Stochastic Stable Control of Vehicular Platoon Time-Delay System Subject to Random Switching Topologies and Disturbances

Abstract

This paper presents a stochastic stable control protocol for heterogeneous vehicle platoon subject to communication topologies change, external disturbance, and information delay. First, a random vehicle platoon system composed entirely of several pure electric vehicles is built. The random variation of data transmission link among the platoon in a natural traffic environment is considered and molded by the Markov chain combined with the directed graph method. The influence of delays and discrete data in wireless communication, road slope, and air resistance on the vehicle platoon is also considered by introducing the external interferences and equivalent information delays. Additionally, to ensure the vehicle platoon’s inner-vehicle stability, the variable-gain distributed controller is proposed based on the Markovian jumping system stability theory and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ H_\infty$</tex-math></inline-formula> control. Finally, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathcal {L}_{2}$</tex-math></inline-formula> stochastic string stability is defined to attenuate perturbations as they propagate through the platoon. Simulation studies about a vehicle platoon under four communication topologies random switching with two different control methods are provided to verify the theoretical result. It is shown that, compared to traditional platoon robust control, it is possible to achieve the vehicle platoon’s stability even if in the continuous mutation of unstable topologies by using the proposed control approach.