H ∞ inverse optimal attitude tracking on the special orthogonal group SO(3)

Abstract

The problem of attitude tracking in the presence of disturbances is addressed by combining inverse optimality and disturbance attenuation. Conditions are provided which ensure that an inverse optimal nonlinear attitude control problem is solved and a meaningful cost function is minimised. The approach results in a PD-type attitude control law on the Special Orthogonal Group which guarantees that, for almost all initial conditions, the energy gain from an exogenous disturbance to a specified error signal respects a given upper bound. For numerical simulations, a satellite attitude tracking problem from literature is considered. The controller gains are tuned using a decoupled linearised single-axis model and the structured control synthesis method. Results indicate that the proposed controller has good tracking and disturbance attenuation capability. In particular, for the problem under consideration, the inverse optimal controller is seen to have better transient performance than its continuous-time quaternion counterpart. Moreover, for initial errors up to radians, it has comparable performance to the shortest-path quaternion PD controller.