A nonlinear optimal control approach for autonomous reentry space vehicles

Nonlinear control for autonomous reentry space vehicles has been a topic of intensive research during the last years in the area of aerospace science and technology. The associated dynamic model is obtained by expressing position variables and orientation angles of the space vehicle in different coordinate frames, namely an earth-fixed, an earth rotating and a body fixed frame. In this article, a nonlinear optimal control approach is proposed for the dynamic model of reentry space vehicles. It is proven that the longitudinal motion dynamic model of reentry space vehicles is differentially flat and a flatness-based controller is designed about it. Next, in the nonlinear optimal control approach, the dynamic model of the reentry space vehicle undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the reentry space vehicle a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.