Despite the theoretical superiority of optimal control, attitude control of operational satellites is still predominantly performed by standard controllers, typically linear state feedbacks, because of the numerical implementation complexity of nonlinear optimal control techniques. In this talk, an inverse optimal control approach is presented, which circumvents the task of numerically solving online the Hamilton Jacobi Bellman (HJB) partial differential equation, representing the dynamic programming formulation of the nonlinear global optimal control problem. The convergence rate of Lyapunov functions is used as a natural player in the optimisation problem. The optimal control objective is to minimise a norm of the control torque, subject to different types of constraints on the convergence rate of a Lyapunov function, under the effect of a benchmark controller. The proposed optimisation method significantly enhances the torque-rapidity trade-off compared to a PD law, used as a benchmark. This optimisation technique can more generally be applied with any stabilizing benchmark controller. The proposed inverse optimal approach is globally stabilising and presents low implementation complexity, which is a significant advantage, given the limited resources onboard small satellites.