A. Ovseevich - Academia.edu (original) (raw)

Papers by A. Ovseevich

Research paper thumbnail of Asymptotic behavior of the Bellman function in a stochastic optimal control problem

Journal of Applied Mathematics and Mechanics, 1981

ABSTRACT A quasi-optimal control giving a near-optimal result under small power resources is foun... more ABSTRACT A quasi-optimal control giving a near-optimal result under small power resources is found by studying the asymptotic behavior of the Bellman function of the optimal control problem for the motion of a system perturbed by white noise with limited control power resources. The determination of the asymptotic behavior of the Bellman function and of the quasi-optimal control calls for solving the partial differential equations introduced in /1/. A converging iteration process is found for solving them.

Research paper thumbnail of Variance of the Number of Departed Messages in a Simple Queueing System

Research paper thumbnail of Ellipsoidal State Estimation of Dynamic Systems

Stochastic Control, 1987

The paper is devoted to guaranteed estimation of state for dynamic systems subject to external di... more The paper is devoted to guaranteed estimation of state for dynamic systems subject to external disturbances in the presence of observation errors. It is assumed that both external disturbances and observation errors are unknown but bounded vector functions of time. Method of guaranteed estimation of state is developed which is based on optimal (in the sense of volume) ellipsoidal approximation of the set of possible state vectors. Cases of discrete and continuous observations are considered. Finite-difference and differential equations of guaranteed filtering are obtained which describe the evolution of the estimating ellipsoid. Numerical results of computer simulation of guaranteed filtering are presented.

Research paper thumbnail of Hamiltonian systems with a specified invariant manifold and some of their applications

Journal of Applied Mathematics and Mechanics, 1984

Research paper thumbnail of Asymptotic Control Theory for a Closed String

Russian Journal of Mathematical Physics

We develop an asymptotical control theory for one of the simplest distributed oscillating systems... more We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit complete damping and an asymptotically exact value of the required time. By using approximate reachable sets instead of exact ones, we design a dry-friction like feedback control, which turns out to be asymptotically optimal. We prove the existence of motion under the control using a rather explicit solution of a nonlinear wave equation. Remarkably, the solution is determined via purely algebraic operations. The main result is a proof of asymptotic optimality of the control thus constructed. Keywords maximum principle, reachable sets, linear system MSC 2010: 93B03, 93B07, 93B52.

Research paper thumbnail of A problem of random choice and its deterministic structure

Research paper thumbnail of On Equations of Ellipsoids Approximating Attainable Sets

Journal of Optimization Theory and Applications, 1997

This paper is devoted to a search for a guaranteed counterpart of the stochastic Kalman filter. W... more This paper is devoted to a search for a guaranteed counterpart of the stochastic Kalman filter. We study the guaranteed filtering of a linear system such that the phase state and external disturbance form a vector subject to an ellipsoidal bound. This seemingly exotic setup can be justified by an analogy with the observation of Gaussian processes. Unfortunately, the resulting guaranteed filtering supplies us an ellipsoid approximating the localization domain for the state vector, but not the localization domain itself, and turns out to be more difficult compared to the Kalman filter. Our main results consist of an explicit evaluation of the Hamiltonians. In principle, this permits us to write explicitly the equations of the guaranteed filter.

Research paper thumbnail of Damping of a system of linear oscillators using the generalized dry friction

Proceedings of the Steklov Institute of Mathematics, 2016

Research paper thumbnail of Explicit Formulae for Ellipsoids Approximating Reachable Sets

AIP Conference Proceedings, 2007

Research paper thumbnail of Motion of a system of oscillators under the generalized dry friction control

Automation and Remote Control, 2015

The problem of the existence and uniqueness of the motion of the system of an arbitrary number li... more The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dryfriction 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 DiPernaLions theory of singular ordinary differential equations.

Research paper thumbnail of A Local Feedback Control Bringing a Linear System to Equilibrium

Journal of Optimization Theory and Applications, 2014

Research paper thumbnail of Structure of the minimum-time damping of a physical pendulum

Research paper thumbnail of Complexity of the minimum-time damping of a pendulum

Research paper thumbnail of Minimum-time damping of a physical pendulum

Research paper thumbnail of Stochastic Comparison of Ellipsoidal and Interval Error Estimation in Vector Operations

Research paper thumbnail of “Splitting times” for Random Fields

Theory of Probability & Its Applications, 1979

Research paper thumbnail of Complexity of the Minimum-Time Damping of a Physical Pendulum

SIAM Journal on Control and Optimization, 2014

We study the minimum-time damping of a physical pendulum by means of a bounded control. In the si... more 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.

Research paper thumbnail of Stochastic approach to the comparison of ellipsoidal and interval estimates

Russian Journal of Mathematical Physics, 2009

Research paper thumbnail of Limit behavior of ellipsoids bounding attainable sets

Journal of Optimization Theory and Applications, 1995

ABSTRACT We study the asymptotic behavior of some ellipsoidal bounds for attainable sets of stabl... more ABSTRACT We study the asymptotic behavior of some ellipsoidal bounds for attainable sets of stable linear control dynamic systems. We show that, in a variety of situations, there is exactly one ellipsoid which can serve as a limit of the above bounds ast→∞. This ellipsoid is shown to be in many cases locally attractive.

Research paper thumbnail of Properties of the Optimal Ellipsoids Approximating the Reachable Sets of Uncertain Systems

Journal of Optimization Theory and Applications, 2000

The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership mod... more The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In the paper, the optimal outer-ellipsoidal approximation of reachable sets is considered, and attention is paid to the criterion associated with the projection of the approximating ellipsoid onto a given direction. The nonlinear differential equations governing the evolution of ellipsoids are analyzed and simplified. The asymptotic behavior of the ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.

Research paper thumbnail of Asymptotic behavior of the Bellman function in a stochastic optimal control problem

Journal of Applied Mathematics and Mechanics, 1981

ABSTRACT A quasi-optimal control giving a near-optimal result under small power resources is foun... more ABSTRACT A quasi-optimal control giving a near-optimal result under small power resources is found by studying the asymptotic behavior of the Bellman function of the optimal control problem for the motion of a system perturbed by white noise with limited control power resources. The determination of the asymptotic behavior of the Bellman function and of the quasi-optimal control calls for solving the partial differential equations introduced in /1/. A converging iteration process is found for solving them.

Research paper thumbnail of Variance of the Number of Departed Messages in a Simple Queueing System

Research paper thumbnail of Ellipsoidal State Estimation of Dynamic Systems

Stochastic Control, 1987

The paper is devoted to guaranteed estimation of state for dynamic systems subject to external di... more The paper is devoted to guaranteed estimation of state for dynamic systems subject to external disturbances in the presence of observation errors. It is assumed that both external disturbances and observation errors are unknown but bounded vector functions of time. Method of guaranteed estimation of state is developed which is based on optimal (in the sense of volume) ellipsoidal approximation of the set of possible state vectors. Cases of discrete and continuous observations are considered. Finite-difference and differential equations of guaranteed filtering are obtained which describe the evolution of the estimating ellipsoid. Numerical results of computer simulation of guaranteed filtering are presented.

Research paper thumbnail of Hamiltonian systems with a specified invariant manifold and some of their applications

Journal of Applied Mathematics and Mechanics, 1984

Research paper thumbnail of Asymptotic Control Theory for a Closed String

Russian Journal of Mathematical Physics

We develop an asymptotical control theory for one of the simplest distributed oscillating systems... more We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit complete damping and an asymptotically exact value of the required time. By using approximate reachable sets instead of exact ones, we design a dry-friction like feedback control, which turns out to be asymptotically optimal. We prove the existence of motion under the control using a rather explicit solution of a nonlinear wave equation. Remarkably, the solution is determined via purely algebraic operations. The main result is a proof of asymptotic optimality of the control thus constructed. Keywords maximum principle, reachable sets, linear system MSC 2010: 93B03, 93B07, 93B52.

Research paper thumbnail of A problem of random choice and its deterministic structure

Research paper thumbnail of On Equations of Ellipsoids Approximating Attainable Sets

Journal of Optimization Theory and Applications, 1997

This paper is devoted to a search for a guaranteed counterpart of the stochastic Kalman filter. W... more This paper is devoted to a search for a guaranteed counterpart of the stochastic Kalman filter. We study the guaranteed filtering of a linear system such that the phase state and external disturbance form a vector subject to an ellipsoidal bound. This seemingly exotic setup can be justified by an analogy with the observation of Gaussian processes. Unfortunately, the resulting guaranteed filtering supplies us an ellipsoid approximating the localization domain for the state vector, but not the localization domain itself, and turns out to be more difficult compared to the Kalman filter. Our main results consist of an explicit evaluation of the Hamiltonians. In principle, this permits us to write explicitly the equations of the guaranteed filter.

Research paper thumbnail of Damping of a system of linear oscillators using the generalized dry friction

Proceedings of the Steklov Institute of Mathematics, 2016

Research paper thumbnail of Explicit Formulae for Ellipsoids Approximating Reachable Sets

AIP Conference Proceedings, 2007

Research paper thumbnail of Motion of a system of oscillators under the generalized dry friction control

Automation and Remote Control, 2015

The problem of the existence and uniqueness of the motion of the system of an arbitrary number li... more The problem of the existence and uniqueness of the motion of the system of an arbitrary number linear oscillators under a generalized dryfriction 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 DiPernaLions theory of singular ordinary differential equations.

Research paper thumbnail of A Local Feedback Control Bringing a Linear System to Equilibrium

Journal of Optimization Theory and Applications, 2014

Research paper thumbnail of Structure of the minimum-time damping of a physical pendulum

Research paper thumbnail of Complexity of the minimum-time damping of a pendulum

Research paper thumbnail of Minimum-time damping of a physical pendulum

Research paper thumbnail of Stochastic Comparison of Ellipsoidal and Interval Error Estimation in Vector Operations

Research paper thumbnail of “Splitting times” for Random Fields

Theory of Probability & Its Applications, 1979

Research paper thumbnail of Complexity of the Minimum-Time Damping of a Physical Pendulum

SIAM Journal on Control and Optimization, 2014

We study the minimum-time damping of a physical pendulum by means of a bounded control. In the si... more 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.

Research paper thumbnail of Stochastic approach to the comparison of ellipsoidal and interval estimates

Russian Journal of Mathematical Physics, 2009

Research paper thumbnail of Limit behavior of ellipsoids bounding attainable sets

Journal of Optimization Theory and Applications, 1995

ABSTRACT We study the asymptotic behavior of some ellipsoidal bounds for attainable sets of stabl... more ABSTRACT We study the asymptotic behavior of some ellipsoidal bounds for attainable sets of stable linear control dynamic systems. We show that, in a variety of situations, there is exactly one ellipsoid which can serve as a limit of the above bounds ast→∞. This ellipsoid is shown to be in many cases locally attractive.

Research paper thumbnail of Properties of the Optimal Ellipsoids Approximating the Reachable Sets of Uncertain Systems

Journal of Optimization Theory and Applications, 2000

The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership mod... more The ellipsoidal estimation of reachable sets is an efficient technique for the set-membership modelling of uncertain dynamical systems. In the paper, the optimal outer-ellipsoidal approximation of reachable sets is considered, and attention is paid to the criterion associated with the projection of the approximating ellipsoid onto a given direction. The nonlinear differential equations governing the evolution of ellipsoids are analyzed and simplified. The asymptotic behavior of the ellipsoids near the initial point and at infinity is studied. It is shown that the optimal ellipsoids under consideration touch the corresponding reachable sets at all time instants. A control problem for a system subjected to uncertain perturbations is investigated in the framework of the optimal ellipsoidal estimation of reachable sets.