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Minimum time control of the rocket attitude reorientation associated with orbit dynamics. (English) Zbl 1338.49046
Authors’ abstract: In this paper, we investigate the minimal time problem for the guidance of a rocket, whose motion is described by its attitude kinematics and dynamics but also by its orbit dynamics. Our approach is based on a refined geometric study of the extremals coming from the application of the Pontryagin maximum principle. Our analysis reveals the existence of singular arcs of higher order in the optimal synthesis, causing the occurrence of a chattering phenomenon, i. e. of an infinite number of switchings when trying to connect bang arcs with a singular arc. We establish a general result for bi-input control-affine systems, providing sufficient conditions under which the chattering phenomenon occurs. We show how this result can be applied to the problem of the guidance of the rocket. Based on this preliminary theo- retical analysis, we implement efficient direct and indirect numerical methods, combined with numerical continuation, in order to compute numerically the optimal solutions of the problem.

49K15 Optimality conditions for problems involving ordinary differential equations
49M05 Numerical methods based on necessary conditions
49M37 Numerical methods based on nonlinear programming
49N90 Applications of optimal control and differential games
90C30 Nonlinear programming
65K10 Numerical optimization and variational techniques
65K05 Numerical mathematical programming methods
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
70P05 Variable mass, rockets
Bocop; HYBRJ; minpack; SOCS
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