Coefficient control in a linear second order ordinary differential equation (Q2266434)

The paper is devoted to the study of an optimal control problem for a linear system described by a second order ordinary differential equation with fixed boundary values. The control appears as the coefficient of the first derivative in the state equation. The original control problem is interpreted as a control problem in Banach spaces with \(H^ 1_ 0\) as the state space and \(L^ 2\) or \(L^{\infty}\) as the control space. Existence and uniqueness of optimal control are proved. There are also given necessary and sufficient conditions for optimality.