Energy Management via Pricing in LQ Dynamic Games

S. Coogan, L. J. Ratliff, D. Calderone, C. Tomlin, and S. S. Sastry
2013 American Controls Conference

Abstract

We investigate the use of pricing mechanisms as a means to achieve a desired feedback control strategy among selfish agents in the context of resource allocation in buildings. We pose the problem of heating, ventilating and air conditioning (HVAC) resource allocation in buildings as a linear-quadratic game with many dynamically coupled Nash followers and an uncoupled leader. The leader influences the game by choosing the quadratic dependence on control actions for each follower's cost function. We show that determining whether the leader can establish the desired feedback control as a Nash equilibrium among the followers is a convex feasibility problem. In addition, we discuss methods for ensuring that the total cost incurred due to the leader's pricing is as close as possible to a specified nominal cost, as well as methods for minimizing the explicit dependence of a player's cost on other players' control inputs. We show that the using the pricing scheme to coordinate the followers in the building proves to be more efficient than standard decentralized control methods