Funding amount: $99,999

Performance period: 8/1/2019 to 7/31/2020

In the first part, finite-time optimal feedback control for traffic networks under information constraints is studied. By utilizing the framework of multi-parametric linear programming, it is demonstrated that when cost/constraints can be modeled or approximated by piecewise-affine functions, the optimal control has a closed-form state-feedback realization. The optimal feedback control law, however, has a centralized structure and requires instantaneous access to the state of the entire network that may lead to prohibitive communication requirements in large-scale networks. We subsequently examine the design of a decentralized (sub)-optimal feedback controller with a one-hop information structure, wherein the optimum outflow rate from each segment of the network depends only on the state of that segment and the state of the segments immediately downstream. The decentralization is based on the relaxation of constraints that depend on state variables that are unavailable according to the information structure. The resulting decentralized control scheme has a simple closed-form representation and is scalable to arbitrary large networks; moreover, we demonstrate that, with respect to certain meaningful performance indexes, the performance loss due to decentralization is zero; namely, the centralized optimal controller has a decentralized real- ization with a one-hop information structure and is obtained at no computational/communication cost.

In the second part, we consider a routing game among non-atomic agents where link latency functions are conditional on an uncertain state of the network. All the agents have the same prior belief about the state, but only a fixed fraction receive private route recommendations or a common message, which are generated by a known randomization, referred to as private or public signal respectively. The remaining non-receiving agents choose route according to Bayes Nash flow with respect to the prior. We develop a computational approach to solve the optimal information design problem, i.e., to minimize expected social latency cost over all public or obedient private signals. For a fixed flow induced by non-receiving agents, design of an optimal private signal is shown to be a generalized problem of moments for polynomial link latency functions, and to admit an atomic solution with a provable upper bound on the number of atoms. This implies that, for polynomial link latency functions, information design over private and public signals, when the non-receiving agents choose route according to Bayes Nash flow, can be equivalently cast as a polynomial optimization problem. This in turn can be arbitrarily lower bounded by a known hierarchy of semidefinite relaxations. The first level of this hierarchy is shown to be exact for the basic two link case with affine latency functions, and it relies on tightening the bound on the number of atoms in the support of optimal signal. We also identify a class of private signals over which the optimal social cost is non-increasing with increasing fraction of receiving agents. This does not require the link latency functions to be polynomial, and is in contrast to existing results where the cost of receiving agents under a fixed signal may increase with their increasing fraction.