constructed. Different from the existing models of network-based systems, the number of delay items is time-varying in the model proposed. Further, this model is converted into a parameter-uncertain discrete-time system with time-varying delay item numbers in terms of matrix theory. Moreover, the less conservative stability condition is obtained by avoiding utilisation of Moon et al.’ inequality and bounding inequalities for quadratic functional terms. By solving a minization problem based on linear matrix inequalities, the state feedback controller is presented. A numerical example is given to illustrate the effectiveness of the proposed method.
文摘Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed.The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.
文摘This paper deals with the problems of bifurcation suppression and bifurcation suppression with stability of nonlinear systems. Necessary conditions and sufficient conditions for bifurcation suppression via dynamic output feedback are presented; Sufficient conditions for bifurcation suppression with stability via dynamic output feedback are obtained. As an application, a dynamic compensator,which guarantees that the bifurcation point of rotating stall in axial flow compressors is stably suppressed, is constructed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11875135)。
文摘Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11875135)。
文摘Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.
文摘In this paper, a Ritt-Wu's characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.