Coalitional Distributed Model Predictive Control Strategy for Vehicle Platooning Applications.

This work aims at developing and testing a novel Coalitional Distributed Model Predictive Control (C-DMPC) strategy suitable for vehicle platooning applications. The stability of the algorithm is ensured via the terminal constraint region formulation, with robust positively invariant sets. To ensure a greater flexibility, in the initialization part of the method, an invariant table set is created containing several invariant sets computed for different constraints values. The algorithm was tested in simulation, using both homogeneous and heterogeneous initial conditions for a platoon with four homogeneous vehicles, using a predecessor-following, uni-directionally communication topology. The simulation results show that the coalitions between vehicles are formed in the beginning of the experiment, when the local feasibility of each vehicle is lost. These findings successfully prove the usefulness of the proposed coalitional DMPC method in a vehicle platooning application, and illustrate the robustness of the algorithm, when tested in different initial conditions.

Ellipsoidal approximations of the minimal robust positively invariant set.

An optimization algorithm is presented in this paper for the minimal robust positively invariant (mRPI) set approximations via sums-of-squares (SOS) optimization. The mRPI set is an effective tool for robust analysis of uncertain systems under bounded disturbances. The approximation of the mRPI set is always characterized by a polyhedron computed after finite time iterations. In this paper, an mRPI set is characterized by an ellipsoidal set while bounded parametric uncertainties act on states. The proposed algorithm optimizes the shape matrix of the ellipsoidal set approximation by minimizing the volume of the ellipsoidal set. The algorithm is designed for discrete-time and continuous-time nonlinear systems respectively. The algorithm has the ability to further minimize the mRPI set by optimizing the state-feedback control law. Examples are employed to validate the effectiveness of the proposed algorithms.