A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT mi...A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.展开更多
We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a ...We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.展开更多
Although the channel-decoupling assumption is often used in design of three-dimensional guidance laws, it loses its rationality for aircrafts with strong kinematics coupling because body rotation arises. To overcome t...Although the channel-decoupling assumption is often used in design of three-dimensional guidance laws, it loses its rationality for aircrafts with strong kinematics coupling because body rotation arises. To overcome this trouble, a novel guiding method was proposed based on Lie-group. After a model of 3D guidance is formulated using vectors, the precision guidance with ending angular constraints can be transformed into a problem involving the relation between directional angles and rotational angular velocities of certain vectors. When the guidance model is imposed a SO(3)-based description, a novel 3D sliding mode guidance law with ending angular constraints can be developed via Lie-group control method and variable structure control theory. Finally, the feasibility and performance of the guidance law were shown by simulating the examples.展开更多
Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Hel...Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .展开更多
In this paper,we derive and analyse waveform relaxation(WR)methods for solving differential equations evolving on a Lie-group.We present both continuous-time and discrete-time WR methods and study their convergence pr...In this paper,we derive and analyse waveform relaxation(WR)methods for solving differential equations evolving on a Lie-group.We present both continuous-time and discrete-time WR methods and study their convergence properties.In the discrete-time case,the novel methods are constructed by combining WR methods with Runge-KuttaMunthe-Kaas(RK-MK)methods.The obtained methods have both advantages of WR methods and RK-MK methods,which simplify the computation by decoupling strategy and preserve the numerical solution of Lie-group equations on a manifold.Three numerical experiments are given to illustrate the feasibility of the new WR methods.展开更多
基金supported by the National University of Defense Technology Innovation Support Project for Outstanding Graduate Student(B100303)
文摘A new non-decoupling three-dimensional guidance law is proposed for bank-to-turn （BTT） missiles with the motion coupling problem. In this method, the different geometry is taken for theoretically modeling on B-IT missiles＇ motion within the threedimensional style without information loss, and meanwhile, Liegroup is utilized to describe the line-of-sight （LOS） azimuth when the terminal angular constraints are considered. Under these cir- cumstances, a guidance kinematics model is established based on differential geometry. Then, corresponding to no terminal angular constraint and terminal angular constraints, guidance laws are re- spectively designed by using proportional control and generalized proportional-derivative （PD） control in SO（3） group. Eventually, simulation results validate that this developed method can effectively avoid the complexity of pure Lie-group method and the information loss of the traditional decoupling method as well.
文摘We transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval[0;1].Then we apply Lie-group shooting method(LGSM)to search a missing initial condition of slope through a weighting factor r 2(0;1).The best r is determined by matching the right-end boundary condition.When the initial slope is available we can apply the group preserving scheme(GPS)to calculate the solution,which is highly accurate.By LGSM we obtain precise radial symmetric solutions of the Yamabe equation.These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations.
基金Sponsored by the National Natural Science Foundation of China (60374006)
文摘Although the channel-decoupling assumption is often used in design of three-dimensional guidance laws, it loses its rationality for aircrafts with strong kinematics coupling because body rotation arises. To overcome this trouble, a novel guiding method was proposed based on Lie-group. After a model of 3D guidance is formulated using vectors, the precision guidance with ending angular constraints can be transformed into a problem involving the relation between directional angles and rotational angular velocities of certain vectors. When the guidance model is imposed a SO(3)-based description, a novel 3D sliding mode guidance law with ending angular constraints can be developed via Lie-group control method and variable structure control theory. Finally, the feasibility and performance of the guidance law were shown by simulating the examples.
文摘Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .
基金supported by the Natural Science Foundation of China(NSFC)under grant 11871393International Science and Technology Cooperation Program of Shaanxi Key Research&Development Plan under grant 2019KWZ-08.
文摘In this paper,we derive and analyse waveform relaxation(WR)methods for solving differential equations evolving on a Lie-group.We present both continuous-time and discrete-time WR methods and study their convergence properties.In the discrete-time case,the novel methods are constructed by combining WR methods with Runge-KuttaMunthe-Kaas(RK-MK)methods.The obtained methods have both advantages of WR methods and RK-MK methods,which simplify the computation by decoupling strategy and preserve the numerical solution of Lie-group equations on a manifold.Three numerical experiments are given to illustrate the feasibility of the new WR methods.
