Properties of the nonlinear transfer function are studied in this paper and the n-th order stabili-ty, n-th order frequency response and n-th order sensitivity as well as a novel theory and implementationon the sensit...Properties of the nonlinear transfer function are studied in this paper and the n-th order stabili-ty, n-th order frequency response and n-th order sensitivity as well as a novel theory and implementationon the sensitivity of nonlinear transfer system are proposed.展开更多
This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commens...This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.展开更多
In this study,We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion,where the leader's dynamics are unknown,and the controlled system's p...In this study,We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion,where the leader's dynamics are unknown,and the controlled system's parameters are uncertain.The multiagent systems are considered a kind of hybrid order nonlinear systems,which relaxes the strict requirement that all agents are of the same order in some existing work.For theoretical analyses,we design a composite energy function with virtual gain parameters to reduce the restriction that the controller gain depends on global information.Considering the stability of the controller,we introduce a smooth continuous function to improve the piecewise controller to avoid possible chattering.Theoretical analyses prove the convergence of the presented algorithm,and simulation experiments verify the effectiveness of the algorithm.展开更多
文摘Properties of the nonlinear transfer function are studied in this paper and the n-th order stabili-ty, n-th order frequency response and n-th order sensitivity as well as a novel theory and implementationon the sensitivity of nonlinear transfer system are proposed.
基金supported by the National Natural Science Foundation of China(60674090)Shandong Natural Science Foundation(ZR2017QF016)
文摘This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China(Grant Nos.62203342,62073254,92271101,62106186,and 62103136)the Fundamental Research Funds for the Central Universities(Grant Nos.XJS220704,QTZX23003,and ZYTS23046)+1 种基金the Project Funded by China Postdoctoral Science Foundation(Grant No.2022M712489)the Natural Science Basic Research Program of Shaanxi(Grant No.2023-JC-YB-585)。
文摘In this study,We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion,where the leader's dynamics are unknown,and the controlled system's parameters are uncertain.The multiagent systems are considered a kind of hybrid order nonlinear systems,which relaxes the strict requirement that all agents are of the same order in some existing work.For theoretical analyses,we design a composite energy function with virtual gain parameters to reduce the restriction that the controller gain depends on global information.Considering the stability of the controller,we introduce a smooth continuous function to improve the piecewise controller to avoid possible chattering.Theoretical analyses prove the convergence of the presented algorithm,and simulation experiments verify the effectiveness of the algorithm.
