Proportional–integral observer-based consensus control for heterogeneous vehicular platoon systems with mixed disturbances and unavailable acceleration information

Abstract

A proportional–integral observer-based consensus control scheme is proposed for heterogeneous vehicular platoon systems (VPSs) subject to model uncertainties, mixed disturbances (external disturbances and measurement noise), and unavailable acceleration information. For each vehicle, this work considers the measurement noise in the velocity channel, then proposes a distributed proportional–integral observer that can accurately estimate the states information of velocity and acceleration. To improve the control performance of the VPSs, a predictive spacing strategy is adopted, which can transform the VPSs stability problem into a leader–follower consensus problem by introducing a new variable. Through utilizing a state linear transformation technique, the consensus problem can be further converted into a partial state stability problem. To facilitate the analysis of partial state stability under the disturbances, the partial state stability problem can be transformed into a multi-objective optimization problem by using the $H_{\infty }$ control method. Based on Lyapunov stability theory and projection lemma, the sufficient conditions are derived to achieve asymptotic stability of the VPSs and satisfy optimization performance indices simultaneously. In addition, the control scheme can also guarantee the ${\mathcal{L}}_2$ string stability for the VPSs. Finally, the effectiveness of the proposed control method is confirmed through numerical simulations and comparisons.