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The problem of controlling traffic using connected automated vehicles is approached by utilizing Lagrangian traffic models. A continuum model with time delay is introduced in the Lagrangian frame in order to capture the open loop dynamics of the traffic behind a vehicle of prescribed motion. The stability of the open loop system is analyzed and compared to that of a benchmark car-following model. Finally, the Lagrangian traffic models are used to propose a longitudinal controller for connected automated vehicles that allows them to respond to connected vehicles behind to stabilize the upstream traffic in a closed loop fashion.

Heterogeneous traffic with a mixture of human-driven and connected automated vehicles is discussed to study how the penetration rate and the control design of connected automated vehicles affect the traffic flow on a large scale. Continuum traffic models are constructed by incorporating time delays to take into account the reaction time of human drivers and the delays in the control loops of connected automated vehicles. It is shown that Lagrangian delayed continuum models are suitable for studying heterogeneity, introducing delay, and taking into account the on-board traffic data used by the controllers of connected automated vehicles. We show that these models possess realistic stability properties and are capable of capturing the large-scale dynamics of vehicle automation-induced and connectivity-induced heterogeneity.

Urea based selective catalytic reduction (SCR) control strategies regulate urea dosing in diesel powertrains with the goal of achieving NOx emissions targets while being robust to transient disturbances such as exhaust temperature. A model based approach is typically pursued, where an estimated quantity of NH3 stored on the SCR catalyst is controlled to a temperature dependent setpoint. The choice of setpoint, however, is typically defined heuristically which leads to suboptimal NOx and NH3 emission trade-offs. Alternatively, this paper approaches SCR control from a stochastic dynamic programming (SDP) perspective. The dosing control law is formulated by solving an infinite-horizon stochastic optimization problem using a probabilistic model of the future SCR disturbances. Simulations over standard drive cycles show the SDP based SCR control laws outperform a standard model based PI control approach, in terms of total NOx emissions for a given level of NH3 slip, by between 5% and 15%. The SDP controllers are shown to move closer to the global optimal result found via deterministic dynamic programming. Additionally, the SDP approach provides a framework to evaluate potential controller performance improvements made available by adding parameters to the control law. In this way, the incremental benefit of having an additional state in the state-feedback control law can be weighed against the increased memory cost of the extra dimension.