arXiv subjects

Alexander Ovseevich

Publications and source records attributed to Alexander Ovseevich.

22 records · Page 2Linked to original sources

arXiv2015

Motion of a system of oscillators under the generalized dry friction control

The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dry-friction type control is studied. This type of control arises in the problem of steering the system to equilibrium. The problem of existence and uniqueness of motion under the suggested control is resolved within the framework of the DiPerna--Lions theory of singular ordinary differential equations.

math.OC↗

arXiv2015

Irregular dynamic systems according to R.J. DiPerna and P.L. Lions

These are notes of a seminar held at the Institute for Problems in Mechanics, RAS in 2003 and aimed at presentation of [R.J. DiPerna and P.L. Lions, Invent. math. 98, 511 (1989)]. We discuss the notion of a generalized solution to a singular Ordinary Differential Equation introduced by DiPerna and Lions. We stress importance of singular dynamic systems from the "philosophia naturalis" point of view, and extend and simplify the original approach by R.J. DiPerna and P.L. Lions. Further extensions are discussed.

math.AP↗

arXiv2014

Birth of the shape of a reachable set

We address a linear control system under geometric constraints on control and study its reachable sets starting at zero time from the origin. The main result is the existence of a limit shape of the reachable sets as the terminal time tends to zero. Here, a shape of a set stands for the set regarded up to an invertible linear transformation. Both autonomous and non-autonomous cases are considered.

math.OC↗

arXiv2013

Complexity of the minimum-time damping of a physical pendulum

We study the minimum-time damping of a physical pendulum by means of a bounded control. In the similar problem for a linear oscillator each optimal trajectory possesses a finite number of control switchings from the maximal to the minimal value. If one considers simultaneously all optimal trajectories with any initial state, the number of switchings can be arbitrary large. We show that for the nonlinear pendulum there is a uniform bound for the switching number for all optimal trajectories. We find asymptotics for this bound as the control amplitude goes to zero.

math.OC↗