Closed-loop Stackelberg strategies in linear-quadratic problems

Linear closed-loop Stackelberg strategies in sequential decision-making problems for linear systems and trace criteria which may be interpreted as the expected value of quadratic criteria when the initial state of the system is uniformly distributed over the unit sphere are considered. Necessary conditions for the solution are developed and an algorithm for numerical solution of two-level Stackelberg problems is presented. Generalization to multilevel Stackelberg problems is described and specific results for the three-level sequential decision-making problem are presented.