A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

Jinbao Li,Wujie Shi,Dapeng Yu 대한수학회 2015 대한수학회보 Vol.52 No.6

In this paper, we characterize some PGL(2, q) by their orders and maximum element orders. We also prove that PSL(2, p) with p ≥ 3 a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if q = pn with p a prime and n > 1, PGL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.

A CHARACTERIZATION OF SOME PGL(2, q) BY MAXIMUM ELEMENT ORDERS

LI, JINBAO,SHI, WUJIE,YU, DAPENG Korean Mathematical Society 2015 대한수학회보 Vol.52 No.6

In this paper, we characterize some PGL(2, q) by their orders and maximum element orders. We also prove that PSL(2, p) with $p{\geqslant}3$ a prime can be determined by their orders and maximum element orders. Moreover, we show that, in general, if $q=p^n$ with p a prime and n > 1, PGL(2, q) can not be uniquely determined by their orders and maximum element orders. Several known results are generalized.

Finite-Time Convergent Guidance Law Based on Second-Order Sliding Mode Control Theory

Ji, Yi,Lin, Defu,Wang, Wei,Lin, Shiyao The Korean Society for Aeronautical and Space Scie 2017 International Journal of Aeronautical and Space Sc Vol.18 No.4

The complex battlefield environment makes it difficult to intercept maneuvering targets for guided missiles. In this paper, a finite-time convergent (FTC) guidance law based on the second-order sliding mode (SOSM) control theory is proposed to achieve the requirements of stability, accuracy and robustness. More specifically, a second-order sliding mode observer (SMOB) is used to estimate and compensate for the total disturbance of the controlled system, while the target acceleration is extracted from the line-of-sight (LOS) angle measurement. The proposed guidance law can drive the LOS angular rate converge to zero in a finite time, which means that the missile will accurately intercept the target. Numerical simulations with some comparisons are performed to demonstrate the superiority of the proposed guidance law.

Finite-Time Convergent Guidance Law Based on Second-Order Sliding Mode Control Theory

Yi Ji,Defu Lin,Wei Wang,Shiyao Lin 한국항공우주학회 2017 International Journal of Aeronautical and Space Sc Vol.18 No.4

The complex battlefield environment makes it difficult to intercept maneuvering targets for guided missiles. In this paper, a finite-time convergent (FTC) guidance law based on the second-order sliding mode (SOSM) control theory is proposed to achieve the requirements of stability, accuracy and robustness. More specifically, a second-order sliding mode observer (SMOB) is used to estimate and compensate for the total disturbance of the controlled system, while the target acceleration is extracted from the line-of-sight (LOS) angle measurement. The proposed guidance law can drive the LOS angular rate converge to zero in a finite time, which means that the missile will accurately intercept the target. Numerical simulations with some comparisons are performed to demonstrate the superiority of the proposed guidance law.

Second-order wave radiation by multiple cylinders in time domain through the finite element method

Wang, C.Z.,Mitra, S.,Khoo, B.C. Techno-Press 2011 Ocean systems engineering Vol.1 No.4

A time domain finite element based method is employed to analyze wave radiation by multiple cylinders. The nonlinear free surface and body surface boundary conditions are satisfied based on the perturbation method up to the second order. The first- and second-order velocity potential problems at each time step are solved through a finite element method (FEM). The matrix equation of the FEM is solved through an iteration and the initial solution is obtained from the result at the previous time step. The three-dimensional (3D) mesh required is generated based on a two-dimensional (2D) hybrid mesh on a horizontal plane and its extension in the vertical direction. The hybrid mesh is generated by combining an unstructured grid away from cylinders and two structured grids near the cylinder and the artificial boundary, respectively. The fluid velocity on the free surface and the cylinder surface are calculated by using a differential method. Results for various configurations including two-cylinder and four-cylinder cases are provided to show the mutual influence due to cylinders on the first and second waves and forces.

Finite element modeling of multiplyconnected three-dimensional areas

Polatov, Askhad M.,Ikramov, Akhmat M.,Razmukhamedov, Daniyarbek D. Techno-Press 2020 Advances in computational design Vol.5 No.3

This article describes the technology for constructing of a multiply-connected three-dimensional area's finite element representation. Representation of finite-element configuration of an area is described by a discrete set that consist of the number of nodes and elements of the finite-element grid, that are orderly set of nodes' coordinates and numbers of finite elements. Corresponding theorems are given, to prove the correctness of the solution method. The adequacy of multiply-connected area topology's finite element model is shown. The merging of subareas is based on the criterion of boundary nodes' coincidence by establishing a simple hierarchy of volumes, surfaces, lines and points. Renumbering nodes is carried out by the frontal method, where nodes located on the outer edges of the structure are used as the initial front.

유한시간 감소차수 관측자의 설계

이기상(Kee-Sang Lee) 대한전기학회 2010 전기학회논문지 Vol.59 No.5

A reduced order observer with finite time convergence characteristics is proposed for linear time invariant systems. The proposed finite time reduced order observer(FTROO) is a dual observer scheme in which two reduced order Luenberger observers with asymptotic convergence characteristics and a finite time delay element are employed. The FTROO can be constructed so as to converge in the designer specified finite time independent of the eigenvalues of the reduced order observers. A numerical example is given to show the finite-time convergence characteristics of the proposed FTROO.

Nonsingular Finite-time Second Order Sliding Mode Attitude Control for Reentry Vehicle

Yongzhi Sheng,Jie Geng,Xiangdong Liu,Liang Wang 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.4

This paper presents nonlinear robust flight control strategies for the reentry vehicle which is nonlinear, coupling, and includes parameter uncertainties and external disturbances. Firstly, a finitetime second order sliding mode attitude control strategy is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. By the proposed controller, the attitude tracking errors are mathematically proved to converge to zero within finite time and the chattering of sliding mode controller is alleviated without any deterioration of robustness and accuracy. For further alleviation of chattering, a smooth second order sliding mode attitude control strategy is then designed based on an improved nonsingular finite-time sliding mode manifold. Finally, the proposed strategies are applied to the attitude control of X-33 RLV in the reentry phase to verify the validity and robustness of the proposed strategies.

Adaptive Continuous Sliding Mode Control for Fractional-order Systems with Uncertainties and Unknown Control Gains

Lu Chen,Jian-an Fang 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.5

The main purpose of this paper is to design the continuous sliding mode control, which resolves the stability problem of fractional-order nonlinear systems by taking into consideration both matched and unmatched uncertainties, and unknown control gains. Three different sliding mode controllers are put forward to attenuate the chattering problem, which pass an adaptive fractional-order filter. The control function constituted of a novel SMC method and backstepping control is proposed to deal with the problem of unmatched uncertainty. Utilizing the fractional-order Lyapunov technology and the finite-time control strategy, the analysis results of this paper are theoretically proved. Finally, the availability and feasibility of the suggested chattering free sliding mode control are also confirmed by the application to the control of the fractional-order horizontal platform system.

Adaptive Fuzzy Finite-time Dynamic Surface Control for High-order Nonlinear System with Output Constraints

Kewen Li,Yong-Ming Li 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.1

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design fora class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logicsystems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function(BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backsteppingrecursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-timeLyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system aresemi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of originin finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practicalsimulation examples are given to illustrate the effectiveness of the proposed control algorithm.