In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance...This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance.On one hand,the reduced order extended state observer(ROESO) and reduced order cascade extended state observer(ROCESO) are proposed for the case that the system state can be measured directly.On the other hand,the extended state observer(ESO) and the cascade extended state observer(CESO) are presented for another case when the system state cannot be measured directly.It is shown that combination of ROCESO and CESO can achieve a highly effective observation result.In addition,the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper.Finally,numerical simulations are given to illustrate the effectiveness of the proposed methods.展开更多
In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relat...In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.展开更多
基金supported by Natural Science Foundation of China（No.11171220） Support Projects of University of Shanghai for Science and Technology（No.14XPM01）
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
基金supported by the National Natural Science Foundation of China(61573332,61601431)Fundamental Research Funds for the Central Universities(WK2100100028)
文摘This paper addresses the problem of designing disturbance observer for fractional order linear time invariant(FO-LTI) systems,where the disturbance includes time series expansion disturbance and sinusoidal disturbance.On one hand,the reduced order extended state observer(ROESO) and reduced order cascade extended state observer(ROCESO) are proposed for the case that the system state can be measured directly.On the other hand,the extended state observer(ESO) and the cascade extended state observer(CESO) are presented for another case when the system state cannot be measured directly.It is shown that combination of ROCESO and CESO can achieve a highly effective observation result.In addition,the way how to tune observer parameters to ensure the stability of the observers and reduce the observation error is presented in this paper.Finally,numerical simulations are given to illustrate the effectiveness of the proposed methods.
文摘In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.
