A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air m...A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.展开更多
The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p + l(1 less than or equal to p...The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p + l(1 less than or equal to p less than or equal to s - 1) provided that the simplifying conditions C(p) (or D(p) with non-zero weights) and B(2p + l) hold, where 1 0, 1, 2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(p) and D(p) with 0 < p <less than or equal to> s. Then this method is symplectic if and only if either p = s or the nonlinear stability matrix M of the method has an (s - p) x (s - p) chief submatrix (M) over cap = 0. (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has been designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying C(p),D(p) and B(2p + l) can be easily computed, where 1 I P less than or equal to s, 0 less than or equal to l less than or equal to 2, s less than or equal to 2p + l less than or equal to 2s.展开更多
文摘A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.
基金the National Natural Science Foundation of China.
文摘The main results of this paper are as follows: (1) Suppose an s stage Runge-Kutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2p + l(1 less than or equal to p less than or equal to s - 1) provided that the simplifying conditions C(p) (or D(p) with non-zero weights) and B(2p + l) hold, where 1 0, 1, 2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(p) and D(p) with 0 < p <less than or equal to> s. Then this method is symplectic if and only if either p = s or the nonlinear stability matrix M of the method has an (s - p) x (s - p) chief submatrix (M) over cap = 0. (3) Using the results (1) and (2) as bases, we present a general approach for the construction of symplectic Runge-Kutta methods, and a software has been designed, by means of which, the coefficients of s stage symplectic Runge-Kutta methods satisfying C(p),D(p) and B(2p + l) can be easily computed, where 1 I P less than or equal to s, 0 less than or equal to l less than or equal to 2, s less than or equal to 2p + l less than or equal to 2s.
