Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints,this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is ...Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints,this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target.In this way,the original maneuvering target is transformed into a stationary one.A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model,one of the coefficients is determined to achieve the impact time constraint,and the other is determined to satisfy a newly defined virtual look angle constraint.For meeting the terminal constraints simultaneously,the guidance command can finally be obtained.The resulting solution is represented as a combination of proportional navigation guidance-like term which is aimed to meet the zero miss distance constraint,a bias term for impact time control by adjusting the length of the homing trajectory,and an additional term for target maneuvers.Numerous simulations demonstrate that the proposed law achieves an acceptable impact time error for various initial conditions against different types of maneuvering targets and shows more effective performance in comparison with those of other existing guidance laws.展开更多
In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such in...In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighbouring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.展开更多
基金co-supported by the Beijing Key Laboratory of UAV Autonomous Control, China and the Key Project of Chinese Ministry of Education (No. 2022CX02702)
文摘Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints,this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target.In this way,the original maneuvering target is transformed into a stationary one.A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model,one of the coefficients is determined to achieve the impact time constraint,and the other is determined to satisfy a newly defined virtual look angle constraint.For meeting the terminal constraints simultaneously,the guidance command can finally be obtained.The resulting solution is represented as a combination of proportional navigation guidance-like term which is aimed to meet the zero miss distance constraint,a bias term for impact time control by adjusting the length of the homing trajectory,and an additional term for target maneuvers.Numerous simulations demonstrate that the proposed law achieves an acceptable impact time error for various initial conditions against different types of maneuvering targets and shows more effective performance in comparison with those of other existing guidance laws.
文摘In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighbouring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.
