Solving the minimax open-loop control problem for carrier rocket fuel consumption

We propose a mathematical formalization and a method for solving the minimax open-loop terminal control problem for fuel consumption of a propulsion system in a carrier rocket. The initial nonlinear model of the control object is linearized along the reference trajectory and approximated by a linear discrete dynamic system. For the approximating system, we formulate the minimax open-loop terminal control problem, taking into account given geometric constraints on the control and disturbance vectors. We propose a new method and a numerical algorithm for solving the problem, which use a modification of the general recurrent algebraic method to construct generalized reachability sets for the linear discrete controlled system. We demonstrate the effectiveness of the proposed solution with computer simulation examples.