Global Stabilization of Attitude Dynamics: SDRE-based Control Designs

The State-Dependant Riccati Equation method has been frequently used to design suboptimal controllers applied to nonlinear dynamic systems. Different methods for local stability analysis of SDRE controlled systems of order higher than two such as the attitude dynamics of a general rigid body have been developed in the literature; however, it is still difficult to show global stability properties of closed-loop system with this controller. In this paper, a reduced-form of SDRE formulation for attitude dynamics of a general rigid body is achieved by using Input-State Linearization technique and solved analytically. By using the solution matrix of the reduced-form SDRE in properly defined Lyapunov functions, a class of nonlinear controllers with global stability properties is developed. Numerical simulations are performed to study the stability properties and optimality for attitude stabilization of a general rigid body, and it is concluded that the designed controllers have the capability to provide a balance between optimality and proper stability characteristics.