# An Integrated Design of Optimization and Physical Dynamics for Energy Efficient Buildings: A Passivity Approach

## TL;DR

This paper presents a passivity-based integrated approach combining optimization and physical dynamics to improve energy efficiency in building HVAC systems, ensuring convergence to optimal temperature setpoints despite disturbances.

## Contribution

It introduces a novel passivity-based framework that unifies optimization and physical dynamics for energy-efficient building temperature control.

## Key findings

- Proved passivity of the optimization dynamics.
- Ensured convergence of room temperatures to optimal values.
- Validated the approach through simulations.

## Abstract

In this paper, we address energy management for heating, ventilation, and air-conditioning (HVAC) systems in buildings, and present a novel combined optimization and control approach. We first formulate a thermal dynamics and an associated optimization problem. An optimization dynamics is then designed based on a standard primal-dual algorithm, and its strict passivity is proved. We then design a local controller and prove that the physical dynamics with the controller is ensured to be passivity-short. Based on these passivity results, we interconnect the optimization and physical dynamics, and prove convergence of the room temperatures to the optimal ones defined for unmeasurable disturbances. Finally, we demonstrate the present algorithms through simulation.