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We propose an optimal control method for simultaneous slewing and vibrationcontrol of flexible spacecraft. Considering dynamics on different time scales,the optimal control problem is discretized on micro and macro time grids usinga multirate variational approach. The description of the system and thenecessary optimality conditions are derived through the discreteLagrange-d'Alembert principle. The discrete problem retains the conservationproperties of the continuous model and achieves high fidelity simulation at areduced computational cost. Simulation results for a single-axis rotationalmaneuver demonstrate vibration suppression and achieve the same accuracy as thesingle rate method at reduced computational cost.

A multirate variational approach to simulation and optimal control for flexible spacecraft