Distributed non-linear model predictive control with Gaussian process dynamics for two-dimensional motion of vehicle platoon

The platoon control of connected and automated vehicles is an important topic in transportation research. The characteristics of non-linearities, external disturbances, and strong coupling are non-negligible in two-dimensional motion control. An integrated longitudinal and lateral vehicle dynamics is required. A Gaussian Process-based Distributed Stochastic Model Predictive Control (GP-DSMPC) for two-dimensional motion is proposed. It achieves global longitudinal stability and lateral error suppression. Gaussian process (GP) regression is employed to approximate the unknown model error. For the two-norm chance constraints, over-approximating the confidence ellipse to an outer polyhedron is an effective way to reduce the conservativeness and coupling effect in longitudinal and lateral motion. A neighbour-average target trajectory is designed with an upper-level optimization for adjustable target coefficients. The sum of the local cost functions is used as a Lyapunov candidate to achieve the global stability of the longitudinal motion. Some conditions on penalty weights and target coefficients among subsystems, and terminal outputs are derived. Simulation results reveal that the proposed method is effective for disturbance attenuation and performs better than distributed non-linear model predictive control without GP estimation under low-friction road conditions.