In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient...In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.展开更多
This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nomina...This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.展开更多
The fault diagnosis problem is investigated for a class of nonlinear neutral systems with multiple disturbances.Time-varying faults are considered and multiple disturbances are supposed to include the unknown disturba...The fault diagnosis problem is investigated for a class of nonlinear neutral systems with multiple disturbances.Time-varying faults are considered and multiple disturbances are supposed to include the unknown disturbance modeled by an exo-system and norm bounded uncertain disturbance.A nonlinear disturbance observer is designed to estimate the modeled disturbance.Then,the fault diagnosis observer is constructed by integrating disturbance observer with disturbance attenuation and rejection performances.The augmented Lyapunov functional approach,which involves the tuning parameter and slack variable,is applied to make the solution of inequality more flexible.Finally,applications for a two-link robotic manipulator system are given to show the efficiency of the proposed approach.展开更多
A design method of robust observer is proposed for a class of nonlinear systems.The advantages of the designed observer,such as simpler design process, strong robustness and wider scope or application,are indicated.Fi...A design method of robust observer is proposed for a class of nonlinear systems.The advantages of the designed observer,such as simpler design process, strong robustness and wider scope or application,are indicated.Finally,some examples are given to show the efectiveness of the design method.展开更多
This paper surveys the results of observer design for linear time-invariant(L-T-I) deterministic irreducible open-loop systems(OLS), the most basic type of OLS. An observer estimates Kxx(t) signal where K is a constan...This paper surveys the results of observer design for linear time-invariant(L-T-I) deterministic irreducible open-loop systems(OLS), the most basic type of OLS. An observer estimates Kxx(t) signal where K is a constant and x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control(SFC) or Kxx(t)-control,and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kxx(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kxx(t) directly is more general than state observer that estimates x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced,is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kxx(t)-control, the observer must be an output feedback controller(OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kxx(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kxx(t)-control is constrained in this new design principle and is therefore called the "generalized SFC"(as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fundamental drawbacks of the existing separation principle. The third category of observers estimate Kxx(t) signal at special applications such as fault detection and identification and systems with time delay effects. Using directly the result of OFC that estimates Kxx(t) of the second category, these observers can be generally and satisfactorily designed.展开更多
基金supported by King Abdullah University of Science and Technology (KAUST),KSA
文摘In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.
基金supported in part by the National Defense Basic Scientific Research Program of China(JCKY2018603C015)Cultivation Plan of Major Research Program of Harbin Institute of Technology(ZDXMPY20180101)
文摘This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.
基金supported by the National Natural Science Foundation of China(6077401360925012)+1 种基金the National High Technology Research and Development Program of China(863 Program) (2008AA12A216)the National Basic Research Program of China (973 Program)(2009CB 724002)
文摘The fault diagnosis problem is investigated for a class of nonlinear neutral systems with multiple disturbances.Time-varying faults are considered and multiple disturbances are supposed to include the unknown disturbance modeled by an exo-system and norm bounded uncertain disturbance.A nonlinear disturbance observer is designed to estimate the modeled disturbance.Then,the fault diagnosis observer is constructed by integrating disturbance observer with disturbance attenuation and rejection performances.The augmented Lyapunov functional approach,which involves the tuning parameter and slack variable,is applied to make the solution of inequality more flexible.Finally,applications for a two-link robotic manipulator system are given to show the efficiency of the proposed approach.
文摘A design method of robust observer is proposed for a class of nonlinear systems.The advantages of the designed observer,such as simpler design process, strong robustness and wider scope or application,are indicated.Finally,some examples are given to show the efectiveness of the design method.
文摘This paper surveys the results of observer design for linear time-invariant(L-T-I) deterministic irreducible open-loop systems(OLS), the most basic type of OLS. An observer estimates Kxx(t) signal where K is a constant and x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control(SFC) or Kxx(t)-control,and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kxx(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kxx(t) directly is more general than state observer that estimates x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced,is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kxx(t)-control, the observer must be an output feedback controller(OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kxx(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kxx(t)-control is constrained in this new design principle and is therefore called the "generalized SFC"(as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fundamental drawbacks of the existing separation principle. The third category of observers estimate Kxx(t) signal at special applications such as fault detection and identification and systems with time delay effects. Using directly the result of OFC that estimates Kxx(t) of the second category, these observers can be generally and satisfactorily designed.
