Minimum time control of the rocket attitude reorientation associated with orbit dynamics.

*(English)*Zbl 1338.49046Authors’ 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.

Reviewer: Costică Moroşanu (Iaşi)

##### MSC:

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 |

##### Keywords:

coupled attitude orbit problem; optimal control; Pontryagin maximum principle; shooting method; continuation; chattering arcs##### References:

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