V. I. Maksimov

On rough inversion of a dynamical system with a disturbance

Abstract A dynamical inversion problem is considered. A regularizing solving algorithm oriented to a quite long time interval of systems functioning is designed. The algorithm is stable with respect to informational noises.

Resource-saving tracking problem with infinite time horizon

We consider the problem on the infinite-duration tracking of a prescribed trajectory of an inaccurately observed control system subjected to an unobservable dynamic disturbance. We construct a solution algorithm that is resource-saving in the sense that the control resources used for solving the problem for small noise values in the state observation channel are little different from the corresponding resources in the “ideal case” where the current values of the dynamic disturbance are available to direct observation.

Algorithm for shadowing the solution of a parabolic equation on an infinite time interval

For a parabolic equation, we consider the problem of constructing a feedback control synthesis algorithm ensuring that the solution of a given equation shadows the solution of another equation with unknown right-hand side. We suggest a noise-immune algorithm based on the extremal shift method well known in guaranteed control theory.

Differential guidance game with incomplete information on the state coordinates and unknown initial state

We study the problem of guaranteed positional guidance of a linear partially observable control system to a convex target set at a given time. The problem is considered in the case of incomplete information. More precisely, it is assumed that the system is subjected to some unknown disturbance; in addition, the initial state is unknown as well. But the sets of admissible disturbances and the set of admissible initial states are known. The latter is assumed to be finite. We construct an algorithm for solving this problem.

On an algorithm for tracking the motion of the reference system with aftereffect when only part of the coordinates is measured

We consider the problem of tracking a given trajectory by a system described by an equation with aftereffect. We suggest an algorithm, stable to information noise and numerical errors, for solving this problem in the case of incomplete information on the phase trajectory (measurement of part of the coordinates). The algorithm is based on the dynamic inversion and guaranteed control method.

On exact stabilization of an uncertain dynamical system

The study is motivated by the problem of stabilizing the concentration of atmospheric carbon, which is widely discussed in the context of global warming nowadays. A key difficulty in the design of stabilization strategies is the uncertainty of the underlying physical model. In the present paper, a general problem setting is suggested and a relevant alanytic framework elaborated. Analysis employs specific qualitative features of an uncertain dynamics, including automatic stabilization of the trajectories in the absence of input disturbances. An asymptotic version of Krasovskiis extremal shift control principle is developed and model-robust strategies stabilizing a state coordinate at a prescribed level are constructed.

Tracking a given solution of a nonlinear distributed second-order equation

We consider a nonlinear distributed second-order equation and present a rule for writing out a tracking differential equation on the basis of the constructions of feedback control theory.

On an algorithm for dynamic reconstruction of the input

We consider the problem of dynamic reconstruction of the input in a system described by a vector differential equation and nonlinear in the state variable. We indicate an algorithm that is stable under information noises and computational errors and is aimed at infinite system operation time. The algorithm is based on the dynamic regularization method.

Control reconstruction under changes of part of the coordinates of a nonlinear delay dynamical system

We consider the problem of dynamic reconstruction of a variable input of a nonlinear delay system on the basis of an inexact measurement of part of the phase vector. We present a solution algorithm on the basis of the method of auxiliary control models.

On a certain problem on feedback control for a parabolic equation with memory

A game control problem for a parabolic differential equation with memory is considered. An algorithm for its solution based on Krasovskii’s method of extreme shift and the method of stable paths is proposed.