Distributed model predictive control approach for cooperative car-following with guaranteed local and string stability

• Published in: Transportation research. Part B: methodological Vol. 128; pp. 69 - 86
• Main Authors: Zhou, Yang, Wang, Meng, Ahn, Soyoung
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2019; Elsevier Science Ltd
• Subjects: Attenuation; Automatic control; Automobiles; Car following; Computer simulation; Connected automated vehicles; Control stability; Cooperative control; Distributed model predictive control; Disturbances; Fuel consumption; l2-norm string stability; Local stability; Longitudinal control; l∞-norm string stability; Mathematical analysis; Matrix methods; Multiple criterion; Predictive control; Robustness (mathematics); Stability criteria; Strings; Distributed model predictive control; Connected automated vehicles; Longitudinal control; l2-norm string stability; l∞-norm string stability; Local stability
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2019.07.001

•A new serial distributed model predictive control (MPC) strategy for connected automated vehicles (CAVs).•A CAV car-following MPC strategy with guaranteed local stability.•A CAV car-following MPC strategy with guaranteed l∞-norm string stability.•A CAV car-following MPC strategy with guaranteed l2-norm string stability when constraints are inactive. In this paper, a serial distributed model predictive control (MPC) approach for connected automated vehicles (CAVS) is developed with local stability (disturbance dissipation over time) and multi-criteria string stability (disturbance attenuation through a vehicular string). Two string stability criteria are considered within the proposed MPC: (i) the l∞-norm string stability criterion for attenuation of the maximum disturbance magnitude and (ii) l2-norm string stability criterion for attenuation of disturbance energy. The l∞-norm string stability is achieved by formulating constraints within the MPC based on the future states of the leading CAV, and the l2-norm string stability is achieved by proper weight matrix tuning over a robust positive invariant set. For rigor, mathematical proofs for asymptotical local stability and multi-criteria string stability are provided. Simulation experiments verify that the distributed serial MPC proposed in this study is effective for disturbance attenuation and performs better than traditional MPC without stability guarantee.