# Surrogate Optimal Control for Strategic Multi-Agent Systems

## TL;DR

This paper develops a mechanism for controlling multi-agent systems where agents are strategic and private, ensuring truthful reporting and system efficiency through a Nash equilibrium-based approach, demonstrated in HVAC control.

## Contribution

It introduces a novel interaction mechanism that guarantees truthful reporting and efficiency in multi-agent control without requiring agents to know system dynamics or others' objectives.

## Key findings

- Mechanism ensures truthful reporting by agents.
- Achieves system efficiency at Nash equilibrium.
- Applicable to distributed MPC in building HVAC systems.

## Abstract

This paper studies how to design a platform to optimally control constrained multi-agent systems with a single coordinator and multiple strategic agents. In our setting, the agents cannot apply control inputs and only the coordinator applies control inputs; however, the coordinator does not know the objective functions of the agents, and so must choose control actions based on information provided by the agents. One major challenge is that if the platform is not correctly designed then the agents may provide false information to the coordinator in order to achieve improved outcomes for themselves at the expense of the overall system efficiency. Here, we design an interaction mechanism between the agents and the coordinator such that the mechanism: ensures agents truthfully report their information, has low communication requirements, and leads to a control action that achieves efficiency by achieving a Nash equilibrium. In particular, we design a mechanism in which each agent does not need to posses full knowledge of the system dynamics nor the objective functions of other agents. We illustrate our proposed mechanism in a model predictive control (MPC) application involving heating, ventilation, air-conditioning (HVAC) control by a building manager of an apartment building. Our results showcase how such a mechanism can be potentially used in the context of distributed MPC.