Stabilization of Stackelberg Game-Based Control Systems

TL;DR

This paper investigates the stabilization of systems governed by Stackelberg game dynamics, providing necessary and sufficient conditions for stabilization and deriving optimal feedback gains using advanced control techniques.

Contribution

It introduces a comprehensive method to determine stabilization conditions and explicitly computes optimal feedback gains for Stackelberg game-based control systems.

Findings

Derived necessary and sufficient stabilization conditions.

Explicitly solved forward and backward difference equations.

Provided optimal feedback gain matrices for the leader.

Abstract

In this paper, we are concerned with the stabilizatbility of Stackelberg game-based systems. In particular, two players are involved in the system where one is the follower to minimize the related cost function and the other is the leader to stabilize the system. The main contribution is to derive the necessary and sufficient condition for the stabilization of the game-based system. The key technique is to explicitly solve the forward and backward difference equations (FBDEs) based on the maximum principle and give the optimal feedback gain matrix of the leader by using the matrix maximum principle.