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The problem of control of rod heating process with nonseparated conditions at intermediate moments of time

Barseghyan Vanya R.

Archives of Control Sciences

2021

Vol. 31, No. 3

481--493

The problem of control of rod heating process by changing the temperature along the rod whose ends are thermally insulated is considered. It is assumed that, along with the classical boundary conditions, nonseparated multipoint intermediate conditions are also given. Using the method of separation of variables and methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions, a constructive approach is proposed to build the sought function of temperature control action. A necessary and sufficient condition is obtained, which the function of the distribution of the rod temperature must satisfy, so that under any feasible initial, nonseparated intermediate, and final conditions, the problem is completely controllable. As an application of the proposed approach, control action with given nonseparated conditions on the values of the rod temperature distribution function at the two intermediate moments of time is constructed.

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka J., Babiarz A., Niezabitowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2016

Vol. 64, nr 1

21--35

The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

Constrained controllability of nonlinear stochastic impulsive systems

Karthikeyan S., Balachandran K.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 2

307-316

This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

Controllability of nonlinear impulsive Ito type stochastic systems

Sakthivel R.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 4

589-595

In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.