Distributed control for cooperative hyperbolic systems involving Schrödinger operator

Abstract

In this paper, some hyperbolic systems involving Schrödinger operator defined on R n have been established. The existence and uniqueness for the state of these systems have been proved, Then the necessary and sufficient conditions of optimality for such systems have been obtained by a set of equations and inequalities.

Boundary Control Problems for 2 × 2 Cooperative Hyperbolic Systems with Infinite Order Operators

“…Majority of the research in this field has focused on discussing the optimal control problem by using several operator types (such as elliptic, parabolic, or hyperbolic operators) [2]- [11], and by varying the nature of control (such as distributed control [6] [11] [12] [13] and boundary control [3] [5] [8]).…”

Distributed Control for Time-Fractional Differential System Involving Schrödinger Operator

“…This discussion was extended to timefractional systems in the sense of Riemann-Liouville in [16][17][18] and in the sense of Caputo in [19]. Recently, the distributed optimal control problem for systems involving Schrödinger operator has been studied for elliptic systems in [20], parabolic systems in [21], and hyperbolic systems in [22].…”

An Optimization Problem of Boundary Type for Cooperative Hyperbolic Systems Involving Schrödinger Operator

“…In [3], we discussed distributed control problem for 2 × 2 cooperative hyperbolic systems involving Schrödinger operator.…”