Fuel-optimal rocket landing with aerodynamic controls

Aerodynamic forces are not negligible for a reusable rocket returning back to Earth. How the aerodynamic controls and propulsion should be coordinated to realize fuel-optimal precise landing is addressed in this paper. To this end, we formulate a model-based optimal control problem with the rocket’s angle of attack, thrust magnitude, and thrust direction as control inputs. This problem is nonconvex and difficult to solve mainly due to the simultaneous presence of the aerodynamic forces and propulsion. To efficiently get the solution of the problem, we will present how to approximate the nonconvex problem with a second-order cone programming problem which is then iteratively solved in polynomial time by state-of-the-art interior-point methods. Some interesting observations on the optimal characteristics of the control inputs will be demonstrated by numerical examples.