Data-driven Variable Speed Limit Design for Highways via Distributionally Robust Optimization

This paper introduces an optimization problem (P) and a solution strategy to design variable-speed-limit controls for a highway that is subject to traffic congestion and uncertain vehicle arrival and departure. By employing a finite data-set of samples of the uncertain variables, we aim to find a data-driven solution that has a guaranteed out-of-sample performance. In principle, such formulation leads to an intractable problem (P) as the distribution of the uncertainty variable is unknown. By adopting a distributionally robust optimization approach, this work presents a tractable reformulation of (P) and an efficient algorithm that provides a suboptimal solution that retains the out-of-sample performance guarantee. A simulation illustrates the effectiveness of this method.Comment: 10 pages, 2 figures, submitted to ECC 201

Formal Synthesis of Control Strategies for Positive Monotone Systems

We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances. Such systems are widely used to model the dynamics of transportation and biological networks. The specifications are described using signal temporal logic (STL), which can express a broad range of temporal properties. We formulate the problem as a mixed-integer linear program (MILP) and show that under the assumptions made in this paper, which are not restrictive for traffic applications, the existence of open-loop control policies is sufficient and almost necessary to ensure the satisfaction of STL formulas. We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions. We also develop a robust model predictive framework to plan controls optimally while ensuring the satisfaction of the specification. Illustrative examples and a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16 pages, double colum

Robust dynamic traffic assignment for single destination networks under demand and capacity uncertainty

In this article, we discuss the system-optimum dynamic traffic assignment (SO-DTA) problem in the presence of time-dependent uncertainties on both traffic demands and road link capacities. Building on an earlier formulation of the problem based on the cell transmission model, the SO-DTA problem is robustly solved, in a probabilistic sense, within the framework of random convex programs (RCPs). Different from traditional robust optimization schemes, which find a solution that is valid for all the values of the uncertain parameters, in the RCP approach we use a fixed number of random realizations of the uncertainty, and we are able to guarantee a priori a desired upper bound on the probability that a new, unseen realization of the uncertainty would make the computed solution unfeasible. The particular problem structure and the introduction of an effective domination criterion for discarding a large number of generated samples enables the computation of a robust solution for medium- to large-scale networks, with low desired violation probability, with a moderate computational effort. The proposed approach is quite general and applicable to any problem that can be formulated through a linear programing model, where the stochastic parameters appear in the constraint constant terms only. Simulation results corroborate the effectiveness of our approach