科创中国

© 2015 Chunye Gong et al. We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N²M), O(NM²), and O(NM(M + N)) compared with O(MN) for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator), short memory principle, fast Fourier transform (FFT) based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus.

Gong Chunye;Bao Weimin;Tang Guojian;Liu Jie;Jiang Yuewen

Mathematical Problems in Engineering

2015

High quality InAlN/InGaN/InAlN/InGaN double channel heterostructures were proposed and grown by metal organic chemical vapor deposition. Benefiting from the adoption of the pulsed growth method and Two-Step AlN interlayer, the material quality and interface characteristics of the double channel heterostructures are satisfactory. The results of the temperature-dependent Hall effect measurement indicated that the transport properties of the double channel heterostructures were superior to those of the traditional single channel heterostructures in the whole test temperature range. Meanwhile, the sheet resistance of the double channel heterostructures reached 218.5 Ω/□ at 300 K, which is the record of InGaN-based heterostructures. The good transport properties of the InGaN double channel heterostructures are beneficial to improve the performance of the microwave power devices based on nitride semiconductors.

Yachao Zhang;Zhizhe Wang;Shengrui Xu;Dazheng Chen;为民 包;金风 张;进成 张;跃 郝

Applied Physics Letters

2017-11-27

Based on sliding mode control, this paper presents a novel differential geometric guidance law for a homing missile against maneuvering targets. The three-dimensional guidance problem is reduced to two-dimensions by an engagement plane rotation reference frame. In the design of guidance law, two well-constructed mild sliding manifolds are introduced to decrease control efforts. Moreover, target maneuver is treated as a disturbance with known upper bound and no algorithm is required to estimate the maneuver. Simulation results illustrate that the mild sliding manifolds can be fast arrived at in finite time and the proposed differential geometric guidance law yields better performance by contrast with other existing guidance laws.

Jingshuai Huang;Hongbo Zhang;Wei Lv;Guojian Tang;为民 包

2019-1-22

The solar vector is one of the most important parameters for attitude control of nanosatellites. This attitude control must be achieved without the sensors adding significantly to its size or mass. This paper presents a photodiode-based miniature sun sensor, which consists of two triangular pyramidal sensor unit structures, with each unit comprising three micro-silicon photodiodes. The two sensor units are installed on the diagonal of the nanosatellite to form a complete sun sensor capable of achieving a full-field range of solar vector measurements. In this paper, the mathematical model of the short-circuit currents of the silicon photodiodes as a function of the solar vector coordinates is deduced. A sensor sample was built and installed on a nanosatellite model, and the temperature compensation coefficient of the silicon photodiodes was obtained experimentally. The dynamic characteristic, linearity, hysteresis and repeatability of the component were measured. The sun sensor introduced in this paper can be placed on any satellite platform to allow a full range solar vector measurement, and this would result in an increase of only 1.86 g and 0.9 cm³ of the satellite's mass and volume, respectively.

Xiaozhou Lü;Yebo Tao;楷 谢;松林 王;小平 李;为民 包;人杰 陈

Measurement Science and Technology

2017-3-15

Mathematic model of the pulse phase estimation problem was addressed, and the effective weighted nonlinear least-square (WNLS) estimator was presented. The weighting matrix of the WNLS estimator was derived by adopting statistical properties of epoch folding noises. The performance of the proposed technique was compared with the Cramér-Rao lower bound (CRLB). The results of numerical simulations and real data experiments indicate that the proposed estimator is asymptotically unbiased and efficient, its asymptotical performance outperforms the nonlinear least square (NLS) estimator and is comparable with the maximum-likelihood (ML) estimator as the observation time increases. As for the experiment of real Crab pulsar data, the position error of the WNLS method is about 400 m less than that of the NLS method when the observation time is 80 s.

Haifeng Sun;为民 包;Haiyan Fang;小平 李

Huazhong Keji Daxue Xuebao (Ziran Kexue Ban)/Journal of Huazhong University of Science and Technology (Natural Science Edition)

2015-11-23

A novel guidance algorithm using feedback linearization and sliding mode control is proposed to realize high precisionguidance and maneuvering flight for hypersonic vehicle in dive phase. First, the longitudinal ellipse trajectory which can satisfy both the terminal impact point and angle constraints is designed, and the lateral maneuver trajectory is also generated to improve the penetration capability. Second, it introduces feedback linearization to decouple the original motion equations into linear guidance subsystems in longitudinal and lateral channel. With the linear equations, the tracker is designed with the help of sliding mode control, and the practical tracking guidance law can also be obtained by substituting the tracker into the original system. In addition, the stability of the guidance system is proven using the Lyapunovtheorem. This tracking guidance is independent of the relative motion information and relative equation, while only the current motion states are needed. Besides, the results of CAV-H vehicle guidance test show that maneuvering flight and high precision guidance can be realized with the novel proposed algorithm, and the robustness is also validated through different guidance missions and Monte Carlo simulation.

Luhua Liu;Jianwen Zhu;Guojian Tang;为民 包

Aerospace Science and Technology

2015-2

Three-dimensional (3D) nonlinear diving guidance strategy considering the coupling between longitudinal and lateral motions for hypersonic vehicle is investigated in this paper. It constructs the complete nonlinear coupling motion equation without any approximations based on diving relative motion relationship directly, and converts it into linear state space equation with the same relative degree by feedback linearization. With the linear equation, slide mode control with strong robustness is employed to design the guidance law, and 3D diving guidance law which can satisfy terminal impact point and falling angle constraints with high precision is obtained by substituting the previous control law into the origin nonlinear guidance system. Besides, regarding lateral overload as the standard, hybrid control strategy which can take full advantage of the excellent characters of both bank-to-turn (BTT) and skid-to-turn (STT) controls is designed to improve the guidance accuracy further. Finally, the results of CAV-H vehicle guidance test show that the algorithm can realize high accuracy guidance even if serious motion coupling exists, and has strong robustness to the path disturbances and navigation errors as well.

Jian Wen Zhu;Lu Hua Liu;Guo Jian Tang;为民 包

Science China Technological Sciences

2014

The Crab pulsar is an isolated rotation-powered pulsar which emits large X-ray fluxes, making it a candidate source for carrying out the X-ray pulsar navigation (XNAV). The long-term stable profiles are considered as the foundation of XNAV. However, systematic studies of the long-term stability of the X-ray pulsar profile and its effect on range accuracy in XNAV are lacking. In this paper, we use the X-ray band (2-16 keV) data monitored by Rossi X-ray timing explorer (RXTE) spacecraft over the latest 11 years, to first investigate the stability of the Crab pulsar including the profiles after the glitches. Furthermore, some measurements of the long-term profile shape, including Pearson correlation coefficient, standard deviation and spectral entropy, are presented both in the time domain and in the frequency domain. In the data processing, the Fourier analysis and cross-correlation are used to deal with the 191 RXTE data sets. With the help of the Cramer-Rao theory, the effect of the profile variation on the error of the range determination in XNAV is studied. Furthermore, after analyzing those errors, the effect of the stability of the Crab pulsar on range determination is confined to more narrow limits. The results demonstrate that the 2-16 keV profiles are almost constant during the period 2001-2012. The profiles after the glitches show no significant discrepancy. The variation of Crab profile inevitably has an influence on the navigation precision to a certain extent. The calculated range error along the pulsar line-of-sight due to the stability of the pulsar profile is 34 m ±25 m.

Hai Feng Sun;为民 包;Hai Yan Fang;小平 李

Wuli Xuebao/Acta Physica Sinica

2014-3-20

Taking six degrees of freedom model of a generic hypersonic vehicle as the research object, this paper proposes a terminal sliding mode attitude control method which can converge to the equilibrium point within finite time globally. In the design of the controller, dynamic inversion is applied to deal with strong couplings among pitch angle, yaw angle and roll angle. In the case of considering the model uncertainties and external disturbances, the terminal sliding mode variable structure control method is used to guarantee the robustness of the system. In addition, by improving the traditional exponential approach law, the control command can be tracked within finite time globally. Based on the Lyapunov stability theory, it is proved that the finite time convergence in both reaching and sliding phases can be achieved. Finally, simulation results demonstrate that the proposed attitude control method is efficient.

Haidong Liu;为民 包;Huifeng Li;Chunye Gong;Yuxin Liao

Beijing Hangkong Hangtian Daxue Xuebao/Journal of Beijing University of Aeronautics and Astronautics

2016-9-1

An optimal guidance law with multi -targets which can satisfy impact point, impact angle and terminal velocity constraints is proposed to solve precise guidance and maneuver penetration problems for hypersonic vehicle in dive phase. Firstly, it analyses the control characters for this kind of vehicle, and establishes relative motion equations in diving-plane and turning-plane. Furthermore, reference motions for the LOS (line-of sight) angle rate with the form of sinusoid are designed, which can be tracked by optimal control with the integrated optimal index consists of maximum terminal velocity, minimum miss distance and impact angle error. Therefore, an optimal guidance law with terminal multiple constraints and can realize maneuvering flight is obtained. In addition, it takes advantage of predictor-corrector to ascertain the maneuver range to consume residual energy in order to satisfy terminal velocity constraint. Finally, the results of CAV-H vehicle simulation test show that the algorithm can realize maneuvering flight, and can satisfy multiple constraints with high precision. Therefore, it can offer references for high precision guidance and maneuver penetration for hypersonic vehicle in dive phase.

Jianwen Zhu;Luhua Liu;Guojian Tang;为民 包

2013