On control of degenerate distributed systems

Abstract

Abstract. We study the controllability of linear distributed control systems described by differential equations in Banach spaces with a degenerate operator at the derivative. A homogeneous part of equations has a degenerate strongly continuous resolving semigroup. For such system with, generally speaking, a time-dependent bounded operator at the control function we find the criteria of -controllability in time and of -controllability in a free time in terms of the operators involved in the equation. General results are used for studying of -controllability of the considered systems with a finite-dimensional input. The obtained conditions are demonstrated by examples of control systems described by partial differential equations and systems of equations unsolved with respect to the time derivative.

Fast‐time complete controllability of nonlinear fractional delay integrodifferential evolution equations with nonlocal conditions and a parameter

“…Remark Definition 3.2 is somewhat similar to the idea of controllability for free time presented in Baleanu et al and Plekhanova and Fedorov 50,51 . But, by contrast, it should be stressed here that the time when system () is steered to the target value may be achieved ahead of the given time a .…”

“…Under the fast-time complete controllability, nonlinearity in the considered system is only supposed to be continuous rather than Lipschitz continuous, and the resolvent operator associated with the system has no compactness conditions. We will further investigate the controllability problems for free time with reference to the theory presented in 50,51 in our future research work.…”

“…Definition 3.2 is somewhat similar to the idea of controllability for free time presented in Baleanu et al and Plekhanova and Fedorov. 50,51 But, by contrast, it should be stressed here that the time when system (1.1) is steered to the target value may be achieved ahead of the given time a. From a conceptual point of view, fast-time complete controllability includes the existing notion of complete controllability (see previous studies [31][32][33][34]37 ) as a special case.…”

Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

“…For various classes of degenerate (ker L = {0}) systems (3) of the order α = 1 the controllability and the approximate controllability were researched in References [10][11][12][13][14]. In References [15][16][17] the approximate controllability issues are studied for system (3) of fractional order α under the condition of (L, p)-boundedness of the operator M, it is a more restrictive condition on the pair of operators L, M than in this work.…”