Inverse Optimal Satellite Attitude Control from a Geometric Viewpoint

A geometric optimal control approach is presented, which circumvents the tedious task of numerically solving online the partial differential equations of the nonlinear global optimal control problem. In practice, operational satellite attitude control is based on standard non optimal control techniques because of the implementation complexity of nonlinear optimal control. An inverse optimal control approach is therefore proposed, based on phase space geometry. It has the advantages of low implementation complexity and low computational demand. The optimal control objective is to minimise a norm of the control torque subject to a rapidity constraint on the convergence rate of a Lyapunov function. The constraint is that the convergence rate has to exceed that of a given stabilising benchmark controller. Two benchmark controllers are considered: PD and maximum rate sliding mode to illustrate the technique. The proposed optimisation method significantly enhances the torque rapidity trade-off compared to the benchmark controller. The only practical issue is the possibility of torque saturation from certain initial conditions, which is resolved through gain scheduling.