Operator methods of the search for extremal controls in linear-quadratic optimal control problems

In the class of bilinear control systems with a state-quadratic optimality criterion, new methods of the search for extremal controls are considered. The approach proposed is based on special versions of the maximum principle that have the form of operator fixed-point problems in the space of controls, which are equivalent to the well-known condition of the maximum principle in the class of linear-quadratic optimal control problems. The operator forms of optimality conditions allows one to construct new iterative algorithms for finding controls satisfy the maximum principle. The comparative efficiency of the operator methods is illustrated by numerical simulations of a well-known model optimization problem for a quantum system characterized by degenerate extremal controls.