String stability analysis of Cooperative Adaptive Cruise Control (CACC) with actuator saturation

Intelligent transportation systems aim at improving the efficiency and safety of transportation. In dense traffic, vehicles are aggregated to vehicle strings that travel on the same lane, whereby it is desired to maintain a small but safe distance between the vehicles. In the literature, this task is captured by the notion of string stability: fluctuations that are introduced by maneuvers of the leader vehicle should be attenuated by the follower vehicles. The literature provides various methods for achieving string stability under the assumption that the vehicles are modeled as linear systems. In this thesis, we study the case where vehicles are modeled as nonlinear systems and hence face actuation constraints as well as state constraints. Different methods are employed. First, a reachability analysis based on the level-set method determines the states that are reachable under limitations on the engine force of vehicles. It turns out in the thesis that, although the reachability analysis is the proper method to analytically address the problem of saturation, it is computationally not feasible due to the large state space of the vehicle model. As a remedy, a further analysis of the model is carried out for the special case of maneuvers. Based on the realistic assumption that the impulse response of the vehicle following model is positive, several sufficient conditions for the input signal of the leader vehicle are derived in order to preserve string stability under actuator saturation. The first set of condition is concerned with the computation of maximum/minimum input signal that generated based on optimal control solution. These maximum/minimum input signals depend on the initial velocity of the vehicle string. The second set of conditions allows computing suitable input signals of the leader vehicle analytically and is hence highly beneficial in practice. The obtained results are illustrated by extensive simulation experiments.