In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetr...In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.展开更多
A kind of adaptive sliding model control algorithm is developed to solve and improve the mathematical model dependency and un-modeled dynamics of a controlled system. The control strategy derived from a kind of data-d...A kind of adaptive sliding model control algorithm is developed to solve and improve the mathematical model dependency and un-modeled dynamics of a controlled system. The control strategy derived from a kind of data-driven control method in essence, thereby the input and output data are utilized by the controller with no information about the control system model. Theoretical analysis proves that this proposed control algorithm can improve the utilization of the estimated pseudo partial derivative information and accelerate the velocity of the convergence. The stability of the control system is further verified by rigorous mathematical analysis. This new discrete-time nonlinear systems model-free control algorithm obtained better control performance through the simulations for the linear motor position and the information tracking speed, which also achieved robust and accurate traceability.展开更多
基金Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No.201410290039the Fundamental Research Funds for the Central Universities under Grant Nos.2015QNA53 and 2015XKQY14+2 种基金the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Minesthe General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2015M570498Natural Sciences Foundation of China under Grant No.11301527
文摘In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.
基金supported by Key Programs for Science and Technology Development of Henan Province(No.102102210197)the Opening Project of Key Laboratory of Mine Informatization,Henan Polytechnic University and the Doctoral Foundation of Henan Polytechnic University(No.B2010-23)
文摘A kind of adaptive sliding model control algorithm is developed to solve and improve the mathematical model dependency and un-modeled dynamics of a controlled system. The control strategy derived from a kind of data-driven control method in essence, thereby the input and output data are utilized by the controller with no information about the control system model. Theoretical analysis proves that this proposed control algorithm can improve the utilization of the estimated pseudo partial derivative information and accelerate the velocity of the convergence. The stability of the control system is further verified by rigorous mathematical analysis. This new discrete-time nonlinear systems model-free control algorithm obtained better control performance through the simulations for the linear motor position and the information tracking speed, which also achieved robust and accurate traceability.
