This paper investigates the persistence and existence of almost periodic solutions for a discrete competitive system with feedback controls based on the comparison theorem of the difference equation and constructing a...This paper investigates the persistence and existence of almost periodic solutions for a discrete competitive system with feedback controls based on the comparison theorem of the difference equation and constructing appropriate Lyapunov function, and several sufficient conditions for the existence of positive almost periodic solutions for the model are obtained.Finally, a numerical example is given to illustrate effectiveness of our main results.展开更多
The problem of stabilizing a hybrid stochastic interval system is studied in this article. A hybrid interval system with suitable controls will become stable in the sense of mean-square exponential stability. State-fe...The problem of stabilizing a hybrid stochastic interval system is studied in this article. A hybrid interval system with suitable controls will become stable in the sense of mean-square exponential stability. State-feedback controls are designed based on the discrete-time state observations. Controls are put both in the drift and diffusion parts of the system. Criteria are derived in terms of linear matrix inequalities( LMI) to get the controllers. Also one example is given to illustrate our techniques.展开更多
For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It...For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.展开更多
By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) period...By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.展开更多
In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain suffi...In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.展开更多
In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis tec...In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 （2008） 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.展开更多
In this paper, we consider an almost periodic multi-species Kolmogorov type com-petitive system with feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive almost per...In this paper, we consider an almost periodic multi-species Kolmogorov type com-petitive system with feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive almost periodic solution to the system is obtained. Our results improve and generalize some existing conclusions.展开更多
In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the glob...In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the global asymptotic stability of the system.展开更多
In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we dis...In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.展开更多
In this paper, we consider the general nonautonomous single-species Kolmogorov type system with delay and feedback controls. Sufficient conditions for the permanence of species are established. Our results generalize ...In this paper, we consider the general nonautonomous single-species Kolmogorov type system with delay and feedback controls. Sufficient conditions for the permanence of species are established. Our results generalize some known results.展开更多
A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system ...A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].展开更多
Sufficient conditions are derived for the existence of globally asymptotically stable solution in a two species competition system with periodic coefficients and feedback controls.
This paper investigates the problem of cluster synchronization of master-slave complex net-works with time-varying delay via linear and adaptive feedback pinning controls.We need not non-delayed and delayed coupling m...This paper investigates the problem of cluster synchronization of master-slave complex net-works with time-varying delay via linear and adaptive feedback pinning controls.We need not non-delayed and delayed coupling matrices to be symmetric or irreducible.We have the advantages of using adaptive control method to reduce control gain and pinning control technology to reduce cost.By con-structing Lyapunov function,some sufficient synchronization criteria are established.Finally,numerical examples are employed to illustrate the effectiveness of the proposed approach.展开更多
Graphene platelets(GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams.Further bonding piezoelectric actuator and sensor layers on ...Graphene platelets(GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams.Further bonding piezoelectric actuator and sensor layers on the surfaces of GPLs-reinforced metal foam beams enables active vibration control,greatly expanding their applications in the aerospace industry.For the first time,this paper investigates the vibration characteristics and active vibration control of GPLs-reinforced metal foam beams with surfacebonded piezoelectric layers.The constant velocity feedback scheme is used to design the closed-loop controller including piezoelectric actuators and sensors.The effects of the GPLs on the linear and nonlinear free vibrations of the beams are numerically studied.The Newmark-βmethod combined with Newton's iteration technique is used to calculate the nonlinear responses of the beams under different load forms including harmonic loads,impact loads,and moving loads.Additionally,special attention is given to the vibration reduction performance of the velocity feedback control on the responses of the beam.展开更多
The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating...The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating the need for knowledge of the physical order of the controlled plant.Utilizing an ideal solution and equivalent dynamics,the approach integrates an adaptive network with feedback and robust controllers to establish a closed-loop system.A learning law is derived under practical conditions of the designed parameters,ensuring effective closed-loop performance based on pure-output feedback.The controller’s effectiveness is validated through both numerical and experimental systems,with results meeting the conditions specified in the main theorem.Comparative analysis highlights the controller’s highly satisfactory performance and its advantages.This research offers a promising approach to adaptive control for discrete-time systems with non-strict dynamics,providing practical solutions for systems with unknown dynamics and indeterminate system order.展开更多
A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity w...A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity with a high accelerating gradient is developed to satisfy the requirements of dual-harmonic acceleration and provide the necessary second-harmonic cavity voltage.However,the MA-loaded cavity exhibits a wideband frequency response,resulting in numerous higher harmonics in the radio-frequency(RF)voltage.These higher harmonics are caused by both the beam-loading effect and distorted amplifier current,which distort the RF bucket,increase the power dissipation in the cavity,and lower the gradient.To address these issues,a multiharmonic independent feedback-control approach is implemented to compensate for higher harmonics.The effectiveness of this control strategy is validated experimentally.This study provides details regarding the feedback-control design and presents the commissioning results.展开更多
This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing...This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.展开更多
For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approa...For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approach is applied to designing the optimal controller to determine the virtual controls, and the control allocation module is used to distribute the desired vitlual controls onto the redundant control effectors. The autopilot holds some attractive characteristics, such as simple structure, good tracking performance and robustness; moreover the actual constraints of the control effectors can be taken into account. Based on this blended control autopilot, it is found that the conflict between stability and fast tracking performance is serious when using the total acceleration as feedback. In order to avoid this problem, the transient factors in total acceleration are eliminated, so the acceleration caused only by angle of attack is used as feedback, and obvious improvement is shown. Finally, how to get reasonable acceleration feedback is discussed, and conclusion is presented that after passing the low-pass filter, the total acceleration can also be used as feedback, and satisfied tracking performance can be obtained.展开更多
The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can ta...The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.展开更多
A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC co...A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11561070)the Natural Scientific Research Fund Project of Yunnan Province(Grant No.2014FD049)
文摘This paper investigates the persistence and existence of almost periodic solutions for a discrete competitive system with feedback controls based on the comparison theorem of the difference equation and constructing appropriate Lyapunov function, and several sufficient conditions for the existence of positive almost periodic solutions for the model are obtained.Finally, a numerical example is given to illustrate effectiveness of our main results.
基金Fundamental Research Funds for the Central Universities,China(No.2232014D3-13)Natural Science Foundation of Shanghai,China(No.17ZR1401300)
文摘The problem of stabilizing a hybrid stochastic interval system is studied in this article. A hybrid interval system with suitable controls will become stable in the sense of mean-square exponential stability. State-feedback controls are designed based on the discrete-time state observations. Controls are put both in the drift and diffusion parts of the system. Criteria are derived in terms of linear matrix inequalities( LMI) to get the controllers. Also one example is given to illustrate our techniques.
基金supported by Russian Foundation for Basic Research(Grant No.08-01-00234,08-01-00411,08-08- 00292)
文摘For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.
文摘By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.
基金This work is supported by the Foundation of Fujian Education Bureau (JA04156).
文摘In this paper, we consider the N-species cooperation system with discrete time delays and feedback controls. By using the differential inequality theory and constructing a suitable Lyapunov functional, we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system.
基金The authors would like to thank the editor and the reviewers for their construcrive comments and suggestions which improved the quality of the paper. This work was supported by the National Natural Science Foundation of China under Grant 11401274, the National Natural Science Foundation of Fujian Province （2013J01010） and the Program for Science and Technology Development Foundation of Fuzhou University （2014-XQ-28）.
文摘In this paper, we consider a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 （2008） 165-178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.
基金the Foundation of Fujian Education Bureau (JA04156).
文摘In this paper, we consider an almost periodic multi-species Kolmogorov type com-petitive system with feedback controls. Applying Schauder’s fixed point theorem, a criterion on the existence of the positive almost periodic solution to the system is obtained. Our results improve and generalize some existing conclusions.
基金Supported by the Foundation of Fujian Education Bureau(No.JA12373)
文摘In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the global asymptotic stability of the system.
文摘In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.
基金supported by the Program for Science and Technology Development Foundation of Fuzhou University (No.2009-XY-18)
文摘In this paper, we consider the general nonautonomous single-species Kolmogorov type system with delay and feedback controls. Sufficient conditions for the permanence of species are established. Our results generalize some known results.
基金supported by the Natural Science Foundation of Fujian Province(2011J01007)the Technology Innovation Platform Project of Fujian Province(2009J1007)
文摘A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].
文摘Sufficient conditions are derived for the existence of globally asymptotically stable solution in a two species competition system with periodic coefficients and feedback controls.
文摘This paper investigates the problem of cluster synchronization of master-slave complex net-works with time-varying delay via linear and adaptive feedback pinning controls.We need not non-delayed and delayed coupling matrices to be symmetric or irreducible.We have the advantages of using adaptive control method to reduce control gain and pinning control technology to reduce cost.By con-structing Lyapunov function,some sufficient synchronization criteria are established.Finally,numerical examples are employed to illustrate the effectiveness of the proposed approach.
基金Project supported by the National Natural Science Foundation of China(Nos.12102015 and 12472003)the R&D Program of Beijing Municipal Education Commission of China(No.KM202110005030)。
文摘Graphene platelets(GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams.Further bonding piezoelectric actuator and sensor layers on the surfaces of GPLs-reinforced metal foam beams enables active vibration control,greatly expanding their applications in the aerospace industry.For the first time,this paper investigates the vibration characteristics and active vibration control of GPLs-reinforced metal foam beams with surfacebonded piezoelectric layers.The constant velocity feedback scheme is used to design the closed-loop controller including piezoelectric actuators and sensors.The effects of the GPLs on the linear and nonlinear free vibrations of the beams are numerically studied.The Newmark-βmethod combined with Newton's iteration technique is used to calculate the nonlinear responses of the beams under different load forms including harmonic loads,impact loads,and moving loads.Additionally,special attention is given to the vibration reduction performance of the velocity feedback control on the responses of the beam.
文摘The paper presents an adaptive controller formulated for a class of nonaffine discrete-time systems with non-strict forms and unknown dynamics.The controller operates based solely on the measured output,thus obviating the need for knowledge of the physical order of the controlled plant.Utilizing an ideal solution and equivalent dynamics,the approach integrates an adaptive network with feedback and robust controllers to establish a closed-loop system.A learning law is derived under practical conditions of the designed parameters,ensuring effective closed-loop performance based on pure-output feedback.The controller’s effectiveness is validated through both numerical and experimental systems,with results meeting the conditions specified in the main theorem.Comparative analysis highlights the controller’s highly satisfactory performance and its advantages.This research offers a promising approach to adaptive control for discrete-time systems with non-strict dynamics,providing practical solutions for systems with unknown dynamics and indeterminate system order.
基金supported by the National Natural Science Foundation of China(Nos.11875270 and 12205317)the Youth Innovation Promotion Association,Chinese Academy of Sciences(No.2018015)。
文摘A dual-harmonic acceleration system is utilized to mitigate the space-charge effect in the rapid-cycling synchrotron of the China Spallation Neutron Source upgrade project(CSNS-II).A magnetic alloy(MA)-loaded cavity with a high accelerating gradient is developed to satisfy the requirements of dual-harmonic acceleration and provide the necessary second-harmonic cavity voltage.However,the MA-loaded cavity exhibits a wideband frequency response,resulting in numerous higher harmonics in the radio-frequency(RF)voltage.These higher harmonics are caused by both the beam-loading effect and distorted amplifier current,which distort the RF bucket,increase the power dissipation in the cavity,and lower the gradient.To address these issues,a multiharmonic independent feedback-control approach is implemented to compensate for higher harmonics.The effectiveness of this control strategy is validated experimentally.This study provides details regarding the feedback-control design and presents the commissioning results.
基金supported by the Research Fund for the Taishan Scholar Project of Shandong Province of China,Shandong Provincial Natural Science Foundation of China(ZR2019MA003)。
文摘This paper proposes a new stochastic eco-epidemiological model with nonlinear incidence rate and feedback controls.First,we prove that the stochastic system has a unique global positive solution.Second,by constructing a series of appropriate stochastic Lyapunov functions,the asymptotic behaviors around the equilibria of deterministic model are obtained,and we demonstrate that the stochastic system exists a stationary Markov process.Third,the conditions for persistence in the mean and extinction of the stochastic system are established.Finally,we carry out some numerical simulations with respect to different stochastic parameters to verify our analytical results.The obtained results indicate that the stochastic perturbations and feedback controls have crucial effects on the survivability of system.
文摘For the missile with blended aero-fin and lateral impulsive thrust, a blended control autopilot is designed, which comprises an optimal controller and a control allocation module. The combined optimal/classical approach is applied to designing the optimal controller to determine the virtual controls, and the control allocation module is used to distribute the desired vitlual controls onto the redundant control effectors. The autopilot holds some attractive characteristics, such as simple structure, good tracking performance and robustness; moreover the actual constraints of the control effectors can be taken into account. Based on this blended control autopilot, it is found that the conflict between stability and fast tracking performance is serious when using the total acceleration as feedback. In order to avoid this problem, the transient factors in total acceleration are eliminated, so the acceleration caused only by angle of attack is used as feedback, and obvious improvement is shown. Finally, how to get reasonable acceleration feedback is discussed, and conclusion is presented that after passing the low-pass filter, the total acceleration can also be used as feedback, and satisfied tracking performance can be obtained.
基金Supported by National Natural Science Foundation of China(604040037 and Fork Ying-Dong Education Foundation(94028)
文摘The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result.
基金Supported by Natural Science Foundation of China(Grant Nos.52072051,51705044)Chongqing Municipal Natural Science Foundation of China(Grant No.cstc2020jcyj-msxmX0956)+1 种基金State Key Laboratory of Mechanical System and Vibration(Grant No.MSV202016)State Key Laboratory of Mechanical Transmissions(Grant No.SKLMT-KFKT-201806).
文摘A comparative study of model predictive control(MPC)schemes and robust Hstate feedback control(RSC)method for trajectory tracking is proposed in this paper.The main objective of this paper is to compare MPC and RSC controllers’performance in tracking predefined trajectory under different scenarios.MPC controller is designed based on the simple longitudinal-yaw-lateral motions of a single-track vehicle with a linear tire,which is an approximation of the more realistic model of a vehicle with double-track motion with a non-linear tire mode.RSC is designed on the basis of the same method as adopted for the MPC controller to achieve a fair comparison.Then,three test cases are built in CarSim-Simulink joint platform.Specifically,the verification test is used to test the tracking accuracy of MPC and RSC controller under well road conditions.Besides,the double lane change test with low road adhesion is designed to find the maximum velocity that both controllers can carry out while guaranteeing stability.Furthermore,an extreme curve test is built where the road adhesion changes suddenly,in order to test the performance of both controllers under extreme conditions.Finally,the advantages and disadvantages of MPC and RSC under different scenarios are also discussed.
