UC Berkeley

Transportation accounts for 28% of energy consumptionin the US, with 75% of that occurring on highways. Workers spent on aggregate over three million driver-years commuting to their jobs, contributing significantly to the nation-wide congestion. Based on 2012 estimates, US commuters experienced an average of 52 hours of delay in 2011, which amounts to $121 billion of fuel costs and opportunity costs due to delay annually. Estimates project that 4.2% of fuel will be wasted in congestion in 2050 with the adoption of autonomous vehicles. Mixed autonomy, the intermediate regime between a system with no adoption of autonomy and a system where autonomy is fully employed, is proposed as a potential solution to fuel consumption reduction and flow capacity improvement.

The mixed autonomy is complicated to characterize and hard to tackle due to the degree of uncertainty in the system dynamics. The understanding of mixed autonomy is however crucial to designing automated and intelligent transportation systems, and to overhauling public policy with autonomous vehicles in the loop.

Approaches to mobile traffic control include machine learning methods, mathematical modeling and optimal control. The machine learning approaches achieve strong empirical results but in general lack optimality guarantees, theoretical studies of the convergence rate, out-of-sample performance guanrantees and interpretability. The mathematical approaches, on the other hand, are supported by highly developed mathematical theory, but suffer from a lack of attention to the theoretical characterization to the model solutions and the actuations function space. This is inevitable as mathematical methods trade model complexity for the tractability of analysis in the optimal control design.

This thesis investigates mathematical models and control algorithms for traffic automation at multiple levels.

At the vehicle level, this thesis demonstrates the lack of guarantee of well-posedness for the solution of the intelligent driver model (IDM) and closes the theoretical gap by proposing several modifications and rigorously showing the existence and uniqueness of their solutions.

At the mixed autonomy vehicle control level, a systematic way to design the basis-based feedback controller is introduced, which is defined by the solution of a finite-dimensional constrained optimization problem. This thesis discusses theoretical characterization of the actuation function space. An optimal Legendre polynomial basis controller is trained with field data and has been evaluated with simulation data and compared with a range of other mobile traffic controllers.

At the full origin-destination demand routing level, this thesis studies the repeated routing game problem on a parallel network with affine latency functions on each edge, transforming the dynamic traffic assignment problem into a control-theoretic problem. The impact of model parameters on the traffic performance is theoretically studied, andan algorithmic solution based on explicit model predictive control (MPC) is proposed.