This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)conditi...This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.展开更多
The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems.The conditions that guarantee the existence of this observer are presented in the form of lin...The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems.The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities(LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H_∞ performance analysis is considered in order to deal with H_∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device.展开更多
This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction of nonlinear Lipschitz systems with unknown upper bound of derivative fault.Firstly,a linear transforming m...This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction of nonlinear Lipschitz systems with unknown upper bound of derivative fault.Firstly,a linear transforming matrix is introduced,which transforms the system into two subsystems,and thus to reduce the dimension of the system.One of the subsystem is affected by fault and disturbances,while the other is free,which simplifies the design of observer.Then,the design method of the observer gain matrix is transformed into a convex optimization problem under linear matrix inequalities(LMIs).A second order non-singular terminal sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault.Considering the unknown upper bound of derivative fault,an adaptive algorithm is designed in the equivalent output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time.Finally,an example demonstrates the effectiveness of the proposed method in the paper.展开更多
In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust ag...In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level ( cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the filter are simultaneously optimized through LMI multiobjective optimization.展开更多
This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditi...This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.展开更多
基金the National Natural Science Foundation of China(No.61403267)the China Postdoctoral Science Foundation(No.2017M611903)。
文摘This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.
文摘The objective of this paper is to propose a reduced-order observer for a class of Lipschitz nonlinear discrete-time systems.The conditions that guarantee the existence of this observer are presented in the form of linear matrix inequalities(LMIs). To handle the Lipschitz nonlinearities, the Lipschitz condition and the Young′s relation are adequately operated to add more degrees of freedom to the proposed LMI. Necessary and sufficient conditions for the existence of the unbiased reduced-order observer are given. An extension to H_∞ performance analysis is considered in order to deal with H_∞ asymptotic stability of the estimation error in the presence of disturbances that affect the state of the system. To highlight the effectiveness of the proposed design methodology, three numerical examples are considered. Then, high performances are shown through real time implementation using the ARDUINO MEGA 2560 device.
基金the National Natural Science Foundation of China(No.61304120)。
文摘This paper considers the design of an adaptive second order terminal observer for robust fault reconstruction of nonlinear Lipschitz systems with unknown upper bound of derivative fault.Firstly,a linear transforming matrix is introduced,which transforms the system into two subsystems,and thus to reduce the dimension of the system.One of the subsystem is affected by fault and disturbances,while the other is free,which simplifies the design of observer.Then,the design method of the observer gain matrix is transformed into a convex optimization problem under linear matrix inequalities(LMIs).A second order non-singular terminal sliding mode observer is designed for the transformed system to realize the accurate estimation of state and fault.Considering the unknown upper bound of derivative fault,an adaptive algorithm is designed in the equivalent output error injection signal to ensure the sliding mode motion reach the sliding surface within limited time.Finally,an example demonstrates the effectiveness of the proposed method in the paper.
文摘In this paper, a new method of filtering for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed filter has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level ( cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the filter are simultaneously optimized through LMI multiobjective optimization.
基金supported by National Natural Science Foundation of China(61174053)National Key Basic Research Program of China(2014CB845301/2/3)+3 种基金Fundamental Research Funds for the Central Universities(2014ZP0021)Cultivation Fund of the Key Scientific and Technical Innovation Project,Ministry of Education of China(708069)partially by Key Laboratory of Autonomous Systems and Networked Control,Ministry of EducationKey Laboratory of Surface Functional Structure Manufacturing of Guangdong Higher Education Institutes
基金supported by the Natural Science Foundation of Tianjin under Grant No.18JCYBJC88000.
文摘This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.
基金Supported by the National Nature Science Foundation of China(61174065)the Jiangsu Provincial Department of Education(10KJB20002)+1 种基金Nature Science Foundation at Nantong University(11Z05511Z056)
