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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., Comment: 53 pages

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., Comment: 34 pages, 19 figures

To cope with varying and highly uncertain traffic patterns, a novel network-wide traffic signal control strategy based on the store-and-forward model of a traffic network is proposed. On one hand, making use of a single loop detector in each road link, we develop an estimation solution for both the link occupancy and the net exogenous demand in every road link of a network. On the other hand, 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 of 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.

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., Comment: 16 pages, 21 figures, 1 table, and 47 equations

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., Comment: 30 pages, 9 figures

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., Comment: 59 pages

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.

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., Comment: 36 pages, 9 figures

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., Comment: 35 pages, 9 figures. arXiv admin note: text overlap with arXiv:2203.02788

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.

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., Comment: 20 pages, submitted to Systems & Control Letters

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., Comment: 36 pages, 11 figures, submitted to IMA Mathematical Control and Information for possible publication

A path-planning algorithm for connected and non-connected automated road vehicles on multilane motorways is derived from the opportune formulation of an optimal control problem. In this framework, the objective function to be minimized contains appropriate respective terms to reflect: the goals of vehicle advancement; passenger comfort; and avoidance of collisions with other vehicles, of road departures and of negative speeds. Connectivity implies that connected vehicles are able to exchange with each other (V2V) or the infrastructure (V2I), real-time information about their last generated path. For the numerical solution of the optimal control problem, an efficient feasible direction algorithm is used. To ensure high-quality local minima, a simplified Dynamic Programming algorithm is also conceived to deliver the initial guess trajectory for the feasible direction algorithm. Thanks to low computation times, the approach is readily executable within a model predictive control (MPC) framework. The proposed MPC-based approach is embedded within the Aimsun microsimulation platform, which enables the evaluation of a plethora of realistic vehicle driving and advancement scenarios. Results obtained on a multilane motorway stretch indicate higher efficiency of the optimally controlled vehicles in driving closer to their desired speed, compared to ordinary Aimsun vehicles. Increased penetration rates of automated vehicles are found to increase the efficiency of the overall traffic flow, benefiting manual vehicles as well. Moreover, connected controlled vehicles appear to be more efficient compared to the corresponding non-connected controlled vehicles, due to the improved real-time information and short-term prediction.

In this paper, we design decentralized control strategies for the two-dimensional movement of autonomous vehicles on lane-free roads. The bicycle kinematic model is used to model the dynamics of the vehicles, and each vehicle determines its control input based only on its own speed and on the distance from other (adjacent) vehicles and the boundary of the road. Potential functions and Barbalat's lemma are employed to prove the following properties, which are ensured by the proposed controller: (i) the vehicles do not collide with each other or with the boundary of the road; (ii) the speeds of all vehicles are always positive, i.e., no vehicle moves backwards at any time; (iii) the speed of all vehicles remain below a given speed limit; (iv) all vehicle speeds converge to a given longitudinal speed set-point; and (v) the accelerations, lateral speeds, and orientations of all vehicles tend to zero. The efficiency of the proposed 2-D cruise controllers is illustrated by means of numerical examples., Comment: 29 pages, 8 figures

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, Comment: arXiv admin note: substantial text overlap with arXiv:2008.10255

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.

The paper deals with the design of nonlinear adaptive cruise controllers for vehicular platoons operating on an open road or a ring-road. The constructed feedback controllers are nonlinear functions of the distance between successive vehicles and their speeds. It is shown that the proposed novel controllers guarantee safety (collision avoidance) and bounded vehicle speeds by explicitly characterizing the set of allowable inputs. Moreover, we guarantee global asymptotic stability of the platoon to a desired configuration as well as string stability. Certain macroscopic properties are also investigated. The efficiency of the nonlinear adaptive cruise controllers is demonstrated by means of a numerical example., Comment: 34 pages, 14 figures, submitted to IEEE Transactions on Automatic Control for possible publication

The paper provides conditions that guarantee existence and uniqueness of classical solutions for a non-local conservation law on a ring-road with possible nudging (or "look behind") terms. The obtained conditions are novel, as they are not covered by existing results in the literature. The paper also provides results which indicate that nudging can increase the flow in a ring-road and, if properly designed, can have a strong stabilizing effect on traffic flow. More specifically, the paper gives results which guarantee local exponential stability of the uniform equilibrium in the L2 state norm even for cases where the uniform equilibrium profile in a ring-road without nudging is not asymptotically stable and the model admits density waves. The efficiency of the use of nudging terms is demonstrated by means of a numerical example.even for cases where the uniform equilibrium profile in a ring-road without nudging is not asymptotically stable and the model admits density waves. The efficiency of the use of nudging terms is demonstrated by means of a numerical example., Comment: 32 pages, 5 figures

A novel paradigm for vehicular traffic in the era of connected and automated vehicles (CAVs) is proposed, which includes two combined principles: lane-free traffic and vehicle nudging, whereby vehicles are "pushing" (from a distance, using communication or sensors) other vehicles in front of them. This traffic paradigm features several advantages, including: smoother and safer driving; increase of roadway capacity; and no need for the anisotropy restriction. The proposed concept provides, for the first time since the automobile invention, the possibility to actively design (rather than describe) the traffic flow characteristics in an optimal way, i.e. to engineer the future CAV traffic flow as an efficient artificial fluid. Options, features, application domains and required research topics are discussed. Preliminary simulation results illustrate some basic features of the concept., Comment: 17 pages, 7 figures

The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are studied: the problem with free speed limits at the inlet and the problem with no speed limits at the inlet. Explicit formulas are provided for respective feedback laws that guarantee stabilization of the desired equilibrium profile. For the first problem, global asymptotic stabilization is achieved; while for the second problem, regional exponential stabilization is achieved. Moreover, the solutions for the corresponding closed-loop systems are guaranteed to be classical solutions, i.e., there are no shocks. The obtained results are illustrated by means of a numerical example., Comment: 18 pages, 7 figures, submitted to Automatica for possible publication

The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the velocity. The proposed model has features that are important from a traffic-theoretic point of view: is completely anisotropic and information travels forward exactly at the same speed as traffic. It is shown that, for all physically meaningful initial conditions, the model admits a globally defined, unique, classical solution that remains positive and bounded for all times. Moreover, it is shown that global stabilization can be achieved for arbitrary equilibria by means of an explicit boundary feedback law. The stabilizing feedback law depends only on the inlet velocity and consequently, the measurement requirements for the implementation of the proposed boundary feedback law are minimal. The efficiency of the proposed boundary feedback law is demonstrated by means of a numerical example., Comment: 33 pages, 5 figures, submitted to Mathematical Control and Related Fields for possible publication

This work is devoted to the construction of explicit feedback control laws for the robust, global, exponential stabilization of general, uncertain, discrete-time, acyclic traffic networks. We consider discrete-time, uncertain network models which satisfy very weak assumptions. The construction of the controllers and the rigorous proof of the robust, global, exponential stability for the closed-loop system are based on recently proposed vector-Lyapunov function criteria, as well as the fact that the network is acyclic. It is shown, in this study, that the latter requirement is necessary for the existence of a robust, global, exponential stabilizer of the desired uncongested equilibrium point of the network. An illustrative example demonstrates the applicability of the obtained results to realistic traffic flow networks., Comment: 28 pages, 9 figures, submitted for possible publication to the International Journal of Control

This paper presents two case studies where a macroscopic model-based approach for traffic state estimation, which we have recently developed, is employed and tested. The estimation methodology is developed for a "mixed" traffic scenario, where traffic is composed of both ordinary and connected vehicles. Only average speed measurements, which may be obtained from connected vehicles reports, and a minimum number (sufficient to guarantee observability) of spot sensor-based total flow measurements are utilised. In the first case study, we use NGSIM microscopic data in order to test the capability of estimating the traffic state on the basis of aggregated information retrieved from moving vehicles and considering various penetration rates of connected vehicles. In the second case study, a longer highway stretch with internal congestion is utilised, in order to test the capability of the proposed estimation scheme to produce appropriate estimates for varying traffic conditions on long stretches. In both cases the performances are satisfactory, and the obtained results demonstrate the effectiveness of the methodology, both in qualitative and quantitative terms., Comment: Submitted to the the 95th Annual Meeting of the Transportation Research Board (TRB) and for publication to Transportation Research Record (TRR) on July 28, 2015

This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme consists of a nominal feedback law, which achieves robust, global, exponential stability properties when the vector of the parameters is known, in conjunction with a nonlinear, dead-beat observer. The obtained results are applicable to highly nonlinear, uncertain discrete-time systems with unknown constant parameters. The applicability of the obtained results to real control problems is demonstrated by the rigorous application of the proposed adaptive control scheme to uncertain freeway models., Comment: 18 pages, 1 figure

A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles. The development relies on the following realistic assumptions: (i) The density and flow of connected vehicles are known at the (local or central) traffic monitoring and control unit on the basis of their regularly reported positions, and (ii) the average speed of conventional vehicles is roughly equal to the average speed of connected vehicles. Thus, complete traffic state estimation (for arbitrarily selected segments in the network) may be achieved by merely estimating the percentage of connected vehicles with respect to the total number of vehicles. A model is derived, which describes the dynamics of the percentage of connected vehicles, utilizing only well-known conservation law equations that describe the dynamics of the density of connected vehicles and of the total density of all vehicles. Based on this model, which is a linear time-varying system, an estimation algorithm for the percentage of connected vehicles is developed employing a Kalman filter. The estimation methodology is validated through simulations using a second-order macroscopic traffic flow model as ground truth for the traffic state. The approach calls for a minimum of spot sensor-based total flow measurements {according to a variety of possible location configurations., Comment: Submitted to the IEEE Conference on Decision and Control on March 24th 2014

This work is devoted to the construction of feedback laws which guarantee the robust global exponential stability of the uncongested equilibrium point for general discrete-time freeway models. The feedback construction is based on a control Lyapunov function approach and exploits certain important properties of freeway models. The developed feedback laws are tested in simulation and a detailed comparison is made with existing feedback laws in the literature. The robustness properties of the corresponding closed-loop system with respect to measurement errors are also studied., Comment: Generalization of previous versions. 32 pages, 9 figures, submitted to the International Journal of Robust and Nonlinear Control for possible publication