Constrained Linear Quadratic Stackelberg Games with Applications in Demand Response

TL;DR

This paper analyzes constrained linear quadratic Stackelberg games with applications in demand response, revealing properties that enable a convergent algorithm for globally optimal solutions in electric vehicle charging and load coordination.

Contribution

It establishes key properties of the game, showing optimal controls align with team solutions and depend monotonically on the coordinator’s control, enabling a new convergent algorithm.

Findings

Optimal agent controls coincide with team problem solutions.

Agent controls are monotonic with respect to the coordinator’s control.

Numerical examples demonstrate the effectiveness of the proposed algorithm.

Abstract

This paper studies a class of dynamic Stackelberg games under open-loop information structure with constrained linear agent dynamics and quadratic utility functions. We show two important properties for this class of dynamic Stackelberg games. First, we prove that under mild conditions, the optimal control of individual agents at the solution of the Stackelberg game coincides with the solution to the team problem, where all agents cooperatively achieve the coordinator's objective. Second, we show that the the agent's control at each time step is non-increasing with respect to the coordinator's control at the same step, and non-decreasing with respect the coordinator's control at other steps. These properties enable us to develop an algorithm that converges to the globally optimal solution to the dynamic Stackelberg game. The proposed algorithm is illustrated by two demand response applications: the coordination of electric vehicle charging and the coordination of thermostatically controlled loads. Numerical examples are shown to demonstrate the effectiveness of the proposed approach.