The closed-loop implementation of the open-loop stackelberg solution in the linear quadratic problems

The present paper deals with the Stackelberg solution of the basic LQ bicriteria dynamic optimization problem. It is shown that the two-point boundary value problem involved in the LQ Stackelberg optimization problem has a Hamiltonian structure. Considering this remarkable structural property, an efficient numerical method for solve it, is presented. The closed-loop implementation of the open-loop Stackelberg strategies is obtained by solving a standard differential Riccati equation associated to an extended ordinary LQ optimization problem (by increasing the system state with an additional multiplier). The proper closed-loop implementation depending only on the system state is possible if a certain differential matrix equation has a continuous solution.