Stackelberg Solutions for Two-Level Singular Systems

This paper studies the optimization problem of two-level singular systems. The system considered is composed of N subsystems, and each is a linear singular system controlled by a local controller and a central controller. The objective function of each local controller assesses the performance of the corresponding subsystem, and the objective function of the central controller assesses the performance of the overall system. In this paper, the Stackelberg approach of game thory is considered for the optimization of such a system. The necessary conditions for the existence of open-loop Stackelberg solutions are derived.