Optimized State-Dependent Riccati Equation Method for Spacecraft Attitude Estimation and Control

This work presents an extension of the state dependent Riccati equation method (SDRE), a powerful technique for optimal estimation and control of nonlinear systems. Following the standard SDRE approach, nonlinear multivariable model equations are recast as a pseudo- linear equations with a state-dependent coeficient matrix. Exploiting the non-uniqueness of that parametrization, an optimization problem is formulated with respect to weighting factors in a generalized state-dependent representation. The measure of performance is the classical infinite-horizon integral quadratic cost. The controller assumes an SDRE-like structure, where the gains becomes nonlinear functions of the decision variables. An off- line numerical solution is implemented via two types of gradient-based iterative methods (steepest descent and Newton). In order to allow for on-line implementation, a simpler algorithm is devised where the controller switches among a finite set of possible SDRE controllers, which are implemented in parallel. The application of the optimized SDRE method to attitude stabilization for rigid body dynamics with full information and actu- ation is developed and illustrated via numerical simulations. Further, the application to attitude and attitude rates estimation is described and implemented on a numerical ex- ample. Extensive Monte-Carlo simulations show satisfying performances of the proposed stabilization and the estimation methods in regard of different nonlinear approaches.