This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester ma...This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).展开更多
A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure ass...A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.展开更多
A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general para...A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.展开更多
The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for ...The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.展开更多
The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results ar...The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results are illustrated by wave and beam equations with simulation.展开更多
In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalize...In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.展开更多
In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the le...In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.展开更多
In this paper,the event-triggered consensus control problem for nonlinear uncertain multi-agent systems subject to unknown parameters and external disturbances is considered.The dynamics of subsystems are second-order...In this paper,the event-triggered consensus control problem for nonlinear uncertain multi-agent systems subject to unknown parameters and external disturbances is considered.The dynamics of subsystems are second-order with similar structures,and the nodes are connected by undirected graphs.The event-triggered mechanisms are not only utilized in the transmission of information from the controllers to the actuators,and from the sensors to the controllers within each agent,but also in the communication between agents.Based on the adaptive backstepping method,extra estimators are introduced to handle the unknown parameters,and the measurement errors that occur during the event-triggered communication are well handled by designing compensating terms for the control signals.The presented distributed event-triggered adaptive control laws can guarantee the boundness of the consensus tracking errors and the Zeno behavior is avoided.Meanwhile,the update frequency of the controllers and the load of communication burden are vastly reduced.The obtained control protocol is further applied to a multi-input multi-output second-order nonlinear multi-agent system,and the simulation results show the effectiveness and advantages of our proposed method.展开更多
In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems.Under certain conditions,simple,general and complete parametric s...In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems.Under certain conditions,simple,general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived.The parametric approach utilizes directly original system data,involves manipulations only on n-dimensional matrices,and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications.A numerical example shows the effect of the proposed approach.展开更多
In this paper. we are concerned with the stability and control problem for aclass of second-order linear systems in Banach space. First. a criterion for the exponentialstability of a first-order linear system is prese...In this paper. we are concerned with the stability and control problem for aclass of second-order linear systems in Banach space. First. a criterion for the exponentialstability of a first-order linear system is presented. Then. the exponential stability as wellas some properties of a class of second-order linear systems is proved. At last. the feedbackcontrol of this class of systems is investigated.展开更多
This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat...This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.展开更多
Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature...Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.展开更多
The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model struc...The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.展开更多
This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different ...This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.展开更多
Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in ...Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.展开更多
Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop ...Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.展开更多
It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H...It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.展开更多
Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitr...Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.展开更多
In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by ...In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.展开更多
In this paper,a novel data-driven bipartite consensus control scheme is proposed for the rotation problem of large workpieces with multi-robot systems(MRSs)under a directed communication topology.The rotation of a lar...In this paper,a novel data-driven bipartite consensus control scheme is proposed for the rotation problem of large workpieces with multi-robot systems(MRSs)under a directed communication topology.The rotation of a large workpiece is described as the MRSs with cooperation and antagonism interaction.By the signed graph theory,it is further transformed into a bipartite consensus control problem,where all followers are uniformly degenerated into the general nonlinear systems based on the lateral error model.To augment the flexibility of control protocol and improve control performance,a higher-dimensional full form dynamic linearization(FFDL)technique is committed to the MRSs.The control input criterion function consists of the data model based on FFDL and the bipartite consensus error based on the signed graph theory,and the proposed control protocol is given by optimizing this criterion function.In this way,this scheme has a higher degree of freedom and better adaptive adjustment capability while not excessively increasing the control method complexity,and it can also be compatible with other forms of dynamic linearization techniques in MRSs.Further,three matrix norm lemmas are introduced to deal with the challenges of stability analysis caused by higher matrix dimensions and more robots.Finally,the effectiveness of the proposed method is verified by numerical simulations.展开更多
文摘This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).
文摘A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.
基金This work was supported by the Chinese National Natural Science Foundation ( No. 69925308).
文摘A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.
文摘The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.
文摘The stabilization problem of second-order bilinear systems with time delay is investigated.Feedback controls are chosen so that the strong and exponential stabilization of the system is ensured.The obtained results are illustrated by wave and beam equations with simulation.
基金This work was supported by National Natural Science Foundation of China(No.60710002)Program for Changjiang Scholars and Innovative Research Team in University(PCSIRT).
文摘In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.
基金supported by the National Natural Science Foundation of China(61203354)
文摘In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.
基金supported by National Key R&D Program of China(No.2018YFA0703800)Science Fund for Creative Research Group of the National Natural Science Foundation of China(No.61621002)。
文摘In this paper,the event-triggered consensus control problem for nonlinear uncertain multi-agent systems subject to unknown parameters and external disturbances is considered.The dynamics of subsystems are second-order with similar structures,and the nodes are connected by undirected graphs.The event-triggered mechanisms are not only utilized in the transmission of information from the controllers to the actuators,and from the sensors to the controllers within each agent,but also in the communication between agents.Based on the adaptive backstepping method,extra estimators are introduced to handle the unknown parameters,and the measurement errors that occur during the event-triggered communication are well handled by designing compensating terms for the control signals.The presented distributed event-triggered adaptive control laws can guarantee the boundness of the consensus tracking errors and the Zeno behavior is avoided.Meanwhile,the update frequency of the controllers and the load of communication burden are vastly reduced.The obtained control protocol is further applied to a multi-input multi-output second-order nonlinear multi-agent system,and the simulation results show the effectiveness and advantages of our proposed method.
文摘In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems.Under certain conditions,simple,general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived.The parametric approach utilizes directly original system data,involves manipulations only on n-dimensional matrices,and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications.A numerical example shows the effect of the proposed approach.
文摘In this paper. we are concerned with the stability and control problem for aclass of second-order linear systems in Banach space. First. a criterion for the exponentialstability of a first-order linear system is presented. Then. the exponential stability as wellas some properties of a class of second-order linear systems is proved. At last. the feedbackcontrol of this class of systems is investigated.
基金supported in part by the National Natural Science Foundation of China(62473221)the Natural Science Foundation of Shandong Province,China(ZR2024MF006)Qingdao Natural Science Foundation(24-4-4-zrjj-165-jch)。
文摘This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.
基金supported in part by the National Natural Science Foundation of China(62322311,62303162,62233007,62203157)the Technology Development Program of Henan Province(242102211052).
文摘Dear Editor,In this letter,several novel controllability results for a class of linear switched and impulsive systems are established.Different from the developed controllability conditions in most existing literature,the important role of switched and impulsive time sequence is considered.Applying the relevant geometric theory of matrix,a necessary and sufficient criterion for the controllability is firstly developed to judge when the controllability of such systems is affected by switched and impulsive time sequence.Furthermore,we further obtain a sufficient controllability condition that can be used to verify the controllability of such systems regardless of the switched and impulsive time sequence.Finally,a numerical example is given to verify the obtained theoretical results.
基金funded by the project new smart and adaptive robotics solutions for personalized minimally invasive surgery in cancer treatment−ATHENA,European Union-NextGenerationEU and Romanian Government,under National Recovery and Resilience Plan for Romania(CF116/15.11.2022)through the Romanian Ministry of Research,Innovation and Digitalization(within Component 9,investment I8)。
文摘The exact feedback linearization method implies an accurate knowledge of the model and its parameters.This assumption is an inherent limitation of the method,suffering from robustness issues.In general,the model structure is only partially known and its parameters present uncertainties.The current paper extends the classical exact feedback linearization to the robust feedback linearization by adding an appropriatelydesigned robust control layer.This is then able to ensure robust stability and robust performance for the given uncertain system in a desired region of attraction.We consider the case of full relative degree input-affine nonlinear systems,which are of great practical importance in the literature.The inner loop contains the feedback linearization input for the nominal system and the resulting residual nonlinearities can always be characterized as inverse additive uncertainties.The constructive proofs provide exact representations of the uncertainty models in three considered scenarios:unmatched,fully-matched,and partially-matched uncertainties.The uncertainty model will be a descriptor system,which also represents one of the novelties of the paper.Our approach leads to a simplified control structure and a less conservative coverage of the uncertainty set compared to current alternatives.The end-to-end procedure is emphasized on an illustrative example,in two different hypotheses.
基金Project supported by the National Natural Science Foundation of China (Grant No. 70571059)
文摘This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.
基金supported in part by the National Natural Science Foundation of China(62222310,61973131,62473379)the National Key Research and Develepment Program of China(2024YFB3310701)+1 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of China,the Major Basic Research of Natural Science Foundation of Shandong Province(ZR2024ZD38,ZR2022ZD34)the Japan Society for the Promotion of Science(21K04129).
文摘Switched linear parameter varying(LPV)systems have,in recent years,inspired a great number of research endeavors owing to their excellent ability to approximate nonlinear systems and handle complex hybrid dynamics in system analysis and synthesis.Nevertheless,numerous difficulties and challenges are also encountered due to the reciprocal effects of switching signals and scheduling parameters in the analysis and synthesis of switched LPV systems.In this paper,the standard description and specific characteristics of switched LPV systems are first introduced.Then,the main methodologies are proposed in the literature to cope with stability and performance analysis,control synthesis,as well as fault diagnosis and fault-tolerant control issues,and the typical applications in various fields are surveyed.Finally,several key open problems and current research activities are also discussed to elucidate the potential research directions in the future.
文摘Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.
基金supported in part by the National Natural Science Foundation of China(62373089).
文摘It is a challenging issue to obtain the minimum amplitude control for linear systems subject to amplitudebounded disturbances.The difficulty is how to accurately give the quantitative relationship between the system H∞norm and control parameters.An optimal-Lyapunov-function-based controller design concept is proposed,and a minimum amplitude control scheme is presented under amplitude-bounded disturbances.Firstly,the optimal Lyapunov function is proposed by analyzing the geometric characteristics of the system H∞norm,and the necessary and sufficient condition of the optimal Lyapunov function parameter matrix is given.Secondly,the optimal Lyapunov function parameter matrix is constructed in the parameterized matrix equation,and the accurate quantitative relationship between the system H∞norm and control parameters is given.Finally,the control parameter optimization method is proposed according to the quantitative relationship between the system H∞norm and control parameters.Unlike robust optimization control methods,the presented minimum amplitude control scheme avoids the improper selection of the Lyapunov function in the controller design,and provides a novel way to design the minimum amplitude control under the given control accuracy.A buck converter example is given to illustrate the effectiveness and practicability of the presented scheme.
文摘Differential inequalities generated in an extended Lyapunov framework are employed in the stability and instability analyses of a class of switched continuous-time second-and higher order linear systems with an arbitrary number of switching matrices.The exponential stability and instability(ESI)conditions so obtained involve the supremum and infimum of ratios of certain quadratic forms of the matrices,leading to global time-averages of their activity intervals.Further,motivated by linear switching system examples of(i)instability with stable matrices and(ii)stability with unstable matrices(found in the literature primarily for second-order systems),the proposed framework is generalized to establish ESI conditions that include both the activity intervals of the matrices and their switching rates,the latter being governed by a certain logarithmic measure of the normalized magnitudes of discontinuities caused by switching.In effect,(the new,globally averaged)dwell-time is flexibly traded,apparently for the first time,but under specific conditions(related,in part,to the eigenvalues of the matrices),for switching discontinuity-based conditions.Two further novel aspects of the proposed approach are:(i)For second-order matrices,switching lines in phase space can be chosen for periodic switching to stabilize or destabilize the system,and even generate oscillations,depending on the eigenvalues of the system matrices.But for third-(and higher)order matrices,such an analytically tractable(and controlled)periodical switching entails solution of an explicit non-convex multi-parameter optimization problem for which a stochastic optimization algorithm from the literature can be invoked.(ii)Lower and upper bounds on the solutions of the system equations can be quantified to reflect the stability/instability/oscillatory property of the system.Illustrative examples,which demonstrate the novelty of the derived stability and instability conditions,are presented in part 2 which is advisedly to be read along with this part 1 for a coherent merging of theory with practice.
文摘In this second part of the paper,bearing the same title as above,but with the last hyphenated phrase replaced by part 1(Theory),the exponential stability and instability(ESI)Theorems 1–4 of part 1 are illustrated by applying them to second-andby,say,third-order linear switched systems with different eigenvalue structures to demonstrate the versatility,novelty and superiority(over many of the results found in the literature,especially for second-order switched lined systems)of the new theoretical results.The computational procedure that is employed with reference to the third-order systems is generic,in the sense that it is applicable to higher(i.e.,greater than third-)order linear switched systems.A pseudo-code for a computer implementation of the stability/instability conditions is also presented.With the principal aim of facilitating an independent reading of this part 2 of the paper,some crucial mathematical notations,definitions and results of part 1 have been repeated,thereby making the contents as self-contained as possible.
基金supported in part by the National Natural Science Foundation of China(62473142,62203161)Special Funding Support for the Construction of Innovative Provinces in Hunan Province(2021GK1010)+1 种基金Guangdong Basic and Applied Basic Research Foundation(2024A1515011579),Project of State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle(72275007).
文摘In this paper,a novel data-driven bipartite consensus control scheme is proposed for the rotation problem of large workpieces with multi-robot systems(MRSs)under a directed communication topology.The rotation of a large workpiece is described as the MRSs with cooperation and antagonism interaction.By the signed graph theory,it is further transformed into a bipartite consensus control problem,where all followers are uniformly degenerated into the general nonlinear systems based on the lateral error model.To augment the flexibility of control protocol and improve control performance,a higher-dimensional full form dynamic linearization(FFDL)technique is committed to the MRSs.The control input criterion function consists of the data model based on FFDL and the bipartite consensus error based on the signed graph theory,and the proposed control protocol is given by optimizing this criterion function.In this way,this scheme has a higher degree of freedom and better adaptive adjustment capability while not excessively increasing the control method complexity,and it can also be compatible with other forms of dynamic linearization techniques in MRSs.Further,three matrix norm lemmas are introduced to deal with the challenges of stability analysis caused by higher matrix dimensions and more robots.Finally,the effectiveness of the proposed method is verified by numerical simulations.
