Model Predictive Control (MPC) plays a pivotal role in the functioning of Adaptive Cruise Control (ACC). In an ACC system employing MPC, the controller continuously assesses the current vehicle dynamics and the behavior of surrounding vehicles. Here's how it works:

1. Prediction Horizon: MPC looks ahead into the future, typically over a short time frame, known as the prediction horizon. During this horizon, it anticipates how the vehicle and the vehicles in its vicinity will move.

2. Vehicle Model: A dynamic model of the host vehicle is used to predict how its speed and position will change over time, considering factors like acceleration and braking capabilities.

3. Target Speed and Distance: ACC users typically set a desired speed and following distance. MPC calculates the optimal speed profile for the host vehicle to reach and maintain the desired following distance while also achieving the target speed.

4. Optimization: Within the prediction horizon, the MPC controller uses optimization techniques to determine the optimal control inputs (throttle, brake, or both) that will minimize a cost function. This cost function usually incorporates factors like safety, comfort, and energy efficiency.

5. Actuation: Based on the calculated optimal control inputs, the MPC system sends commands to the vehicle's throttle and brake systems to execute the required actions. This enables the vehicle to maintain a safe distance from the leading vehicle while adhering to the desired speed.

6. Continuous Updates: MPC continuously repeats this process, updating its predictions and control inputs as new data becomes available. This allows the ACC system to adapt to changing traffic conditions and maintain a safe and comfortable driving experience.