In this article, a class of distributed optimization problems for multiagent systems subject to time-varying coupling equality constraint is investigated. The global objective function is a sum of local convex objective functions and only local information is exchanged among the agents over a connected and undirected communication network. Based on convex optimization and Lyapunov stability theory, we show that the multiagent system in closed loop with the proposed distributed protocol is able to converge to the time-dependent unique optimum within a specified time. Remarkably, the convergence time is independent of the initial conditions and can be specified in advance making the proposed scheme suitable for application with strict requirements on the convergence. We validate through simulations the effectiveness of the theoretical results.

Highway congestion leads to significant delays and pollution. Regulating the outflow from the Service Station can help alleviate this congestion. Notably, traffic flows follow recurring patterns over days and weeks, allowing for the application of Iterative Learning Control (ILC). Building on these insights, we propose an ILC approach based on the Cell Transmission Model with service stations (CTM-s). It is shown that ILC can effectively compensate for potential inaccuracies in model parameter estimates by leveraging historical data.

The paper introduces Split-as-a-Pro, a control framework that integrates behavioral systems theory, operator splitting methods, and alternating projection algorithms. The framework reduces dynamic optimization problems - arising in both control and estimation - to efficient projection computations. Split-as-a-Pro builds on a non-parametric formulation that exploits system structure to separate dynamic constraints imposed by individual subsystems from external ones - such as interconnection constraints and input/output constraints. This enables the use of arbitrary system representations, as long as the associated projection is efficiently computable, thereby enhancing scalability and compatibility with gray-box modeling. We demonstrate the effectiveness of Split-as-a-Pro by developing a distributed algorithm for solving finite-horizon linear quadratic control problems and illustrate its use in predictive control. Our numerical case studies show that algorithms obtained using Split-as-a-Pro significantly outperform their centralized counterparts in runtime and scalability across various standard graph topologies, while seamlessly leveraging both model-based and data-driven system representations.

This paper analyzes the differences between Nash and Stackelberg equilibria of Autonomous Mobility-on-Demand (AMoD) systems in mixed traffic conditions, whereby self-driving robotaxis provide on-demand mobility, possibly pooling users together, while sharing the road with selfish private cars. In particular, we first introduce the optimal fleet routing problem in mixed traffic conditions, considering a car-road network where also private, selfish vehicles are present. Second, we model the interactions between the centrally controlled AMoD fleet and the private cars with two equilibrium formulations: the first corresponds to a Nash equilibrium, where each agent (the fleet and the private users) reacts to the other agent's action until convergence is reached. For the second approach, corresponding to a Stackelberg equilibrium, the leader (the fleet) can predict the best response of the follower (private users) and plan the strategy accordingly. The results of a case study of Sioux Falls, USA, indicate that the two equilibria are very similar in terms of the fleet's objective function, suggesting that even if the operator can predict the best response of the private users, no benefit arises.

In this article, we consider a dc microgrid composed of distributed generation units (DGUs) trading energy among each other, where the energy price depends on the total current generated by all the DGUs. We then use a Cournot aggregative game to describe the self-interested interaction among the DGUs, where each DGU aims at minimizing the deviation with respect to the given reference signals and maximizing the revenue from the sale of the generated power. Thus, we design a fully distributed continuous-time equilibrium-seeking algorithm to compute the generalized Nash equilibrium (GNE) of the game. We interconnect the designed decision-making algorithm with the dynamics of the microgrid in a passive way, and, by leveraging passivity theory, we prove the convergence of the closed-loop system trajectory to a feasible operating point that is also a Nash equilibrium of the collective aggregative game. Finally, we present extensive simulation results that validate the proposed distributed optimal control scheme, showing excellent performance.

This paper proposes a nonmonetary traffic demand management scheme, named CARMA, as a fair solution to the morning commute congestion. We consider heterogeneous commuters traveling through a single bottleneck that differ in both the desired arrival time and value of time (VOT). We consider a generalized notion of VOT by allowing it to vary dynamically on each day (e.g., according to trip purpose and urgency) rather than being a static characteristic of each individual. In our CARMA scheme, the bottleneck is divided into a fast lane that is kept in free flow and a slow lane that is subject to congestion. We introduce a nontradable mobility credit, named karma, that is used by commuters to bid for access to the fast lane. Commuters who get outbid or do not participate in the CARMA scheme instead use the slow lane. At the end of each day, karma collected from the bidders is redistributed, and the process repeats day by day. We model the collective commuter behaviors under CARMA as a dynamic population game (DPG), in which a stationary Nash equilibrium (SNE) is guaranteed to exist. Unlike existing monetary schemes, CARMA is demonstrated, both analytically and numerically, to achieve (a) an equitable traffic assignment with respect to heterogeneous income classes and (b) a strong Pareto improvement in the long-term average travel disutility with respect to no policy intervention. With extensive numerical analysis, we show that CARMA is able to retain the same congestion reduction as an optimal monetary tolling scheme under uniform karma redistribution and even outperform tolling under a well-designed redistribution scheme. We also highlight the privacy-preserving feature of CARMA, that is, its ability to tailor to the private preferences of commuters without centrally collecting the information.

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.

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.

In this paper, we propose the METANET with service station (METANET-s) model, a second-order macro-scopic traffic model that, compared to the classical METANET, incorporates the dynamics of service stations on highways. Specifically, we employ the (so-called) store-and-forward links to model the stop of vehicles and the possible queue forming in the process of merging back into the highway mainstream. We explore the capability of the METANET-s to capture well both traffic back propagation and capacity drops, which are typically caused by the presence of vehicles joining again the mainstream traffic from the service station. Therefore, capturing these effects is crucial to improving the model's predictive capabilities. Finally, we perform a comparative analysis with the Cell Transmission Model with service station (CTM-s), showcasing that the METANET-s describes the traffic evolution much better than its first-order counterpart.

In this paper, we propose a novel infrastructure-dependent ramp-metering control for the recently proposed METANET with service station (METANET-s) model, i.e., a second-order macroscopic traffic model that, compared to the classical METANET, incorporates the dynamics of service stations on highways. We study the effect of a ramp-metering control scheme on a highway stretch with a service station and show that it is capable of actively regulate internal traffic demand attempting to exit the service station via its on-ramp, on top of contributing to decrease the traffic congestion on the mainstream. In fact, the proposed control scheme effectively prevents the backlog of vehicles attempting to merge back onto the mainstream. This dynamic control mechanism is further endowed by a route guidance control strategy increasing the share of vehicles stopping at the service station during main-stream congestion periods, e.g. via incentives. The combined effect of our control schemes allows to take full advantage of the presence of service stations, reducing the overall traffic congestion. Simulation results demonstrate the effectiveness of the proposed control strategies.

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.

The morning commute bottleneck congestion problem has classically been modelled as a static game in which commuters act strategically based on their immediate Value of Time (VOT). This has restricted existing congestion mitigation techniques to rely on essentially monetary incentives to affect the static costs of the commuters. In contrast, a dynamic model enables characterizing the strategic tradeoff between immediate and future resource access rights and inspires the design of new classes of fair, non-monetary congestion mitigation schemes. In this paper, we show how the recently proposed Dynamic Population Game (DPG) framework can be leveraged to study a non-monetary economy for bottleneck congestion management based on karma, a non-tradable mobility credit. Our DPG model allows to consider an elastic demand of commuters that only travel if congestion is reduced, and we show that a Stationary Nash Equilibrium (SNE) is guaranteed to exist despite of the dynamic participation of these commuters. Through numerical case studies we illustrate how our tools can assist policy makers in taking informed decisions about complex policy outcomes. In particular, we show how the dynamic karma scheme is robust to a potentially detrimental rebound effect that would manifest in a static monetary scheme.

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.

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.

In this letter, our objective is to explore how two well-known projection dynamics can be used as dynamic controllers for stabilization of nonlinear systems. Combining the properties of projection operators, Lyapunov stability theory and LaSalle's theorem, we confirm that the projection dynamics on the feasible set and tangent cone are Krasovskii passive. To show the effectiveness of the proposed approach, we use the projection dynamics on the tangent cone for stabilizing boost converters in a DC microgrid while satisfying predefined input constraints.

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 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 this paper we propose an original distributed control framework for DC microgrids. We first formulate the (optimal) control objectives as an aggregative game suitable for the energy trading market. Then, based on duality, we analyze the equivalent distributed optimal condition for the proposed aggregative game and design a distributed control scheme to solve it. By interconnecting the DC microgrid and the designed distributed control system in a power preserving way, we steer the DC microgrid's state to the desired optimal equilibrium, satisfying a predefined set of local and coupling constraints. Finally, based on singular perturbation system theory, we analyze the convergence of the closed-loop system. The simulation results show excellent performance of the proposed control framework.