Distributed Adaptive Backstepping Control for Vehicular Platoons with Mismatched Disturbances Using Vector String Stability

Zihao Song, Shirantha Welikala, Panos J. Antsaklis, Hai Lin

In this paper, we consider the problem of platooning control with mismatched disturbances using the distributed adaptive backstepping method. The main challenges to be addressed are: (1) the derivative explosion arising from the involved adaptive control laws, and (2) the lack of verification conditions for string stability. To accommodate this, we first propose a novel notion of string stability called "Vector String Stability (VSS)" based on an associated "Vector String Lyapunov Function". Then, a small-gain type verification condition is presented through the input-to-state-stability of a comparison system. Moreover, the internal stability and string stability are formally proved under our proposed backstepping controller and the VSS notion. The proposed VSS notion reduces the complexity of deriving a backstepping based distributed controller in a vector sense and makes the controller more compact. Finally, a simulation example is provided to illustrate the effectiveness of the proposed control algorithm.

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