arXiv subjects

Markos Papageorgiou

Publications and source records attributed to Markos Papageorgiou.

At least 19 recordsLinked to original sources

arXiv2026

Monte-Carlo Tree Search with Neural Network Guidance for Lane-Free Autonomous Driving

Lane-free traffic environments allow vehicles to better harness the lateral capacity of the road without being restricted to lane-keeping, thereby increasing the traffic flow rates. As such, we have a distinct and more challenging setting for autonomous driving. In this work, we consider a Monte-Carlo Tree Search (MCTS) planning approach for single-agent autonomous driving in lane-free traffic, where the associated Markov Decision Process we formulate is influenced from existing approaches tied to reinforcement learning frameworks. In addition, MCTS is equipped with a pre-trained neural network (NN) that guides the selection phase. This procedure incorporates the predictive capabilities of NNs for a more informed tree search process under computational constraints. In our experimental evaluation, we consider metrics that address both safety (through collision rates) and efficacy (through measured speed). Then, we examine: (a) the influence of isotropic state information for vehicles in a lane-free environment, resulting in nudging behaviour--vehicles' policy reacts due to the presence of faster tailing ones, (b) the acceleration of performance for the NN-guided variant of MCTS, and (c) the trade-off between computational resources and solution quality.

cs.AI↗

arXiv2025

Sufficient Conditions for String Stability

Zhong-Ping Jiang devoted a large part of his work to the study of the stability properties of interconnected systems. In this short paper we celebrate Zhong-Ping Jiang's 60th birthday by studying a special class of families of interconnected systems: the so-called strings. We develop trajectory-based and Lyapunov-based tools that allow the verification of string stability to homogeneous bidirectional strings. The obtained results are applied to the problem of cruise controller design for a string of vehicles.

math.OC↗

arXiv2025

Conditional Max-Sum for Asynchronous Multiagent Decision Making

In this paper we present a novel approach for multiagent decision making in dynamic environments based on Factor Graphs and the Max-Sum algorithm, considering asynchronous variable reassignments and distributed message-passing among agents. Motivated by the challenging domain of lane-free traffic where automated vehicles can communicate and coordinate as agents, we propose a more realistic communication framework for Factor Graph formulations that satisfies the above-mentioned restrictions, along with Conditional Max-Sum: an extension of Max-Sum with a revised message-passing process that is better suited for asynchronous settings. The overall application in lane-free traffic can be viewed as a hybrid system where the Factor Graph formulation undertakes the strategic decision making of vehicles, that of desired lateral alignment in a coordinated manner; and acts on top of a rule-based method we devise that provides a structured representation of the lane-free environment for the factors, while also handling the underlying control of vehicles regarding core operations and safety. Our experimental evaluation showcases the capabilities of the proposed framework in problems with intense coordination needs when compared to a domain-specific baseline without communication, and an increased adeptness of Conditional Max-Sum with respect to the standard algorithm.

cs.MA↗

arXiv2025

Nonlinear Cruise Controllers with Bidirectional Sensing for a String of Vehicles

We introduce a nonlinear cruise controller that is fully decentralized (by vehicle) and uses spacing and speed measurements from the preceding and following vehicles to decide on the appropriate control action (acceleration) for each vehicle. The proposed cruise controller is studied on both a ring-road and an open road and guarantees that there are no collisions between vehicles, while their speeds are always positive and never exceed the road speed limits. For both cases of the open road and the ring-road, we rigorously prove that the set of equilibrium points is globally asymptotically stable and provide KL estimates that guarantee uniform convergence to the said set. Moreover, we show that for the ring-road, and under certain conditions, there is a single equilibrium point which is exponentially attractive.

math.OC↗

arXiv2024

Feedback-feedforward Signal Control with Exogenous Demand Estimation in Congested Urban Road Networks

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to implement traffic-responsiveness. In this paper, we take a novel perspective and show that it is possible to use the already necessary sensing infrastructure to estimate the uncertain quantities in real time. Specifically, resorting to the store-and-forward model, we design a novel network-wide traffic-responsive strategy that estimates the occupancy and exogenous demand in each link, i.e., entering (exiting) vehicle flows at the origins (destinations) of the network or within links, in real time. Borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback-feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations for the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.

eess.SY↗

arXiv2024

From Road Congestion to Vehicle-Control Enabled Artificial Traffic Fluids

This article provides an overview of the design of nonlinear feedback Cruise Controllers (CCs) for automated vehicles on lane-free roads. The feedback design problem is particularly challenging because of the various state constraints (e.g., collision-free movement, road geometry, speed limits) as well as the nature of the control objective (globally stabilizing distributed controllers that require measurements from neighboring vehicles only). Therefore, the resulting nonlinear control system is defined on an open set (not necessarily diffeomorphic to a linear space) for which the set of desired equilibria is non-compact. The proposed design of the CCs is based on energy-like control Lyapunov functions which combine potential functions with kinetic energy terms and other appropriate penalty terms. The feedback design in the microscopic level is accompanied by the derivation of the corresponding macroscopic traffic flow models. Explicit relations are established between selectable CC features and the obtained macroscopic traffic flow characteristics. This facilitates the active design of efficient traffic flow with desired properties, i.e., the construction of artificial traffic fluids.

math.OC↗

arXiv2024

A Comparative Study of Numerical Methods for Approximating the Solutions of a Macroscopic Automated-Vehicle Traffic Flow Model

In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles.

math.NA↗

arXiv2023

Controlling Automated Vehicles on Large Lane-free Roundabouts (Extended Version)

Controlling automated vehicles on large lane-free roundabouts is challenging because of the geometrical complexity and frequent conflicts among entering, rotating, and exiting vehicles. This paper proposes a comprehensive methodology to control the vehicles within the roundabout and the connected road branches. The developed real-time vehicle movement strategy relies on offline-computed wide overlapping movement corridors, one for each Origin-Destination (OD) movement, which delineate the admissible movement zones of corresponding OD vehicles. Also, space-dependent desired orientations are determined by destination, so as to mitigate potential vehicle conflicts and reduce trip distance. A distributed (per vehicle) movement control strategy, using two nonlinear feedback controllers (NLFC), for circular and straight movements, respectively, is employed to navigate each vehicle within the respective OD corridor toward its destination, accounting for the desired orientation and avoiding collisions with other vehicles; while boundary controllers guarantee that the corridor boundaries will not be violated, and the exit will not be missed. As an overly complicated case study, we consider the famous roundabout of Place Charles de Gaulle in Paris, featuring a width of 38 m and comprising a dozen of bidirectional radial streets, hence a total of 144 ODs. The pertinence and effectiveness of the presented method is verified via microscopic simulation and evaluation of macroscopic data.

eess.SY↗

arXiv2023

Forward Completeness and Applications to Control of Automated Vehicles

Forward complete systems are guaranteed to have solutions that exist globally for all positive time. In this paper, a relaxed Lyapunov-like condition for forward completeness is presented for finite-dimensional systems defined on open sets that does not require boundedness of the Lyapunov-like function along the solutions of the system. The corresponding condition is then exploited for the design of autonomous two-dimensional movement, with focus on lane-free cruise controllers for automated vehicles described by the bicycle kinematic model. The derived feedback laws (cruise controllers) are decentralized and can account for collision avoidance, roads of variable width, on-ramps and off-ramps as well as different desired speed for each vehicle.

math.OC↗

arXiv2023

Optimal Trajectory Planning for Connected and Automated Vehicles in Lane-free Traffic with Vehicle Nudging

The paper presents a movement strategy for Connected and Automated Vehicles (CAVs) in a lane-free traffic environment with vehicle nudging by use of an optimal control approach. State-dependent constraints on control inputs are considered to ensure that the vehicle moves within the road boundaries and to prevent collisions. An objective function, comprising various weighted sub-objectives, is designed, whose minimization leads to vehicle advancement at the desired speed, when possible, while avoiding obstacles. A nonlinear optimal control problem (OCP) is formulated for the minimization of the objective function subject to constraints for each vehicle. A computationally efficient Feasible Direction Algorithm (FDA) is called, on event-triggered basis, to compute in real-time the numerical solution for finite time-horizons within a Model Predictive Control (MPC) framework. The approach is applied to each vehicle on the road, while running simulations on a lane-free ring-road, for a wide range of vehicle densities and different types of vehicles. From the simulations, which create myriads of driving episodes for each involved vehicle, it is observed that the proposed approach is highly efficient in delivering safe, comfortable and efficient vehicle trajectories, as well as high traffic flow outcomes. The approach is under investigation for further use in various lane-free road infrastructures for CAV traffic.

eess.SY↗

arXiv2023

A Particle Method for 1-D Compressible Fluid Flow

This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities that hold for the fluid model are preserved by the particle method: mass is conserved, mechanical energy is decaying, and a modified mechanical energy functional is also decaying. The proposed particle method can be used both as a numerical method and as a method of proving existence of solutions for compressible fluid models.

math.AP↗

arXiv2022

Modified Dynamic Programming Algorithms for GLOSA Systems with Stochastic Signal Switching Times

A discrete-time stochastic optimal control problem was recently proposed to address the GLOSA (Green Light Optimal Speed Advisory) problem in cases where the next signal switching time is decided in real time and is therefore uncertain in advance. The corresponding numerical solution via SDP (Stochastic Dynamic Programming) calls for substantial computation time, which excludes problem solution in the vehicle's on-board computer in real time. To overcome the computation time bottleneck, as a first attempt, a modified version of Dynamic Programming, known as Discrete Differential Dynamic Programming (DDDP) was recently employed for the numerical solution of the stochastic optimal control problem. The DDDP algorithm was demonstrated to achieve results equivalent to those obtained with the ordinary SDP algorithm, albeit with significantly reduced computation times. The present work considers a different modified version of Dynamic Programming, known as Differential Dynamic Programming (DDP). For the stochastic GLOSA problem, it is demonstrated that DDP achieves quasi-instantaneous (extremely fast) solutions in terms of CPU times, which allows for the proposed approach to be readily executable online, in an MPC (Model Predictive Control) framework, in the vehicle's on-board computer. The approach is demonstrated by use of realistic examples. It should be noted that DDP does not require discretization of variables, hence the obtained solutions may be slightly superior to the standard SDP solutions.

math.OC↗

arXiv2022

A Nonlinear Heat Equation Arising from Automated-Vehicle Traffic Flow Models

In this paper, a new nonlinear heat equation is studied that arises as a model of the collective behavior of automated vehicles. The properties of the solutions of this equation are studied by introducing the appropriate notion of a weak solution that requires certain entropy-like conditions. To obtain an approximation of the solution of the nonlinear heat equation, a new conservative first-order finite difference scheme is proposed that respects the corresponding entropy conditions, and certain links between the weak solution and the numerical scheme are provided. Finally, a traffic simulation scenario and a comparison with the Lighthill-Witham-Richards (LWR) model are provided, illustrating the benefits of the use of automated vehicles.

math.NA↗

arXiv2022

Cruise Controllers for Lane-Free Ring-Roads based on Control Lyapunov Functions

The paper introduces novel families of cruise controllers for autonomous vehicles on lane-free ring-roads. The design of the cruise controllers is based on the appropriate selection of a Control Lyapunov Function expressed on measures of the energy of the system with the kinetic energy expressed in ways similar to Newtonian or relativistic mechanics. The derived feedback laws (cruise controllers) are decentralized (per vehicle), as each vehicle determines its control input based on: (i) its own state; (ii) either only the distance from adjacent vehicles (inviscid cruise controllers) or the state of adjacent vehicles (viscous cruise controllers); and (iii) its distance from the boundaries of the ring-road. A detailed analysis of the differences and similarities between lane-free straight roads and lane-free ring-roads is also presented.

math.OC↗

arXiv2022

Constructing Artificial Traffic Fluids by Designing Cruise Controllers

In this paper, we apply a Control Lyapunov Function methodology to design two families of cruise controllers for the two-dimensional movement of autonomous vehicles on lane-free roads using the bicycle kinematic model. The control Lyapunov functions are based on measures of the energy of the system with the kinetic energy expressed in ways similar to Newtonian or relativistic mechanics. The derived feedback laws (cruise controllers) are decentralized, as each vehicle determines its control input based on its own speed and on the relative speeds and distances from adjacent vehicles and from the boundary of the road. Moreover, the corresponding macroscopic models are derived, obtaining fluid-like models that consist of a conservation equation and a momentum equation with pressure and viscous terms. Finally, we show that, by selecting appropriately the parameters of the feedback laws, we can determine the physical properties of the "traffic fluid", i.e. we get free hand to create an artificial fluid that approximates the emerging traffic flow.

math.OC↗

arXiv2021

Stability Analysis of Nonlinear Inviscid Microscopic and Macroscopic Traffic Flow Models of Bidirectional Cruise-Controlled Vehicles

The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise Control (ACC) model that uses only spacing information from the preceding and following vehicles in order to select the proper control action to avoid collisions and maintain a desired speed. KL estimates that guarantee uniform convergence of the ACC model to the set of equilibria are provided. Moreover, the corresponding macroscopic model is derived, consisting of a conservation equation and a momentum equation that contains a nonlinear relaxation term. It is shown that, if the density is sufficiently small, then the macroscopic model has a solution that approaches exponentially the equilibrium speed (in the sup norm) while the density converges exponentially to a traveling wave. Numerical simulations are also provided, illustrating the properties of the microscopic and macroscopic inviscid ACC models.

math.OC↗

arXiv2021

Optimal internal boundary control of lane-free automated vehicle traffic

A recently proposed paradigm for vehicular traffic in the era of CAV (connected and automated vehicles), called TrafficFluid, involves lane-free vehicle movement. Lane-free traffic implies that incremental road widening (narrowing) leads to corresponding incremental increase (decrease) of capacity; and this opens the way for consideration of real-time internal boundary control on highways and arterials, in order to flexibly share the total (both directions) road width and capacity among the two directions in dependence of the bi-directional demand and traffic conditions, so as to maximize the total (two directions) flow efficiency. The problem is formulated as a convex QP (Quadratic Programming) problem that may be solved efficiently, and representative case studies shed light on and demonstrate the features, capabilities and potential of the novel control action.

eess.SY↗

arXiv2021

Linear-Quadratic regulators for internal boundary control of lane-free automated vehicle traffic

Lane-free vehicle movement has been recently proposed for connected automated vehicles (CAV) due to various potential advantages. One such advantage stems from the fact that incremental changes of the road width in lane-free traffic lead to corresponding incremental changes of the traffic flow capacity. Based on this property, the concept of internal boundary control was recently introduced to flexibly share the total road width and capacity among the two traffic directions of a highway in real-time, in response to the prevailing traffic conditions, so as to maximize the cross-road (both directions) infrastructure utilization. Feedback-based Linear-Quadratic regulators with or without Integral action (LQI and LQ regulators) are appropriately developed in this paper to efficiently address the internal boundary control problem. Simulation investigations, involving a realistic highway stretch and different demand scenarios, demonstrate that the proposed simple regulators are robust and similarly efficient as an open-loop nonlinear constrained optimal control solution, while circumventing the need for accurate modelling and external demand prediction

eess.SY↗