Optimal control of system of material points in a straight line with dry friction

The motion of three and more identical point masses along a straight line with dry friction that appears in varying the system’s configuration is considered. The optimal-control problem of the system is solved; here, the purpose of the optimal control is to maximize the system’s displacement in a fixed time with zero velocities and the coincidence of the positions of all points at the beginning and the end of the motion in the absence of restrictions on the interacting forces of masses. The nonuniqueness of an optimal solution is demonstrated and an optimal solution is found whereby the distance between any two points does not exceed an assigned value on the entire interval of the motion.