Dynamic Incentive Selection for Hierarchical Convex Model Predictive Control

TL;DR

This paper introduces a method for designing incentives in hierarchical model predictive control systems modeled as Stackelberg games, enabling simpler optimization and iterative incentive computation, demonstrated on a dynamic price control example.

Contribution

It presents a novel incentive design framework for hierarchical MPC systems as Stackelberg games, with an efficient reformulation and scalable algorithm for multiple lower-level controllers.

Findings

Reformulation simplifies hierarchical MPC incentive problems.

Iterative incentive computation does not require knowledge of the lower-level cost.

Algorithm scales well to large populations of electric vehicles.

Abstract

In this paper, we discuss incentive design for hierarchical model predictive control (MPC) systems viewed as Stackelberg games. We consider a hierarchical MPC formulation where, given a lower-level convex MPC (LoMPC), the upper-level system solves a bilevel MPC (BiMPC) subject to the constraint that the lower-level system inputs are optimal for the LoMPC. Such hierarchical problems are challenging due to optimality constraints in the BiMPC formulation. We analyze an incentive Stackelberg game variation of the problem, where the BiMPC provides additional incentives for the LoMPC cost function, which grants the BiMPC influence over the LoMPC inputs. We show that for such problems, the BiMPC can be reformulated as a simpler optimization problem, and the optimal incentives can be iteratively computed without knowing the LoMPC cost function. We extend our formulation for the case of multiple LoMPCs and propose an algorithm that finds bounded suboptimal solutions for the BiMPC. We demonstrate our algorithm for a dynamic price control example, where an independent system operator (ISO) sets the electricity prices for electric vehicle (EV) charging with the goal of minimizing a social cost and satisfying electricity generation constraints. Notably, our method scales well to large EV population sizes.