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

摘要

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 coefficient 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 offline 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 actuation is developed and illustrated via numerical simulations. Further, the application to attitude and attitude rates estimation is described and implemented on a numerical example. Extensive Monte-Carlo simulations show satisfying performances of the proposed stabilization and the estimation methods in regard of different nonlinear approaches .