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

Abstract

AbstractThe 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.