Abstract <p>The problem of correctly constructing feedback control for a general operator equation of the second kind is investigated. Correctness is understood in the sense that (1) the controlled operator equation remains solvable under control variations; (2) solution to the equation depends continuously on the control; and (3) there exists an optimal control with respect to a given functional in the constructed class of controls. The solution of the problem of correctly constructing a class of feedback controls relies heavily of the author’s previous results concerning the preservation of solvability of second-kind operator equations, which are based on the concept of a cone norm. As an example, a controlled ordinary differential equation in a Banach space is considered.</p>