Stability of distributed MPC in an intersection scenario

The research topic of autonomous cars and the communication among them has attained much attention in the last years and is developing quickly. Among others, this research area spans fields such as image recognition, mathematical control theory, communication networks, and sensor fusion. We consider an intersection scenario where we divide the shared road space in different cells. These cells form a grid. The cars are modelled as an autonomous multi-agent system based on the Distributed Model Predictive Control algorithm (DMPC). We prove that the overall system reaches stability using Optimal Control for each multi-agent and demonstrate that by numerical results.