This paper addresses the problem of the input design of large-scale complex networks.Two types of network components,redundant inaccessible strongly connected component(RISCC)and intermittent inaccessible strongly con...This paper addresses the problem of the input design of large-scale complex networks.Two types of network components,redundant inaccessible strongly connected component(RISCC)and intermittent inaccessible strongly connected component(IISCC)are defined,and a subnetwork called a driver network is developed.Based on these,an efficient method is proposed to find the minimum number of controlled nodes to achieve structural complete controllability of a network,in the case that each input can act on multiple state nodes.The range of the number of input nodes to achieve minimal control,and the configuration method(the connection between the input nodes and the controlled nodes)are presented.All possible input solutions can be obtained by this method.Moreover,we give an example and some experiments on real-world networks to illustrate the effectiveness of the method.展开更多
Parallel connection of multiple inverters is an important means to solve the expansion,reserve and protection of distributed power generation,such as photovoltaics.In view of the shortcomings of traditional droop cont...Parallel connection of multiple inverters is an important means to solve the expansion,reserve and protection of distributed power generation,such as photovoltaics.In view of the shortcomings of traditional droop control methods such as weak anti-interference ability,low tracking accuracy of inverter output voltage and serious circulation phenomenon,a finite control set model predictive control(FCS-MPC)strategy of microgrid multiinverter parallel system based on Mixed Logical Dynamical(MLD)modeling is proposed.Firstly,the MLD modeling method is introduced logical variables,combining discrete events and continuous events to form an overall differential equation,which makes the modeling more accurate.Then a predictive controller is designed based on the model,and constraints are added to the objective function,which can not only solve the real-time changes of the control system by online optimization,but also effectively obtain a higher tracking accuracy of the inverter output voltage and lower total harmonic distortion rate(Total Harmonics Distortion,THD);and suppress the circulating current between the inverters,to obtain a good dynamic response.Finally,the simulation is carried out onMATLAB/Simulink to verify the correctness of the model and the rationality of the proposed strategy.This paper aims to provide guidance for the design and optimal control of multi-inverter parallel systems.展开更多
Nowadays,AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment.To tackle the problems of control difficulty,strategy complexity,and poor d...Nowadays,AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment.To tackle the problems of control difficulty,strategy complexity,and poor dynamic performance of AC electronic load with energy recovery of the conventional control strategy,a control strategy of AC electronic load with energy recovery based on Finite Control Set Model Predictive Control(FCSMPC)is developed.To further reduce the computation burden of the FCS-MPC,a simplified FCS-MPC with transforming the predicted variables and using sector to select expected state is proposed.Through simplified model and equivalent approximation analysis,the transfer function of the system is obtained,and the stability and robustness of the system are analyzed.The performance of the simplified FCS-MPC is compared with space vector control(SVPWM)and conventional FCS-MPC.The results show that the FCS-MPC method performs better dynamic response and this advantage is more obvious when simulating high power loads.The simplified FCS-MPC shows similar control performance to conventional FCS-MPC at less computation burden.The control performance of the system also shows better simulation results.展开更多
Permanent magnet synchronous motors(PMSMs)have been widely employed in the industry. Finite-control-set model predictive control(FCS-MPC), as an advanced control scheme, has been developed and applied to improve the p...Permanent magnet synchronous motors(PMSMs)have been widely employed in the industry. Finite-control-set model predictive control(FCS-MPC), as an advanced control scheme, has been developed and applied to improve the performance and efficiency of the holistic PMSM drive systems. Based on the three elements of model predictive control, this paper provides an overview of the superiority of the FCS-MPC control scheme and its shortcomings in current applications. The problems of parameter mismatch, computational burden, and unfixed switching frequency are summarized. Moreover, other performance improvement schemes, such as the multi-vector application strategy, delay compensation scheme, and weight factor adjustment, are reviewed. Finally, future trends in this field is discussed, and several promising research topics are highlighted.展开更多
To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed ...To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed in this paper.Two new look-up tables are proposed,these are derived on the basis of the control of the electromagnetic torque and stator flux using all the feasible voltage vectors and their associated switching states.Finite control set model predictive control(FCS-MPC)has then been adopted to select the optimal switching state that minimizes the cost function related to the electromagnetic torque.Finally,the experimental results are shown to verify the reduced torque ripple performance of the proposed MPC-based DTC method.展开更多
The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of sw...The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.展开更多
The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of s...The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.展开更多
This paper presents an improved finite control set model predictive current control(FCS-MPCC)of a five-phase permanent magnet synchronous motor(PMSM).First,to avoid including all the 32 voltage vectors provided by a t...This paper presents an improved finite control set model predictive current control(FCS-MPCC)of a five-phase permanent magnet synchronous motor(PMSM).First,to avoid including all the 32 voltage vectors provided by a two-level five-phase inverter into the control set,virtual voltage vectors are adopted.As the third current harmonics can be much reduced by virtual voltage vectors automatically,the harmonic items in the cost function of conventional FCS-MPCC are not considered.Furthermore,an adaptive control set is proposed based on voltage prediction.Best control set with proper voltage vector amplitude corresponding to different rotor speed can be achieved by this method.Consequently,current ripples can be largely reduced and the system performs much better.At last,simulations are established to verify the steady and transient performance of the proposed FCS-MPCC,and experiments based on a 2 kW five-phase motor are carried out.The results have validated the performance improvement of the proposed control strategy.展开更多
In the process of grid-connected photovoltaic power generation,there are high requirements for the quality of the power that the inverter breaks into the grid.In this work,to improve the power quality of the grid-conn...In the process of grid-connected photovoltaic power generation,there are high requirements for the quality of the power that the inverter breaks into the grid.In this work,to improve the power quality of the grid-connected inverter into the grid,and the output of the system can meet the grid-connected requirements more quickly and accurately,we exhibit an approach toward establishing a mixed logical dynamical(MLD)model where logic variables were introduced to switch dynamics of the single-phase photovoltaic inverters.Besides,based on the model,our recent efforts in studying the finite control set model predictive control(FCS-MPC)and devising the output current full state observer are exciting for several advantages,including effectively avoiding the problem of the mixed-integer quadratic programming(MIQP),lowering the THD value of the output current of the inverter circuit,improving the quality of the power that the inverter breaks into the grid,and realizing the current output and the grid voltage same frequency and phase to meet grid connection requirements.Finally,the effectiveness of the mentioned methods is verified by MATLAB/Simulink simulation.展开更多
A program control was applied in the fuel gas shuttle kiln,and its principle and disadvantge were analyzed.An advanced set point control method,in which the change rate of temperature is the controlled variable,is als...A program control was applied in the fuel gas shuttle kiln,and its principle and disadvantge were analyzed.An advanced set point control method,in which the change rate of temperature is the controlled variable,is also described,and the new control system makes the control precision of temperature improved.展开更多
Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a contr...Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a controller is studied. A control node corresponds to a gene that expression can be controlled. Here, a Boolean network is used as a model of gene regulatory networks, and control specifications on attractors, which represent cell types or states of cells, are imposed. It is important to design a gene regulatory network that has desired attractors and has no undesired attractors. Using a matrix-based representation of BNs, this problem can be rewritten as an integer linear programming problem. Finally, the proposed method is demonstrated by a numerical example on a WNT5A network, which is related to melanoma.展开更多
The increasing demand on robotic system performance leads to the use of advanced con- trol strategies. This paper proposes a method of nonlinear feedback control introducing fuzzy infer- ence into model-following adap...The increasing demand on robotic system performance leads to the use of advanced con- trol strategies. This paper proposes a method of nonlinear feedback control introducing fuzzy infer- ence into model-following adaptive control for the nonlinear robot manipulator systems. The fuzzy inference is introduced to treat the nonlinearities of the control systems. Furthermore, the stability of the system is discussed by the fuzzy stability theory based on the Lyapunov's direct method. In the closed loop, the robotic system asymptotically converge to the reference trajectory with a pre- scribed transient response.展开更多
This paper is concerned with a systematic method of smooth switching linear parameter- varying (LPV) controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as a...This paper is concerned with a systematic method of smooth switching linear parameter- varying (LPV) controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as an LPV system, whose scheduling parameter is the variation rate of the wing sweep angle. By dividing the scheduling parameter set into subsets with overlaps, output feedback controllers which consider smooth switching are designed and the controllers in over- lapped subsets are interpolated from two adjacent subsets. A switching law without constraint on the average dwell time is obtained which makes the conclusion less conservative. Furthermore, a systematic algorithm is developed to improve the efficiency of the controllers design process. The parameter set is divided into the fewest subsets on the premise that the closed-loop system has a desired performance. Simulation results demonstrate the effectiveness of this approach.展开更多
Finite control set-model predictive control (FCS-MPC) is employed in this paper to control the operation of a three-phase grid-connected string inverter based on a direct PQ control scheme. The main objective is to ac...Finite control set-model predictive control (FCS-MPC) is employed in this paper to control the operation of a three-phase grid-connected string inverter based on a direct PQ control scheme. The main objective is to achieve high-performance decoupled control of the active and reactive powers injected to the grid from distributed energy resources (DER).The FCS-MPC scheme instantaneously searches for and applies the optimum inverter switching state that can achieve certain goals, such as minimum deviation between reference and actual power;so that both power components (P and Q) are well controlled to their reference values.In addition, an effective method to attenuate undesired cross coupling between the P and Q control loops, which occurs only during transient operation, is investigated. The proposed method is based on the variation of the weight factors of the terms of the FCS-MPC cost function, so a higher weight factor is assigned to the cost function term that is exposed to greater disturbance. Empirical formulae of optimum weight factors as functions of the reference active and reactive power signals are proposed and mathematically derived. The investigated FCS-MPC control scheme is incorporated with the LVRT function to support the grid voltage in fulfilling and accomplishing the up-to-date grid codes. The LVRT algorithm is based on a modification of the references of active and reactive powers as functions of the instantaneous grid voltage such that suitable values of P and Q are injected to the grid during voltage sag.The performance of the elaborated FCS-MPC PQ scheme is studied under various operating scenarios, including steady-state and transient conditions. Results demonstrate the validity and effectiveness of the proposed scheme with regard to the achievement of high-performance operation and quick response of grid-tied inverters during normal and fault modes.展开更多
Control strategies play a key role for operation of electric machines,which would directly affect the whole system performance.In fact,different control strategies have been executed and explored for electric machines...Control strategies play a key role for operation of electric machines,which would directly affect the whole system performance.In fact,different control strategies have been executed and explored for electric machines,which bring great impacts to industrial development and human society.This paper investigates and discusses the advantages control strategies for electric machines,including the field oriented control(FOC),direct torque control(DTC),finite control set model predictive control(FCS-MPC),sensorless control,and fault tolerant control(FTC).The corresponding control principles,control targets,fundamental approaches,advanced approaches,methodologies,merits and shortcomings are revealed and analyzed in detail.展开更多
In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six t...In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six types of equi-invariability.As a by-product,two new dichotomy theorems for the control system on the control sets are established.展开更多
基金supported in part by the National Natural Science Foundation of China(U1808205,62173079)the Natural Science Foundation of Hebei Province of China(F2000501005)。
文摘This paper addresses the problem of the input design of large-scale complex networks.Two types of network components,redundant inaccessible strongly connected component(RISCC)and intermittent inaccessible strongly connected component(IISCC)are defined,and a subnetwork called a driver network is developed.Based on these,an efficient method is proposed to find the minimum number of controlled nodes to achieve structural complete controllability of a network,in the case that each input can act on multiple state nodes.The range of the number of input nodes to achieve minimal control,and the configuration method(the connection between the input nodes and the controlled nodes)are presented.All possible input solutions can be obtained by this method.Moreover,we give an example and some experiments on real-world networks to illustrate the effectiveness of the method.
基金supported by the Major Science and Technology Projects of Gansu Province(Grant No.20ZD7GF011)Gansu Province Higher Education Industry Support Plan Project:Research on the Collaborative Operation of Solar Thermal Storage+Wind-Solar Hybrid Power Generation--Based on“Integrated Energy Demonstration of Wind-Solar Energy Storage in Gansu Province”(Project No.2022CYZC-34).
文摘Parallel connection of multiple inverters is an important means to solve the expansion,reserve and protection of distributed power generation,such as photovoltaics.In view of the shortcomings of traditional droop control methods such as weak anti-interference ability,low tracking accuracy of inverter output voltage and serious circulation phenomenon,a finite control set model predictive control(FCS-MPC)strategy of microgrid multiinverter parallel system based on Mixed Logical Dynamical(MLD)modeling is proposed.Firstly,the MLD modeling method is introduced logical variables,combining discrete events and continuous events to form an overall differential equation,which makes the modeling more accurate.Then a predictive controller is designed based on the model,and constraints are added to the objective function,which can not only solve the real-time changes of the control system by online optimization,but also effectively obtain a higher tracking accuracy of the inverter output voltage and lower total harmonic distortion rate(Total Harmonics Distortion,THD);and suppress the circulating current between the inverters,to obtain a good dynamic response.Finally,the simulation is carried out onMATLAB/Simulink to verify the correctness of the model and the rationality of the proposed strategy.This paper aims to provide guidance for the design and optimal control of multi-inverter parallel systems.
文摘Nowadays,AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment.To tackle the problems of control difficulty,strategy complexity,and poor dynamic performance of AC electronic load with energy recovery of the conventional control strategy,a control strategy of AC electronic load with energy recovery based on Finite Control Set Model Predictive Control(FCSMPC)is developed.To further reduce the computation burden of the FCS-MPC,a simplified FCS-MPC with transforming the predicted variables and using sector to select expected state is proposed.Through simplified model and equivalent approximation analysis,the transfer function of the system is obtained,and the stability and robustness of the system are analyzed.The performance of the simplified FCS-MPC is compared with space vector control(SVPWM)and conventional FCS-MPC.The results show that the FCS-MPC method performs better dynamic response and this advantage is more obvious when simulating high power loads.The simplified FCS-MPC shows similar control performance to conventional FCS-MPC at less computation burden.The control performance of the system also shows better simulation results.
基金supported in part by the National Natural Science Foundation of China(51875261)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX21_3331)+1 种基金the Faculty of Agricultural Equipment of Jiangsu University(NZXB20210103)。
文摘Permanent magnet synchronous motors(PMSMs)have been widely employed in the industry. Finite-control-set model predictive control(FCS-MPC), as an advanced control scheme, has been developed and applied to improve the performance and efficiency of the holistic PMSM drive systems. Based on the three elements of model predictive control, this paper provides an overview of the superiority of the FCS-MPC control scheme and its shortcomings in current applications. The problems of parameter mismatch, computational burden, and unfixed switching frequency are summarized. Moreover, other performance improvement schemes, such as the multi-vector application strategy, delay compensation scheme, and weight factor adjustment, are reviewed. Finally, future trends in this field is discussed, and several promising research topics are highlighted.
基金This work was supported in part by the Hunan Provincial Key Laboratory of Power Electronics Equipment and Grid under Grant 2018TP1001in part by the National Natural Science Foundation of China under Grant 61903382,51807206,61933011+1 种基金in part by the Major Project of Changzhutan Self-Dependent Innovation Demonstration Area under Grant 2018XK2002in part by the Natural Science Foundation of Hunan Province,China under Grant 2020JJ5722 and 2020JJ5753.
文摘To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed in this paper.Two new look-up tables are proposed,these are derived on the basis of the control of the electromagnetic torque and stator flux using all the feasible voltage vectors and their associated switching states.Finite control set model predictive control(FCS-MPC)has then been adopted to select the optimal switching state that minimizes the cost function related to the electromagnetic torque.Finally,the experimental results are shown to verify the reduced torque ripple performance of the proposed MPC-based DTC method.
文摘The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of aperiodic systems are presented,respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.
文摘The controllability for switched linear systems with time_delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time_delay in control functions is mainly investigated. The sufficient and necessary conditions for the one_periodic, multiple_periodic controllability of periodic_type systems and controllability of periodic systems are presented, respectively.
基金This work was supported in part by the National Natural Science Foundation of China under 61374125。
文摘This paper presents an improved finite control set model predictive current control(FCS-MPCC)of a five-phase permanent magnet synchronous motor(PMSM).First,to avoid including all the 32 voltage vectors provided by a two-level five-phase inverter into the control set,virtual voltage vectors are adopted.As the third current harmonics can be much reduced by virtual voltage vectors automatically,the harmonic items in the cost function of conventional FCS-MPCC are not considered.Furthermore,an adaptive control set is proposed based on voltage prediction.Best control set with proper voltage vector amplitude corresponding to different rotor speed can be achieved by this method.Consequently,current ripples can be largely reduced and the system performs much better.At last,simulations are established to verify the steady and transient performance of the proposed FCS-MPCC,and experiments based on a 2 kW five-phase motor are carried out.The results have validated the performance improvement of the proposed control strategy.
基金supported by the National Natural Science Foundation of China(Grant No.51667013)the Science and Technology Project of State Grid Corporation of China(Grant No.52272219000 V).
文摘In the process of grid-connected photovoltaic power generation,there are high requirements for the quality of the power that the inverter breaks into the grid.In this work,to improve the power quality of the grid-connected inverter into the grid,and the output of the system can meet the grid-connected requirements more quickly and accurately,we exhibit an approach toward establishing a mixed logical dynamical(MLD)model where logic variables were introduced to switch dynamics of the single-phase photovoltaic inverters.Besides,based on the model,our recent efforts in studying the finite control set model predictive control(FCS-MPC)and devising the output current full state observer are exciting for several advantages,including effectively avoiding the problem of the mixed-integer quadratic programming(MIQP),lowering the THD value of the output current of the inverter circuit,improving the quality of the power that the inverter breaks into the grid,and realizing the current output and the grid voltage same frequency and phase to meet grid connection requirements.Finally,the effectiveness of the mentioned methods is verified by MATLAB/Simulink simulation.
文摘A program control was applied in the fuel gas shuttle kiln,and its principle and disadvantge were analyzed.An advanced set point control method,in which the change rate of temperature is the controlled variable,is also described,and the new control system makes the control precision of temperature improved.
文摘Design of control strategies for gene regulatory networks is a challenging and important topic in systems biology. In this paper, the problem of finding both a minimum set of control nodes (control inputs) and a controller is studied. A control node corresponds to a gene that expression can be controlled. Here, a Boolean network is used as a model of gene regulatory networks, and control specifications on attractors, which represent cell types or states of cells, are imposed. It is important to design a gene regulatory network that has desired attractors and has no undesired attractors. Using a matrix-based representation of BNs, this problem can be rewritten as an integer linear programming problem. Finally, the proposed method is demonstrated by a numerical example on a WNT5A network, which is related to melanoma.
文摘The increasing demand on robotic system performance leads to the use of advanced con- trol strategies. This paper proposes a method of nonlinear feedback control introducing fuzzy infer- ence into model-following adaptive control for the nonlinear robot manipulator systems. The fuzzy inference is introduced to treat the nonlinearities of the control systems. Furthermore, the stability of the system is discussed by the fuzzy stability theory based on the Lyapunov's direct method. In the closed loop, the robotic system asymptotically converge to the reference trajectory with a pre- scribed transient response.
基金supported by the National Natural Science Foundation of China(Nos.61273083 and 61374012)
文摘This paper is concerned with a systematic method of smooth switching linear parameter- varying (LPV) controllers design for a morphing aircraft with a variable wing sweep angle. The morphing aircraft is modeled as an LPV system, whose scheduling parameter is the variation rate of the wing sweep angle. By dividing the scheduling parameter set into subsets with overlaps, output feedback controllers which consider smooth switching are designed and the controllers in over- lapped subsets are interpolated from two adjacent subsets. A switching law without constraint on the average dwell time is obtained which makes the conclusion less conservative. Furthermore, a systematic algorithm is developed to improve the efficiency of the controllers design process. The parameter set is divided into the fewest subsets on the premise that the closed-loop system has a desired performance. Simulation results demonstrate the effectiveness of this approach.
文摘Finite control set-model predictive control (FCS-MPC) is employed in this paper to control the operation of a three-phase grid-connected string inverter based on a direct PQ control scheme. The main objective is to achieve high-performance decoupled control of the active and reactive powers injected to the grid from distributed energy resources (DER).The FCS-MPC scheme instantaneously searches for and applies the optimum inverter switching state that can achieve certain goals, such as minimum deviation between reference and actual power;so that both power components (P and Q) are well controlled to their reference values.In addition, an effective method to attenuate undesired cross coupling between the P and Q control loops, which occurs only during transient operation, is investigated. The proposed method is based on the variation of the weight factors of the terms of the FCS-MPC cost function, so a higher weight factor is assigned to the cost function term that is exposed to greater disturbance. Empirical formulae of optimum weight factors as functions of the reference active and reactive power signals are proposed and mathematically derived. The investigated FCS-MPC control scheme is incorporated with the LVRT function to support the grid voltage in fulfilling and accomplishing the up-to-date grid codes. The LVRT algorithm is based on a modification of the references of active and reactive powers as functions of the instantaneous grid voltage such that suitable values of P and Q are injected to the grid during voltage sag.The performance of the elaborated FCS-MPC PQ scheme is studied under various operating scenarios, including steady-state and transient conditions. Results demonstrate the validity and effectiveness of the proposed scheme with regard to the achievement of high-performance operation and quick response of grid-tied inverters during normal and fault modes.
基金Supported by the general program of National Natural Science Foundation of China under Grant 51677159a grant(Project No.CityU 21201216)from the Research Grants Council of HKSAR,China.
文摘Control strategies play a key role for operation of electric machines,which would directly affect the whole system performance.In fact,different control strategies have been executed and explored for electric machines,which bring great impacts to industrial development and human society.This paper investigates and discusses the advantages control strategies for electric machines,including the field oriented control(FOC),direct torque control(DTC),finite control set model predictive control(FCS-MPC),sensorless control,and fault tolerant control(FTC).The corresponding control principles,control targets,fundamental approaches,advanced approaches,methodologies,merits and shortcomings are revealed and analyzed in detail.
基金National Natural Science Foundation of China(Grant No.11771459)supported by Research Funds of Guangdong University of Foreign Studies(Grant Nos.299-X5218165 and 299-X5219222)+3 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110932)supported by National Natural Science Foundation of China(Grant Nos.11701584 and 11871228)the Natural Science Research Project of Guangdong Province(Grant No.2018KTSCX122)。
文摘In this paper,we introduce the notions of bounded invariance complexity,bounded invariance complexity in the mean and mean Lyapunov-stability for control systems.Then we characterize these notions by introducing six types of equi-invariability.As a by-product,two new dichotomy theorems for the control system on the control sets are established.