Urban traffic congestion remains a pressing chal-lenge in our rapidly expanding cities, despite the abundance of available data and the efforts of policymakers. By leveraging behavioral system theory and data-driven control, this paper exploits the Data-enabled Predictive Control (DeePC) algorithm in the context of urban traffic control performed via dynamic traffic lights. To validate our approach, we consider a high-fidelity case study using the state-of-the-art simulation software package Simulation of Urban MObility (SUMO). Preliminary results indicate that DeePC outperforms existing approaches across various key metrics, including travel time and CO₂ emissions, demonstrating its potential for effective traffic management.

Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence guarantees or computational efficiency, due to the absence of smoothness and convexity. In this work, we bridge this gap by designing a first-order hypergradient-based algorithm for Stackelberg games and mathematically establishing its convergence using tools from nonsmooth analysis. To evaluate the hypergradient, namely, the gradient of the upper-level objectve, we develop an online scheme that simultaneously computes the lower level equilibrium and its Jacobian. Crucially, this scheme exploits and preserves the original hierarchical and distributed structure of the problem, which renders it scalable and privacy-preserving. We numerically verify the computational efficiency and scalability of our algorithm on a large-scale hierarchical demand-response model.

This paper analyzes how the presence of service stations on highways affects traffic congestion. We focus on the problem of optimally designing a service station to achieve beneficial effects in terms of total traffic congestion and peak traffic reduction. We propose a genetic algorithm based on the recently proposed Cell Transmission Model with service station (CTM-s), that efficiently describes the dynamics of a service station. Then, we leverage the algorithm to train a neural network capable of solving the same problem, avoiding to implement the CTM-s. Finally, we validate the performance of our algorithms by using real data from Dutch highways.

We study the problem of routing plug-in electric and conventional fuel vehicles on a city scale using incentives. In our model, commuters selfishly aim to minimize a local cost that combines travel time and the financial expenses of using city facilities, i.e., parking and service stations. The traffic authority can influence the commuters' routing choice via personalized discounts on parking tickets and on the energy price at service stations. We formalize the problem of optimally designing these monetary incentives to induce traffic decongestion as a large-scale bilevel game, where constraints arise at both levels due to the finite capacities of city facilities and incentives budget. Then, we develop an efficient scalable solution scheme with convergence guarantees based on BIG Hype, a recently-proposed hypergradient-based algorithm for bilevel games. Finally, we validate our approach via numerical simulations over the Anaheim's traffic network, showcasing its advantages in terms of traffic decongestion and scalability.

Mitigating the energy use in buildings, together with satisfaction of comfort requirements are the main objectives of efficient building control systems. Augmenting building energy systems with batteries can improve the energy use of a building, while posing the challenge of considering battery degradation during control operation. We demonstrate the performance of a data-enabled predictive control (DeePC) approach applied to a single multizone building and an energy hub comprising an electric heat pump and a battery. In a comparison with a standard rule-based controller, results demonstrate that the performance of DeePC is superior in terms of satisfaction of comfort constraints without increasing grid power consumption. Moreover, DeePC achieved two-fold decrease in battery degradation over one year, as compared to a rule-based controller.

A popular remedy for the morning commute bottleneck congestion is to split the highway capacity into a managed lane that is kept in free-flow and a general purpose lane that is subject to congestion. A classical theoretical result is that the more capacity is allocated to the managed lane the less the resulting congestion. However, existing approaches to restrict access to the managed lane are primarily monetary, e.g., tolls, which severely limits the public willingness to accept them due to equity concerns. Following up on recent work which introduces karma as a completely non-monetary credit used to control access to a so-called Karma Priority (KP) lane, we first review the strategic problem of the commuters which is modeled as a dynamic population game. We then numerically investigate the effect of varying the KP lane capacity. The karma scheme is equitable with respect to different income classes irrespective of the capacity split, meanwhile achieving near-optimal traffic reduction. Thus, managing a larger fraction of the bottleneck could be more socially feasible under a karma scheme than a monetary scheme.

This paper studies the capacity drops phenomena on a macroscopic, first-order model for freeway traffic. In particular, we focus on the effect that a Service Station (ST) has on the mainstream traffic evolution. We propose a modified formulation of the Cell Transmission Model with service station (CTM-s) that considers this important phenomenon, and use a micro-simulation based on Aimsun Next to identify the model parameters via a structured identification procedure. Finally, we validate the ability of the CTM-s with capacity drops to better describe the traffic evolution with respect to the classical formulation.

Ensuring safety in optimization is challenging if the underlying functional forms of either the constraints or the objective function are unknown. The challenge can be addressed by using Gaussian processes to provide confidence intervals used to find solutions that can be considered safe. To iteratively find a trade-off between finding the solution and ensuring safety, the SafeOpt algorithm builds on algorithms using only the upper bounds (UCB-type algorithms) by performing an exhaustive search on the entire search space to find a safe iterate. That approach can quickly become computationally expensive. We reformulate the exhaustive search as a series of optimization problems to find the next recommended points. We show that the proposed reformulation allows using a wide range of available optimization solvers, such as derivative-free methods. We show that by exploiting the properties of the solver, we enable the introduction of new stopping criteria into safe learning methods and increase flexibility in trading off solver accuracy and computational time. The results from a non-convex optimization problem and an application for controller tuning confirm the flexibility and the performance of the proposed reformulation.

We propose an incentive-based traffic demand management policy to alleviate traffic congestion on a road stretch that creates a bottleneck for the commuters. The incentive targets electric vehicles owners by proposing a discount on the energy price they use to charge their vehicles if they are flexible in their departure time. We show that, with a sufficient monetary budget, it is possible to completely eliminate the traffic congestion and we compute the optimal discount. We analyse also the case of limited budget, when the congestion cannot be completely eliminated. We compute analytically the policy minimising the congestion and estimate the level of inefficiency for different budgets. We corroborate our theoretical findings with numerical simulations that allow us to highlight the power of the proposed method in providing practical advice for the design of policies.

In modern buildings renewable energy generators and storage devices are spreading, and consequently the role of the users in the power grid is shifting from passive to active. We design a demand response scheme that exploits the prosumers' flexibility to provide ancillary services to the main grid. We propose a hierarchical scheme to coordinate the interactions between the distribution system operator and a community of smart prosumers. The framework inherits characteristics from price-based and incentive-based schemes and it retains the advantages of both. We cast the problem as a Stackelberg game with the prosumers as followers and the distribution system operator as leader. We solve the resulting bilevel optimization program via a KKT reformulation, proving the existence and the convergence to a local Stackelberg equilibrium.

In this paper, we propose a novel model that describes how the traffic evolution on a highway stretch is affected by the presence of a service station. The presented model enhances the classical Cell Transmission Model (CTM) dynamics by adding the dynamics associated with the service stations, where the vehicles may stop before merging back in the main stream. We name it Cell Transmission Model with service station (CTM-s). We discuss its flexibility in describing different complex scenarios where multiple stations are characterized by different drivers' average stopping times corresponding to different services. The model has been developed to help designing control strategies aimed to decrease traffic congestion. Thus, we discuss how classical control schemes can interact with the proposed CTM-s. Finally, we demonstrate the proposed model through numerical simulations and assess the effects of service stations on traffic evolution, which appear to be beneficial especially for relatively short congested periods.

We consider network aggregative games where each player minimizes a cost function that depends on its own strategy and on a convex combination of the strategies of its neighbors. As a first contribution, we propose a class of distributed algorithms that can be used to steer the strategies of the rational agents to a Nash equilibrium configuration, with guaranteed convergence under different sufficient conditions depending on the cost functions and on the network. A distinctive feature of the proposed class of algorithms is that agents use optimal responses instead of gradient type of strategy updates. As a second contribution, we show that the algorithm suggested for network aggregative games can also be used to recover a Nash equilibrium of average aggregative games (i.e., games where each agent is affected by the average of the strategies of the whole population) in a distributed fashion, that is, without requiring a central coordinator. We apply our theoretical results to multi-dimensional, convex-constrained opinion dynamics and to demand-response schemes for energy management.

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme using a smoothed fast gradient method that is equipped with explicit bounds on the approximation error. We further demonstrate how the presented scheme can be used for approximating the chemical master equation through the zero-information moment closure method, and for an approximate dynamic programming approach in the context of constrained Markov decision processes with uncountable state and action spaces.

This article presents an approximation scheme for the infinite-dimensional linear programming formulation of discrete-time Markov control processes via a finite-dimensional convex program, when the dynamics are unknown and learned from data. We derive a probabilistic explicit error bound between the data-driven finite convex program and the original infinite linear program. We further discuss the sample complexity of the error bound which translates to the number of samples required for an a priori approximation accuracy. Our analysis sheds light on the impact of the choice of basis functions for approximating the true value function. Finally, the relevance of the method is illustrated on a truncated LQG problem.

We present an approximation method to a class of parametric integration problems that naturally appear when solving the dual of the maximum entropy estimation problem. Our method builds up on a recent generalization of Gauss quadratures via an infinite-dimensional linear program, and utilizes a convex clustering algorithm to compute an approximate solution which requires reduced computational effort. It shows to be particularly appealing when looking at problems with unusual domains and in a multi-dimensional setting. As a proof of concept we apply our method to an example problem on the unit disc.

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted.

We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space. We then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process, we also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally, we demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.