We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-...We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.展开更多
Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constrai...Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the Hohmann transfer. Two sets of feasible solutions are found: one corresponding to the Hohmann transfer is the global minimum and the other is a local minimum. We next formulate the Hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.展开更多
基金Project supported by the National Natural Science Foundation of China(No.61374084)。
文摘We consider optimal two-impulse space interception problems with multiple constraints.The multiple constraints are imposed on the terminal position of a space interceptor,impulse and impact instants,and the component-wise magnitudes of velocity impulses.These optimization problems are formulated as multi-point boundary value problems and solved by the calculus of variations.Slackness variable methods are used to convert all inequality constraints into equality constraints so that the Lagrange multiplier method can be used.A new dynamic slackness variable method is presented.As a result,an indirect optimization method is developed.Subsequently,our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles.A number of conclusions for local optimal solutions have been drawn based on highly accurate numerical solutions.Specifically,by numerical examples,we show that when time and velocity impulse constraints are imposed,optimal two-impulse solutions may occur;if two-impulse instants are free,then a two-impulse space interception problem with velocity impulse constraints may degenerate to a one-impulse case.
基金supported by the National Natural Science Foundation of China(No.61374084)
文摘Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the Hohmann transfer. Two sets of feasible solutions are found: one corresponding to the Hohmann transfer is the global minimum and the other is a local minimum. We next formulate the Hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.
