Abstract:
The problem of correct construction of feedback control for operator equations of the second kind of general form is investigated. Correctness is understood as resolving the following three issues: 1) preservation of solvability of the controlled operator equation under variation of the control; 2) continuous dependence of the equation solution on the control; 3) existence of an optimal control for a given functional on the constructed class of controls. When solving the problem of correct construction of the class of feedback controls, the author's previous results on preserving the solvability of operator equations of the second kind, based on the concept of cone norm, are essentially used. As an example, a controlled ordinary differential equation in a Banach space is considered.
Key words:operator equation of the second kind in Banach space, ordinary differential equation in Banach space, feedback control, preservation of solvability, continuous dependence of state on control, existence of optimal control.
