Computationally Efficient Nonlinear H_∞ Control Designs for a Rigid Body Spacecraft

In this paper, we consider nonlinear control of a symmetric spacecraft about its axis of symmetry with two control torques. Using a computationally efficient ℋ_∞ control design procedure, attitude regulation and trajectory tracking problems of the axi-symmetric spacecraft were solved. Resorting to higher order Lyapunov functions, the employed nonlinear ℋ_∞ control approach reformulates the difficult Hamilton-Jacobian-Isaacs (HJI) inequalities as semi-definite optimization conditions. Sum-of-squares (SOS) programming techniques are then applied to obtain computationally tractable solutions, from which nonlinear control laws will be constructed. The proposed nonlinear ℋ_∞ designs will be able to exploit the most suitable forms of Lyapunov function for spacecraft control and the resulting controllers will perform better than existing nonlinear control laws.