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

Journal of Computer and Systems Sciences International - The motion of three and more identical point masses along a straight line with dry friction that appears in varying the system’s...     

Quasi-Static Motion of a Two-Link System along a Horizontal Plane

Quasi-static motion of a two-link system along a rough horizontal plane is considered. Dry friction acts between the links of the system and the plane. During the motion, the configuration of the linkage changes, whereas the points of contact of the linkage and the plane remain the same. The control torque applied at the joint of the linkage is chosen so as to provide equilibrium condition for each of the links. It is shown that the quasi-static motion of the two-link system is uncontrollable and the uniqueness of this motion is proved for given initial position of the linkage. The trajectories of the vertices are found, depending on the parameters of the system.     

Optimal motion control for a system of two bodies on a straight line

The optimal control problem for motions of a system of two rigid bodies on an inclined straight line in a plane that are periodic in velocity is solved. The external body (frame) moves on a plane under the action of a force from the inner body in the course of its motions relative to the frame under dry friction between the frame and plane. The acceleration of the inner body relative to the outer one is the control whose absolute value is bounded. An optimal control that maximizes the average velocity of the system motion for a given period is found. It is shown that optimal relative acceleration of the inner body has three intervals of constancy on this period, and the outer body is in the state of rest on a part of the period (in the case of horizontal straight line, it is in a state of rest on half a period), and during the rest of the period, it moves in the desired direction and never performs a reversion. It is established that, for the found control law and under an additional constraint on the amplitude of oscillations of the inner body, it is possible to make the motion velocity of the system arbitrarily large under arbitrarily large accelerations of the inner body and an under arbitrarily large frequency of its oscillations simultaneously.     

On the Existence,Uniqueness, and Stability of Periodic Modes of Motion of a Locomotion System with a Mobile Internal Mass

Journal of Computer and Systems Sciences International - In this paper, we consider the rectilinear motion of a locomotion system consisting of a hull and an internal mass in a resisting medium...