Missing data are an unavoidable complication frequently encountered in many causal discovery tasks. When a missing process depends on the missing values themselves (known as self-masking missingness), the recovery of the joint distribution becomes unattainable, and detecting the presence of such self-masking missingness remains a perplexing challenge. Consequently, due to the inability to reconstruct the original distribution and to discern the underlying missingness mechanism, simply applying existing causal discovery methods would lead to wrong conclusions. In this work, we found that the recent advances additive noise model has the potential for learning causal structure under the existence of the self-masking missingness. With this observation, we aim to investigate the identification problem of learning causal structure from missing data under an additive noise model with different missingness mechanisms, where the `no self-masking missingness' assumption can be eliminated appropriately. Specifically, we first elegantly extend the scope of identifiability of causal skeleton to the case with weak self-masking missingness (i.e., no other variable could be the cause of self-masking indicators except itself). We further provide the sufficient and necessary identification conditions of the causal direction under additive noise model and show that the causal structure can be identified up to an IN-equivalent pattern. We finally propose a practical algorithm based on the above theoretical results on learning the causal skeleton and causal direction. Extensive experiments on synthetic and real data demonstrate the efficiency and effectiveness of the proposed algorithms.

In this paper, a hierarchical control strategy of vehicle platoons is presented, in which the longitudinal and lateral coupling property of vehicles is taken into account. A three-degree-of-freedom dynamic model of vehicles is approximated to a “global” linear model by the Koopman operator theory. A synchronous distributed predictive control scheme of vehicle platoons is proposed as an upper-level controller, where both the linear vehicle model and a linear parametric-varying lane-keeping model are adopted to predict the dynamic of vehicles, and keep vehicles in the designated lane. Thus, it can avoid the solution of nonlinear optimization problems and reduce the computational burden accordingly. A lower-level controller is designed, where the desired longitudinal control force determined by the upper-level controller is transformed into the desired throttle angle and brake pressure through an inverse longitudinal dynamics model of vehicles. The joint simulation results by PreScan, CarSim and MATLAB/Simulink show that when the leader vehicle accelerates or decelerates, the following vehicles in the platoon can keep the same velocity as the leader vehicle, and maintain the desired safety distance between the front and rear vehicles. In addition, joint simulation in the curved road scenario show that the performance of lane keeping can be guaranteed for vehicle platoons with the proposed control strategy.