Terminal control of moving objects in the classes of piecewise constant and piecewise continuous functions

This paper presents a terminal control problem with the separation of object's state coordinates into two types: the slowly changing coordinates figuring in boundary conditions and the coordinates of the stabilization loop. A predictive model of the object is introduced to design the control action. A differential equation is derived for predicted mismatches in the boundary conditions. The original system is discretized in time based on this equation. This problem is solved step-by-step in the classes of piecewise constant and piecewise continuous control actions. As an illustrative example, the problem of controlling the fuel consumption of a stage of a liquid-propellant launch vehicle is considered. The class of control actions is extended from piecewise constant to piecewise continuous functions in order to cover additional requirements for the control process. The continuous functions on intervals between control jumps are chosen using the local boundary conditions obtained during the terminal control design in the class of piecewise constant functions.