Global Stabilization of Attitude Dynamics: SDRE-based Control Laws

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 greater than two such as the attitude dynamics of a general rigid body have been extended in 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. Choosing quaternions as attitude representation parameters gives an analytic solution of the resulting SDRE. 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. The proposed control laws are nonsingular due to using quaternions. Numerical simulations are performed to study the performance of the controllers in attitude stabilization of a general rigid body with different moments of inertia matrices. It is revealed that the designed control laws can provide a balance between optimality and proper stability characteristics. Furthermore, the minimum convergence rate of the closed-loop system with the designed controllers is analytically achieved which can be tuned simply by changing the SDRE weighting matrices.