The design of cruise controllers for autonomous vehicles is essentially a feedback control problem. This feedback control problem has certain features that are not met frequently in other control systems, such as:
the fact that the state-space is not a linear space; there are severe state constraints (speed limits, no-collision constraints, road boundaries, etc.),
the fact that the set where we want to stabilize the system is not a singleton (and it may not even be a compact set),
the connection with n-body problems in Hamiltonian systems (you actually have an n-body system of self-driven particles),
the fact that there are severe input constraints (vehicles cannot apply accelerations of arbitrary magnitude-there are technical limitations),
special stability notions (like string stability) are very important in certain cases (e.g., 1-D lane-based movement).
I have worked with Markos Papageorgiou and Dionysios Theodosis on the design of cruise controllers in various cases (e.g., open roads, ring roads, lane-based movement, lane-free movement, etc.). The important issue here is to notice that as the number of vehicles tends to infinity we obtain a "fluid" with the vehicles as "molecules": the so-called "traffic fluid", which is used in classical traffic models with PDEs. The design of cruise controllers allows us to affect the "physical properties" of the traffic fluid.
Here is a list of papers that contain results for cruise controllers and the resulting traffic fluids.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Constructing Artificial Traffic Fluids by Designing Cruise Controllers”, Systems & Control Letters, 167, 2022, 105317.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Stability Analysis of Nonlinear Inviscid Microscopic and Macroscopic Traffic Flow Models of Bidirectional Cruise-Controlled Vehicles”, IMA Journal of Mathematical Control and Information, 39(2), 2022, pp. 609–642.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Lyapunov-Based Two-Dimensional Cruise Control of Autonomous Vehicles on Lane-Free Roads”, Automatica, 145, 2022, 110517.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Nonlinear Adaptive Cruise Control of Vehicular Platoons”, International Journal of Control, 96(1), 2023, pp. 147-169.
D. Theodosis, I. Karafyllis and M. Papageorgiou, “Cruise Controllers for Lane-Free Ring-Roads Based on Control Lyapunov Functions”, Journal of the Franklin Institute, 360, 2023, pp. 6131-6161.
D. Theodosis, I. Karafyllis, G. Titakis, I. Papamichail and M. Papageorgiou, “A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models”, Journal of Computational and Applied Mathematics, 437, 2024, 115443.
G. Titakis, I. Karafyllis, D. Theodosis, I. Papamichail and M. Papageorgiou, “A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model”, Computers and Mathematics with Applications, 176, 2024, pp. 469–490.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Forward Completeness in Open Sets and Applications to Control of Automated Vehicles”, IEEE Transactions on Automatic Control, 70(4), 2025, pp. 2406-2421.
I. Karafyllis, D. Theodosis and M. Papageorgiou, “Nonlinear Cruise Controllers with Bidirectional Sensing for a String of Vehicles”, European Journal of Control, 85, 2025, 101341.
I. Karafyllis, D. Theodosis, M. Papageorgiou and M. Krstic, "From Road Congestion to Vehicle-Control Enabled Artificial Traffic Fluids", Annual Reviews in Control, 59, 2025, 100989.