This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and no...This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.展开更多
This paper mainly addresses control problems of strict-feedback systems(SFSs)with increasing dimensions.Compared with the commonly-considered SFSs where the subsystems have the same dimension,we aim to handle more com...This paper mainly addresses control problems of strict-feedback systems(SFSs)with increasing dimensions.Compared with the commonly-considered SFSs where the subsystems have the same dimension,we aim to handle more complex cases,i.e.,the subsystems in the considered SFSs are assumed to have increasing dimensions.By transforming the systems into highorder fully-actuated system(HOFAS)models,the stabilizing controllers can be directly given.Besides first-order SFSs,secondorder and high-order SFSs are also considered.展开更多
A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain st...A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.展开更多
In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by intr...In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by introducing several key transformation functions and selecting the initial value of the time-varying scaling function,the symmetric prescribed performance with global and semi-global properties can be handled uniformly,without the need for control re-design.Secondly,to handle the problem of unknown time-varying control coefficient with an unknown sign,we propose an enhanced Nussbaum function(ENF)bearing some unique properties and characteristics,with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required.Thirdly,by utilizing the core-function information technique,the nonparametric uncertainties in the system are gracefully handled so that no approximator is required.Furthermore,simulation results verify the effectiveness and benefits of the approach.展开更多
The distributed leader-following consensus for nonlinear multi-agent systems in strict-feedback forms is investigated under directed topology. Firstly, each follower node is modeled by an integrator incorporating with...The distributed leader-following consensus for nonlinear multi-agent systems in strict-feedback forms is investigated under directed topology. Firstly, each follower node is modeled by an integrator incorporating with nonlinear dynamics. The leader node is modeled as an autonomous nonlinear system which sends its information to one or more followers. Then, a simple and novel distributed protocol is proposed based only on the state feedback, under which the states of the followers ultimately synchronize to the leader. By using Lyapunov stability theorem and matrix theory, it is proved that the distributed leader-following consensus of nonlinear multi-agent systems with strict-feedback form is guaranteed by Lipschitz continuous control laws. Finally, some numerical simulations are provided to show the effectiveness of the developed method.展开更多
This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two...This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.展开更多
In this paper,we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction.Due to the existence of unk...In this paper,we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction.Due to the existence of unknown nonlinearities and uncertainties,it is challenging to design a controller that can ensure the stability of closed-loop system within a predetermined finite time while maintaining the specified transient performance.The underlying problem becomes further complex as the control directions are unknown.To deal with the above problems,a special translation function as well as Nussbaum type function are introduced in the prescribed performance control(PPC)framework.Finally,a PPC as well as preset finite time tracking control scheme is designed,and its effectiveness is confirmed by both theoretical analysis and numerical simulation.展开更多
This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected gr...This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected graphs,two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric,and the derived weight error systems exist n-step delays.Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying(LTV)systems with different phenomena including the nonsymmetric Laplacian matrix and time delays.Subsequently,an adaptive neural network(NN)control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law.Then,by using two novel lemmas on the extended exponential convergence of LTV systems,estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced.The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the“mod”function and proper time series.A simulation comparison is shown to demonstrate the validity of the proposed DCL method.展开更多
In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation p...In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.展开更多
The article is devoted to the almost disturbance decoupling problem for high-order fully actuated(HOFA)nonlinear systems with strict-feedback form.Using the full-actuation feature of high-order fully actuated systems ...The article is devoted to the almost disturbance decoupling problem for high-order fully actuated(HOFA)nonlinear systems with strict-feedback form.Using the full-actuation feature of high-order fully actuated systems and Lyapunov stability theory,a state feedback control law and virtual control laws are designed.The unknown disturbances are handled by almost disturbance decoupling(ADD)method.Finally,the effectiveness of the control strategy is verified by stability analysis and simulation.展开更多
This paper investigates the prescribed-time control(PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbance...This paper investigates the prescribed-time control(PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbances makes PTC synthesis nontrivial. In this work, a control method that does not involve infinite time-varying gain is proposed, leading to a practical and global prescribed time tracking control solution for the strict-feedback systems, in spite of both the mismatched and nonvanishing uncertainties. Different from methods based on control switching to avoid the issue of infinite control gain that involves control discontinuity at the switching point, in our method a softening unit is exclusively included to ensure the continuity of the control action. Furthermore, in contrast to most existing prescribed-time control works where the control scheme is only valid on a finite time interval, in this work, the proposed control scheme is valid on the entire time interval. In addition, the prior information on the upper or lower bound of gi is not in need,enlarging the applicability of the proposed method. Both the theoretical analysis and numerical simulation confirm the effectiveness of the proposed control algorithm.展开更多
基金supported in part by the National Key Research and Development Program of China(2023YFA1011803)the National Natural Science Foundation of China(62273064,61991400/61991403,61933012,62250710167,62203078)+2 种基金Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0588)the Central University Project(2023CDJKYJH047)the Innovation Support Program for International Students Returning to China(cx2022016)
文摘This paper investigates the prescribed-time tracking control problem for a class of multi-input multi-output(MIMO)nonlinear strict-feedback systems subject to non-vanishing uncertainties. The inherent unmatched and non-vanishing uncertainties make the prescribed-time control problem become much more nontrivial. The solution to address the challenges mentioned above involves incorporating a prescribed-time filter, as opposed to a finite-time filter, and formulating a prescribed-time Lyapunov stability lemma(Lemma 5). The prescribed-time Lyapunov stability lemma is based on time axis shifting time-varying yet bounded gain, which establishes a novel link between the fixed-time and prescribed-time control method. This allows the restriction condition that the time-varying gain function must satisfy as imposed in most exist prescribed-time control works to be removed. Under the proposed control method, the desire trajectory is ensured to closely track the output of the system in prescribed time. The effectiveness of the theoretical results are verified through numerical simulation.
基金partly supported by Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)the National Natural Science Foundation of China(NSFC)(62350055)。
文摘This paper mainly addresses control problems of strict-feedback systems(SFSs)with increasing dimensions.Compared with the commonly-considered SFSs where the subsystems have the same dimension,we aim to handle more complex cases,i.e.,the subsystems in the considered SFSs are assumed to have increasing dimensions.By transforming the systems into highorder fully-actuated system(HOFAS)models,the stabilizing controllers can be directly given.Besides first-order SFSs,secondorder and high-order SFSs are also considered.
基金supported by the National Natural Science Foundation of China(11502288)the Natural Science Foundation of Hunan Province(2016JJ3019)+1 种基金the Aeronautical Science Foundation of China(2017ZA88001)the Scientific Research Project of National University of Defense Technology(ZK17-03-32)
文摘A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.
基金supported in part by the National Key Research and Development Program of China(2021ZD0201300)in part by the National Natural Science Foundation of China(61860206008,61933012)。
文摘In this paper,we present a novel adaptive performance control approach for strict-feedback nonparametric systems with unknown time-varying control coefficients,which mainly includes the following steps.Firstly,by introducing several key transformation functions and selecting the initial value of the time-varying scaling function,the symmetric prescribed performance with global and semi-global properties can be handled uniformly,without the need for control re-design.Secondly,to handle the problem of unknown time-varying control coefficient with an unknown sign,we propose an enhanced Nussbaum function(ENF)bearing some unique properties and characteristics,with which the complex stability analysis based on specific Nussbaum functions as commonly used is no longer required.Thirdly,by utilizing the core-function information technique,the nonparametric uncertainties in the system are gracefully handled so that no approximator is required.Furthermore,simulation results verify the effectiveness and benefits of the approach.
基金National Natural Science Foundation of China(No.61374024)
文摘The distributed leader-following consensus for nonlinear multi-agent systems in strict-feedback forms is investigated under directed topology. Firstly, each follower node is modeled by an integrator incorporating with nonlinear dynamics. The leader node is modeled as an autonomous nonlinear system which sends its information to one or more followers. Then, a simple and novel distributed protocol is proposed based only on the state feedback, under which the states of the followers ultimately synchronize to the leader. By using Lyapunov stability theorem and matrix theory, it is proved that the distributed leader-following consensus of nonlinear multi-agent systems with strict-feedback form is guaranteed by Lipschitz continuous control laws. Finally, some numerical simulations are provided to show the effectiveness of the developed method.
基金supported by the National Natural Science Foundation of China(61821004,U1964207,20221017-10)。
文摘This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.
基金supported in part by the National Key Research and Development Program of China under grant(No.2022YFB4701400/4701401)by the National Natural Science Foundation of China under grant(No.61991400,No.61991403,No.62250710167,No.61860206008,No.61933012,No.62273064,No.62203078)+2 种基金in part by the National Key Research and Development Program of China under grant(No.2021ZD0201300)in part by the Innovation Support Program for International Students Returning to China under grant(No.cx2022016)in part by the Chongqing Medical Scientific Research Project under grant(No.2022DBXM001).
文摘In this paper,we consider the practical prescribed-time performance guaranteed tracking control problem for a class of uncertain strict-feedback systems subject to unknown control direction.Due to the existence of unknown nonlinearities and uncertainties,it is challenging to design a controller that can ensure the stability of closed-loop system within a predetermined finite time while maintaining the specified transient performance.The underlying problem becomes further complex as the control directions are unknown.To deal with the above problems,a special translation function as well as Nussbaum type function are introduced in the prescribed performance control(PPC)framework.Finally,a PPC as well as preset finite time tracking control scheme is designed,and its effectiveness is confirmed by both theoretical analysis and numerical simulation.
基金supported in part by the Guangdong Natural Science Foundation(2019B151502058)in part by the National Natural Science Foundation of China(61890922,61973129)+1 种基金in part by the Major Key Project of PCL(PCL2021A09)in part by the Guangdong Basic and Applied Basic Research Foundation(2021A1515012004)。
文摘This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected graphs,two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric,and the derived weight error systems exist n-step delays.Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying(LTV)systems with different phenomena including the nonsymmetric Laplacian matrix and time delays.Subsequently,an adaptive neural network(NN)control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law.Then,by using two novel lemmas on the extended exponential convergence of LTV systems,estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced.The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the“mod”function and proper time series.A simulation comparison is shown to demonstrate the validity of the proposed DCL method.
文摘In this paper, a fuzzy adaptive tracking control for uncertain strict-feedback nonlinear systems with unknown bounded disturbances is proposed. The generalized fuzzy hyperbolic model (GFHM) with better approximation performance is used to approximate the unknown nonlinear function in the system. The dynamic surface control (DSC) is used to design the controller, which not only avoids the “explosion of complexity” problem in the process of repeated derivation, but also makes the control system simpler in structure and lower in computational cost because only one adaptive law is designed in the controller design process. Through the Lyapunov stability analysis, all signals in the closed loop system designed in this paper are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the method is verified by a simulation example.
基金This research was supported by the Taishan Scholar Project of Shandong Province of China under Grant Nos.2015162 and tsqn201812093.
文摘The article is devoted to the almost disturbance decoupling problem for high-order fully actuated(HOFA)nonlinear systems with strict-feedback form.Using the full-actuation feature of high-order fully actuated systems and Lyapunov stability theory,a state feedback control law and virtual control laws are designed.The unknown disturbances are handled by almost disturbance decoupling(ADD)method.Finally,the effectiveness of the control strategy is verified by stability analysis and simulation.
基金supported by the National Natural Science Foundation of China (61991400, 61991403, 62273064, 62250710167,61860206008, 61933012, 62203078)in part by the National Key Research and Development Program of China (2022YFB4701400/4701401)+1 种基金the Innovation Support Program for International Students Returning to China(cx2022016)the CAAI-Huawei MindSpore Open Fund。
文摘This paper investigates the prescribed-time control(PTC) problem for a class of strict-feedback systems subject to non-vanishing uncertainties. The coexistence of mismatched uncertainties and non-vanishing disturbances makes PTC synthesis nontrivial. In this work, a control method that does not involve infinite time-varying gain is proposed, leading to a practical and global prescribed time tracking control solution for the strict-feedback systems, in spite of both the mismatched and nonvanishing uncertainties. Different from methods based on control switching to avoid the issue of infinite control gain that involves control discontinuity at the switching point, in our method a softening unit is exclusively included to ensure the continuity of the control action. Furthermore, in contrast to most existing prescribed-time control works where the control scheme is only valid on a finite time interval, in this work, the proposed control scheme is valid on the entire time interval. In addition, the prior information on the upper or lower bound of gi is not in need,enlarging the applicability of the proposed method. Both the theoretical analysis and numerical simulation confirm the effectiveness of the proposed control algorithm.
