On an approach to the problems of control of dynamic systems with nonseparated multipoint intermediate conditions

Abstract

Consideration was given to the problems of control of the linear dynamic systems with given initial, final, and nonseparated (nonlocal) multipoint intermediate conditions and the problems of optimal control with the performance index defined over the entire time interval. An explicit form of the control action was constructed, and a method to solve the problem of optimal control was proposed. Solutions of particular problems were presented.

A Model of the Control Problem of the Thermal Effect of a Laser Beam on a Two-Layer Biomaterial

“…Here and below, "n" in the lower index of the letter means "for the first n" modes. Relation (34) implies the validity of the following statement about complete controllability [23,24]. Proposition 1.…”

“…. , n) relations (33) are usually chosen and the problem of control synthesis is solved using methods of control theory for finitedimensional systems [23,24]. We will solve the problem following this approach.…”

“…The control action u n (t) satisfying the integral relation (34) can be represented in the form [22][23][24] u n (t…”

On the Problem of Optimal Control of the Motion of Two-Link Planar Manipulator with Nonseparated Multipoint Intermediate Conditions

“…be given, where α is a two-dimensional column vector, F k are (2 × 4)-dimensional matrices (k = 1, 2), whose elements are real numbers [4].…”

“…The study of these problems is of great importance for both theory and applications. Some issues of control and optimal control of linear dynamical systems with nonseparated multipoint intermediate conditions are examined, in particular, in [1][2][3][4][5][6].…”