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

摘要

This work presents an extension of the state dependent Riccati equa-tion method (SDRE), a powerful technique for optimal estimation andcontrol of nonlinear systems. Following the standard SDRE approach,nonlinear model equations are recast as pseudolinear equations witha state-dependent coefficient matrix. Exploiting the non-uniquenessof this parametrization, this work formulates a nonlinear optimizationproblem with respect to the weights of linear combination of primarystate-dependent coefficient matrices. The measure of performance isthe classical infinite-horizon integral cost quadratic with respect to thestate and the control. The controller assumes an SDRE-like structure,but where the gains becomes nonlinear functions of the decision vari-ables. The proposed solution implements two types of gradient-basediterative methods (steepest descent and Newton steps) where the gra-dient of the integral cost is numerically evaluated. In order to allow foron-line implementation, a simpler suboptimal algorithm is devised wherethe controller switches among a finite set of possible SDRE controllers,which are implemented in parallel. The application of the optimizedSDRE method to attitude stabilization for rigid body dynamics withfull information and actuation is developed and illustrated via numeri-cal simulations. Further, the application to attitude and attitude ratesestimation is described and implemented on a numerical example. Ex-tensive Monte-Carlo simulations show satisfying performances of boththe stabilization and the estimation applications.