## Applied Distributed Model Predictive Control for Energy Efficient Buildings and Ramp Metering

- Author(s): Koehler, Sarah Muraoka
- Advisor(s): Borrelli, Francesco
- et al.

## Abstract

Industrial large-scale control problems present an interesting algorithmic design challenge. A number of controllers must cooperate in real-time on a network of embedded hardware with limited computing power in order to maximize system efficiency while respecting constraints and despite communication delays. Model predictive control (MPC) can automatically synthesize a centralized controller which optimizes an objective function subject to a system model, constraints, and predictions of disturbance. Unfortunately, the computations required by model predictive controllers for large-scale systems often limit its industrial implementation only to medium-scale slow processes.

Distributed model predictive control (DMPC) enters the picture as a way to decentralize a large-scale model predictive control problem. The main idea of DMPC is to split the computations required by the MPC problem amongst distributed processors that can compute in parallel and communicate iteratively to find a solution. Some popularly proposed solutions are distributed optimization algorithms such as dual decomposition and the alternating direction method of multipliers (ADMM). However, these algorithms ignore two practical challenges: substantial communication delays present in control systems and also problem non-convexity.

This thesis presents two novel and practically effective DMPC algorithms. The first DMPC algorithm is based on a primal-dual active-set method which achieves fast convergence, making it suitable for large-scale control applications which have a large communication delay across its communication network. In particular, this algorithm is suited for MPC problems with a quadratic cost, linear dynamics, forecasted demand, and box constraints. We measure the performance of this algorithm and show that it significantly outperforms both dual decomposition and ADMM in the presence of communication delay. The second DMPC algorithm is based on an inexact interior point method which is suited for nonlinear optimization problems. The parallel computation of the algorithm exploits iterative linear algebra methods for the main linear algebra computations in the algorithm. We show that the splitting of the algorithm is flexible and can thus be applied to various distributed platform configurations.

The two proposed algorithms are applied to two main energy and transportation control problems. The first application is energy efficient building control. Buildings represent 40% of energy consumption in the United States. Thus, it is significant to improve the energy efficiency of buildings. The goal is to minimize energy consumption subject to the physics of the building (e.g. heat transfer laws), the constraints of the actuators as well as the desired operating constraints (thermal comfort of the occupants), and heat load on the system. In this thesis, we describe the control systems of forced air building systems in practice. We discuss the “Trim and Respond” algorithm which is a distributed control algorithm that is used in practice, and show that it performs similarly to a one-step explicit DMPC algorithm. Then, we apply the novel distributed primal-dual active-set method and provide extensive numerical results for the building MPC problem.

The second main application is the control of ramp metering signals to optimize traffic flow through a freeway system. This application is particularly important since urban congestion has more than doubled in the past few decades. The ramp metering problem is to maximize freeway throughput subject to freeway dynamics (derived from mass conservation), actuation constraints, freeway capacity constraints, and predicted traffic demand. In this thesis, we develop a hybrid model predictive controller for ramp metering that is guaranteed to be persistently feasible and stable. This contrasts to previous work on MPC for ramp metering where such guarantees are absent. We apply a smoothing method to the hybrid model predictive controller and apply the inexact interior point method to this nonlinear non-convex ramp metering problem.