The computations of the high-order partial derivatives in a given problem are often cumbersome or not accurate. To combat such shortcomings, a new method for calculating exact high-order sensitivities using multicomplex numbers is presented. Inspired by the recent complex step method that is only valid for firstorder sensitivities, the new multicomplex approach is valid to arbitrary order. The mathematical theory behind this approach is revealed, and an efficient procedure for the automatic implementation of the method is described. Several applications are presented to validate and demonstrate the accuracy and efficiency of the algorithm. The results are compared to conventional approaches such as finite differencing, the complex step method, and two separate automatic differentiation tools. The multicomplex method performs favorably in the preliminary comparisons and is therefore expected to be useful for a variety of algorithms that exploit higher order derivatives.

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International audienceThe aim of this paper is to consider the modelling and control issues arising in the design of a station keeping system for geostationary satellites based on electric propulsion. In particular, a linear time-varying model for the dynamics of a geostationary satellite affected by perturbations is derived and the longitude and latitude station keeping problem is then formulated as a constrained linear quadratic optimal control problem. A direct method based on the so-called differential inclusion approach is then proposed. Simulation results showing the feasibility of the control task on a spacecraft equipped with electric thrusters are also presented and discussed

International audienceThe aim of this paper is to consider the modelling and control issues arising in the design of a station keeping system for geostationary satellites based on on-off electric thrusters. In particular, a model for the dynamics of a geostationary satellite affected by perturbations is derived and the electric station keeping problem is then formulated as an optimisation problem with mixed (continuous and discrete) constraints. Simulation results showing the feasibility of the control task on a spacecraft equipped with electric thrusters are also presented and discussed