Trajectory Controllability of Semilinear Systems with Delay

A Constructive Method of Solving Local Boundary Value Problems for Nonlinear Systems with Perturbations and Control Delays

“…In [53], it is shown that the solution of the auxiliary system (24), closed with the auxiliary stabilizing control (30) in the domain (26), satisfies the estimate:…”

“…Here the constant K η depends on the domain ( 5), (26). We substitute ῡ(τ), introduced in the statement of Problem 2, into the right-hand sides of the first n equations of (24) and close it by the auxiliary control ω(τ).…”

“…The study of BVPs over finite time intervals for such types of systems includes finding necessary and sufficient conditions of complete, local, constrained, relative, or approximate controllability for linear [14][15][16][17][18][19][20][21][22], bilinear [23], semilinear [24][25][26], and nonlinear [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] systems of differential equations; studying and estimating the attainability domain (see [20,46,47]); and developing methods to construct controls under which the trajectory connects the given points in the phase space (see [20,45]). For linear stationary systems, there exist criteria of complete controllability in terms of the matrices of the right-hand side, which take into account a time delay in control [14,15] or several delays in the system state [31].…”

“…Necessary and sufficient conditions of controllability and relative controllability in the class of linear nonstationary systems with single and multiple delays in the control and phase state in terms of the matrices of the system right-hand side and the transition matrix were presented in references [17][18][19][20][21]. Sufficient conditions of controllability, and as well relative and constrained controllability of bilinear and semilinear systems with delay in controls were derived in [20,[22][23][24][25][26]35]. In [24], the sufficient condition of controllability for semilinear system with lumped (also called discrete) and distributed delays in the state variables was given.…”

Trajectory Controllability of Fractional Integro‐Differential Systems in Hilbert Spaces

“…T‐controllability is a stronger notion of controllability. Details on T‐controllability can be found in .…”