Fastest Motion of a System of Interacting Mass Points along a Rough Horizontal Straight Line

Abstract

An optimal control problem for a system of material points that move along a horizontal rough line is considered. The system moves due to forces of the interaction between the points and the forces of Coulomb’s dry friction acting between points and the underlying line. Only forward movement is allowed. A control algorithm is proposed which provides the fastest transition of the system from one state of rest to another.