ESA GNC Conference Papers Repository

The State-Dependent Riccati Equation (SDRE) technique is a promising control methodology for systematic design of sub-optimal feedback controllers for nonlinear systems. The method provides a unifying approach for solving the infinite horizon optimal control of nonlinear systems problem, avoiding the direct solution of the associated Hamilton-Jacobi-Bellman partial differential equation (generally unviable), while guaranteeing local stability, local optimality, real-time implementability, and robustness with respect to unmodeled dynamics and parametric uncertainties. Such characteristics make the method appealing for numerous applications, in particular in the aerospace field that has always stimulated the development of optimal control methods. SDRE has been successfully applied to missiles, aircrafts, unmanned aerial vehicles, satellite and spacecraft. Other practical contributions can be found in the literature regarding ships, autonomous underwater vehicles, automotive systems, biological and biomedical systems, robotics and general process control [1]. The aim of this work is to provide a general overview of the method, and propose possible modifications of the classic SDRE technique, with particular focus on the development of guidance laws for relative motion control in space. More specifically, bearing in mind the requirements of common relative motion applications, such as rendezvous and formation flying, we propose some modifications of the classic SDRE methodology, inspired by results from linear optimal control theory. The proposed modifications aim to increase local stability, and reduce control effort and computational cost. The discussion is supported by numerical simulations set up considering two different mission scenarios: a debris mitigation mission in lower Earth orbits inspired to the Active Space Debris Removal System proposed in [2], and the NASA's deep space formation flying concept mission New World Observer [3]. The most notable difference between the two scenario lies in the relative dynamics. The dynamics that characterize the former scenario is based on a classic two-body problem setup. In the latter scenario the formation orbits around the L2 libration point of the Earth/Moon - Sun systems, thus relative motion dynamics must be derived considering a three-body problem.