Nonlinear H_infinity Control Designs with Axisymmetric Spacecraft Control

Abstract

In this paper, we study nonlinear control of a spacecraft symmetric about its principal axis with two control torques. Using a computationally efficient H ∞ control design procedure, attitude stabilization and command tracking problems of the axisymmetric spacecraft are solved locally. The proposed nonlinear H ∞ control approach uses higher order Lyapunov functions and reformulates the difficult Hamilton―Jacobian―Isaacs inequalities as semidefinite optimization conditions. Sum-of-squares programming techniques are then applied to obtain computationally tractable solutions, from which nonlinear control laws will be constructed. The nonlinear H ∞ control designs for spacecraft are capable of exploiting the most suitable forms of Lyapunov functions for performance improvement.