# Adaptive Cruise Control for Eco-Driving Based on Model Predictive Control Algorithm
## 1 Introduction
Besides the objective of safe car-following, driving comfortability is of great significance when promoting the performance of ACC system, according to the report on ACC by the National Highway Traffic Safety Administration (NHTSA) [17]. Hence, if the target of the controlled host vehicle in the ACC system is to reduce fuel consumption as well as securing driving safety, guaranteeing the car-following and driving comfortability, an ACC system with multi-objectives must be developed. Many scholars have been working on designing different control strategies for the ACC system, including classic proportional-integral-derivative (PID) control, linear quadratic regulator (LQR) control, sliding mode control, neural network and machine learning, fuzzy logic control, and model predictive control (MPC) [18; 19; 20; 21]. To achieve the research goal, the MPC framework is adopted to design the ACC system, because MPC has the preview capability to predict future state within a prediction horizon and the characteristic of receding horizon optimization for performance evaluation index under restricted conditions. Compared with existing microscopic and macroscopic traffic simulation models, such as Gipps' model, Newell model, cellular automata model, IDM model, etc., elaborated in [22], MPC may handle the traffic-imposed constraints more systematically. As an emerging research topic recently, introducing the MPC algorithm into the ACC system has been provided with high interest academically. Based on the design of the intelligent ACC system, the feasibility of applying a hybrid MPC framework into vehicle tracking control was studied [23]. The simulation results validated the effectiveness and industrial viability of the developed hybrid MPC algorithm. A multi-objective coordinated optimization strategy for the ACC system was designed based on the MPC method, which includes tracking capability, driving comfortability, and minimizing fuel consumption [24; 25]. However, the distinctness of the cut-in driving situation and related specifics of designing an MPC-based ACC system is not clearly explained. Furthermore, the concrete fuel economy performance improvement of the proposed MPC-based ACC system compared with the classic controller-based ACC system is not clarified. Accordingly, a new multiple objectives ACC optimization strategy in the framework of MPC is explored in this brief. The proposed method can be implemented practically in real-time optimization by quantitatively providing an acceleration command to achieve eco-driving. Besides, it covers the shortage of existing microscopic traffic models in handling multiple traffic-related constraints. Most importantly, it offers a possible solution for reducing fuel consumption, to realize eco-driving as well as improving the driving comfortability compared with the existing PID-based ACC system, which pales in considering comfort and fuel economy. The kinematic relationship between the preceding and the host vehicles is depicted in Figure 1. An ACC-equipped vehicle can follow an expected spacing when a preceding vehicle is detected, or follow a desired predefined velocity if no vehicle is running ahead. It considers the basic traffic situation--car-following process, during which, with a combination of MPC algorithm, an ACC-equipped vehicle simultaneously is capable of achieving the objective of eco-driving--improving the fuel economy. The contribution of this paper are as follows: to begin with, the \"Bicycle model\" for vehicle dynamics is established for the host vehicle. Next, the longitudinal dynamics ACC system model is developed. In the proposed ACC system model, not only the inter-distance and speed error between host and preceding vehicles are considered, but also the acceleration and acceleration variation rate, jerk, of host vehicle are included. The objective of fuel economy is achieved mainly by setting constraints to acceleration and jerk.