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Routing electric commercial vehicles requires taking into account their limited driving range, which is affected by several uncertain factors such as traffic conditions. This paper presents the time-dependent Electric Vehicle Routing Problem with Chance-Constraints (EVRP-CC) and partial recharging. The routing method is divided into two stages, where the first finds the best paths and the second optimizes the routes. A probabilistic Bayesian machine learning approach is proposed for predicting the expected energy consumption and variance for the road links, paths and routes. Hence it is possible to consider the uncertainty in energy demand by planning charging within a confidence interval. The energy estimation is validated with data from electric buses driving a public transport route in Gothenburg-Sweden as well as with realistic simulations for 24 hours traffic in the city of Luxembourg connected to a high fidelity vehicle model. Routing solutions are compared with a deterministic formulation of the problem similar to the ones found in the literature. The results indicate high accuracy for the energy prediction as well as energy savings and more reliability for the routes.

The paper proposes an eco-cruise control strategy for urban public transport buses. The aim of the velocity control is ensuring timetable adherence, while considering upstream queue lengths at traffic lights in a probabilistic way. The contribution of the paper is twofold. First, the shockwave profile model (SPM) is extended to capture the stochastic nature of traffic queue lengths. The model is adequate to describe frequent traffic state interruptions at signalized intersections. Based on the distribution function of stochastic traffic volume demand, the randomness in queue length, wave fronts, and vehicle numbers are derived. Then, an outlook is provided on its applicability as a full-scale urban traffic network model. Second, a shrinking horizon model predictive controller (MPC) is proposed for ensuring timetable reliability. The intention is to calculate optimal velocity commands based on the current position and desired arrival time of the bus while considering upcoming delays due to red signals and eventual queues. The above proposed stochastic traffic model is incorporated in a rolling horizon optimization via chance-constraining. In the optimization, probabilistic guarantees are formulated to minimize delay due to standstill in queues at signalized intersections. Optimization results are analyzed from two particular aspects, (i) feasibility and (ii) closed-loop performance point of views. The novel stochastic profile model is tested in a high fidelity traffic simulator context. Comparative simulation results show the viability and importance of stochastic bounds in urban trajectory design. The proposed algorithm yields smoother bus trajectories at an urban corridor, suggesting energy savings compared to benchmark control strategies.

The paper presents modeling, control and analysis of an urban public transport network. First, a centralized system description is given, built up from the dynamics of individual buses and bus stops. Aiming to minimize three conflicting goals (equidistant headways, timetable adherence, and minimizing passenger waiting times), a reference tracking model predictive controller formulated based on the piecewise-affine system model. The closed-loop system is analyzed with three methods. Numerical simulations on a simple experimental network showed that the temporal evolution of headways and passenger numbers could maintain their periodicity with the help of velocity control. With the help of randomized simulation scenarios, sensitivity of the system is analyzed. Finally, infeasible regions for the bus network control was sought using by formulating an explicit model predictive controller.

We consider the problem of altruistic control of connected automated vehicles (CAVs) on mixed-autonomy multi-lane highways to mitigate moving traffic jams resulting from car-following dynamics of human-driven vehicles (HDVs). In most of the existing studies on CAVs in multi-lane settings, vehicle controller design philosophy is based on a selfish driving strategy that exclusively addresses the ego vehicle objectives. To improve overall traffic smoothness, we propose an altruistic control strategy for CAVs that aims to maximize the driving comfort and traffic efficiency of both the ego vehicle and surrounding HDVs. We formulate the problem of altruistic control under a model predictive control (MPC) framework to optimize acceleration and lane change sequences of CAVs. In order to efficiently solve the resulting non-convex mixed-integer nonlinear programming (MINLP) problem, we decompose it into three non-convex subproblems, each of which can be transformed into a convex quadratic program via penalty based reformulation of the optimal velocity with relative velocity (OVRV) car-following model. Simulation results demonstrate significant improvements in traffic flow via altruistic CAV actions over selfish strategies on both single- and multi-lane roads.

In this paper, we propose a hierarchical control strategy for a line of electric buses with the double objective of minimizing energy consumption and providing regular service to the passengers. The state-space model for the buses is formulated in space rather than in time, which alleviates the need for integer decision variables to capture their behavior at bus stops. This enables us to first assemble a fully-centralized multi-objective line problem in the continuous nonlinear optimization framework. It is then reassembled into a hierarchical structure with two levels of control in order to improve on scalability and reliability. This new supervisory structure consists of a centralized line level controller which handles the time headway regularity of the buses, and of decentralized bus level controllers which simultaneously manage the energy consumption of each individual bus. Our method demonstrates good battery energy savings and regularity performances when compared to a classical holding strategy.

When planning routes for fleets of electric commercial vehicles, it is necessary to precisely predict the energy required to drive and plan for charging whenever needed, in order to manage their driving range limitations. Although there are several energy estimation models available in the literature, so far integration with Vehicle Routing Problems has been limited and without demonstrated accuracy. This paper introduces the Two-stage Electric Vehicle Routing Problem (2sEVRP) that incorporates improved energy consumption estimation by considering detailed topography and speed profiles. First, a method to calculate energy cost coefficients for the road network is outlined. Since the driving cycle is unknown, the model generates an approximation based on a linear function of mass, as the latter is only determined while routing. These coefficients embed information about topography, speed, powertrain efficiency and the effect of acceleration and braking at traffic lights and intersections. Secondly, an integrated two-stage approach is described, which finds the best paths between pairs of destinations and then finds the best routes including battery and time-window constraints. Energy consumption is used as objective function including payload and auxiliary systems. The road cost coefficients are aggregated to generate the path cost coefficients that are used in the routing problem. In this way it is possible to get a proper approximation of the complete driving cycle for the routes and accurate energy consumption estimation. Lastly, numerical experiments are shown based on the road network from Gothenburg-Sweden. Energy estimation is compared with real consumption data from an all-electric bus from a public transport route and with high-fidelity vehicle simulations. Routing experiments focus on trucks for urban distribution of goods. The results indicate that time and energy estimations are significantly more precise than existing methods. Consequently the planned routes are expected to be feasible in terms of energy demand and that charging stops are properly included when necessary.

In this work, we propose an algorithm performing short-term predictions of the flux of vehicles on a stretch of road, using past measurements of the flux. This algorithm is based on a physics-aware recurrent neural network. A discretization of a macroscopic traffic flow model (using the so-called Traffic Reaction Model) is embedded in the architecture of the network and yields flux predictions based on estimated and predicted space-time dependent traffic parameters. These parameters are themselves obtained using a succession of LSTM ans simple recurrent neural networks. Besides, on top of the predictions, the algorithm yields a smoothing of its inputs which is also physically-constrained by the macroscopic traffic flow model. The algorithm is tested on raw flux measurements obtained from loop detectors., 17 pages, 11 figures, 2 tables

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated.

Human driven vehicles (HDVs) with selfish objectives cause low traffic efficiency in an un-signalized intersection. On the other hand, autonomous vehicles can overcome this inefficiency through perfect coordination. In this paper, we propose an intermediate solution, where we use vehicular communication and a small number of autonomous vehicles to improve the transportation system efficiency in such intersections. In our solution, two connected autonomous vehicles (CAVs) lead multiple HDVs in a double-lane intersection in order to avoid congestion in front of the intersection. The CAVs are able to communicate and coordinate their behavior, which is controlled by a deep reinforcement learning (DRL) agent. We design an altruistic reward function which enables CAVs to adjust their velocities flexibly in order to avoid queuing in front of the intersection. The proximal policy optimization (PPO) algorithm is applied to train the policy and the generalized advantage estimation (GAE) is used to estimate state values. Training results show that two CAVs are able to achieve significantly better traffic efficiency compared to similar scenarios without and with one altruistic autonomous vehicle.

This paper presents a velocity control/advise algorithm relying on vehicle-to-vehicle communication, to ensure the headway homogeneity of buses on a joint corridor, i.e. when multiple lines merge and travel on the same route. The proposed control method first schedules merging buses prior to entering a common line. Second, based on the position and velocity of the bus ahead of the controlled one, a shrinking horizon model predictive controller (MPC) calculates a proper velocity profile for the merging bus. The model is able to predict short time- space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to reach the merging point with equidistant headways, taking all buses from different lines into account. The controller is tested in a high fidelity traffic simulator with realistic scenarios.

In this paper a mode dependent variable speed limit (VSL) control strategy is developed for motorway networks. The suggested rolling horizon and coordinated algorithm uses switching mode Cell Transmission Model (CTM) and purports to maximize network throughput. In this line, first, a VSL signal scheduled piecewise affine switching mode CTM is derived based on the polyhedral description of Godunov fluxes. Second, a two-stage, coordinated, rolling horizon VSL sequence generation procedure is proposed. The set of possible VSL signs is selected by applying input constraints in order to eliminate spatial and temporal VSL oscillations. Then, the set of modes is further reduced according to the stable and adjacent reachable modes of the switching mode CTM. Over the remaining set of input signals, network capacity is maximized with the help of solving a mixed integer optimization problem under the form of reference density tracking objective. The method is implemented in simulation environment to demonstrate its computational efficiency and viability to attenuate shockwaves.

In this paper, a model-based perimeter control policy for large-scale urban vehicular networks is proposed. Assuming a homogeneously loaded vehicle network and the existence of a well-posed Network Fundamental Diagram (NFD), we describe a protected network throughout its aggregated dynamics including nonlinear exit flow characteristics. Within this framework of constrained optimal boundary flow gating, two main performance metrics are considered: (a) first, connected to the NFD, the concept of average network travel time and delay as a performance metric is defined; (b) second, at boundaries, we take into account additional external network queue dynamics governed by uncontrolled inflow demands. External queue capacities in terms of finite-link lengths are used as the second performance metric. Hence, the corresponding performance requirement is an upper bound of external queues. While external queues represent vehicles waiting to enter the protected network, internal queue describes the protected network’s aggregated behavior. By controlling the number of vehicles joining the internal queue from the external ones, herewith a network traffic flow maximization solution subject to the internal and external dynamics and their performance constraints is developed. The originally non-convex optimization problem is transformed to a numerically efficiently convex one by relaxing the performance constraints into time-dependent state boundaries. The control solution can be interpreted as a mechanism which transforms the unknown arrival process governing the number of vehicles entering the network to a regulated process, such that prescribed performance requirements on travel time in the network and upper bound on the external queue are satisfied. Comparative numerical simulation studies on a microscopic traffic simulator are carried out to show the benefits of the proposed method.

The paper proposes a control design method in order to gate input flow to a protected urban vehicular network such that travel time Quality of Service (QoS) constraints are preserved within the network. In view of the network to be protected (also called the region), two types of queues are distinguished: external and internal. While external queues represent vehicles waiting to enter the protected network, an internal queue can be used to describe the network's aggregated behaviour. By controlling the number of vehicles entering the internal queue, the travel time within the network subject to the vehicular conservation law and the Network Fundamental Diagram (NFD) can be subsequently controlled. The admission controller can thus be interpreted as a mechanism which transforms the unknown arrival process governing the number of vehicles entering the network to a regulated process, such that prescribed QoS requirements on travel time in the network and upper bound on the external queue are satisfied. The admission control problem is formulated as a constrained convex optimization problem and a Model Predictive Control (MPC) problem. A case study demonstrates the benefits of the admission control mechanisms proposed.

A set-theoretical approach is presented for a multi-objective control design of the local ramp metering problem. Two control objectives are specified: first, the optimization of traffic performance, by the minimization of total time spent.Second, the emission factor of CO2 is minimized. The optimal state for traffic emission however lies in the unstable domain of the system. To resolve this inconsistency, the control problem is formalized in a set-theoretical context. For this purpose, the nonlinear METANET model is rewritten in a shifted coordinate frame in a parameter-varying, polytopic representation. Bounds on state-, input- and disturbance variables are expressed by convex polytopes. These sets are then used for the design of an interpolated H∞ controller that is capable of improving traffic conditions according to the prescribed multi-objective criteria.

This paper proposes a novel method to compute an upper bound on the induced L2- gain for a linear parameter varying (LPV) system with rational parameter dependence. The proposed method relies on a standard dissipation inequality condition. The storage function is a quadratic function of the state and a rational function of the parameters. The specific parameter dependence is restricted to involve (fixed) rational functions and an affine term with free decision variables. Finsler's lemma and affine annihilators are used to formulate sufficient linear matrix inequality (LMI) conditions for the dissipativity relation. The dimension and conservatism of the resulting LMI problem are reduced by the joint application of minimal generators and maximal annihilators. An LPV model of a pendulum-cart system is used to demonstrate the proposed method and compare it to existing techniques in the literature.

The paper suggests a novel alternative to generalized traffic incident descriptions within the macroscopic traffic model framework. The contribution of the paper is twofold. First, by extending already existing second order macroscopic conservation laws to characterize off-nominal traffic conditions, we define two main incident parameters such as direct and indirect ones. Physical interpretations of this incident parametrization is provided. These incident indicators are relative in view of the nominal traffic flow model parameters and carries physically meaningful macroscopic content. Second, the paper proposes to use a constrained and nonlinear, joint traffic state- and incident parameter reconstruction method and validates the suggested modeling idea via real traffic measurements fitting. Evaluation of the numerical results demonstrate the effectiveness of the methodology.

Developed in the paper, is a systematic design framework for parameter-dependent fault diagnosis, with noise corrupted measurements of the scheduling parameter. A stochastic fault estimation filter design method is addressed for a class of discrete-time Linear Parameter Varying (LPV) systems. First, the average valued filter stability is ensured by means of a quadratic dissipativity condition. Apart stability, within the same mean square framework a robust performance objective is defined. Conditions to satisfy robust stability requirements are translated to an optimization problem subject to Bilinear Matrix Inequality (BMI) constraints. A comparative numerical example is given to illustrate and validate the proposed methodology.

For an urban bus network to operate efficiently, conflicting objectives have to be considered: providing sufficient service quality while keeping energy consumption low. The paper focuses on energy efficient operation of bus lines, where bus stops are densely placed, and buses operate frequently with possibility of bunching. The proposed decentralized, bus fleet control solution aims to combine four conflicting goals incorporated into a multi-objective, nonlinear cost function. The multi-objective optimization is solved under a receding horizon model predictive framework. The four conflicting objectives are as follows. One is ensuring periodicity of headways by watching leading and following vehicles i.e. eliminating bus bunching. Equal headways are only a necessary condition for keeping a static, predefined, periodic timetable. The second objective is timetable tracking. A conflicting objective to the former is minimizing passenger waiting time. When more than the expected passengers are waiting for the bus it is desirable to haste the vehicle in order to prevent bunching. The final objective is energy efficiency. To this end, an energy consumption model is formulated considering battery electric vehicles with recuperation during braking. Different weighting strategies are compared and evaluated through realistic scenarios, realized in a validated microscopic traffic simulation environment. Simulation results suggest 3–8% network level energy saving compared to bus holding control while maintaining punctuality and periodicity of buses.

A novel model based local ramp metering method is presented in the paper by means of incident scheduled freeway traffic control solution. First, second order macroscopic freeway model is used with appropriate incident parametrization to describe eventual and unattended traffic variation caused by off-nominal traffic conditions (e.g. accidents). These traffic anomalies are captured by adequate model parameters, i.e. incident parameters that can be on-line estimated. The paper is motivated by incident scheduled ramp-meter solution to encounter real-time incident parameter information. The main idea is to use local freeway control solution triggered by available incident parameter values. The proposed approach is local in the sense of considering only non-coordinated ramp meter solution, first. Furthermore, we apply locally optimal (linearized) control solution to satisfy throughput maximization objective. The formal controller synthesis involves parameters to correct, compensate the effect of incidents. The proposed method is evaluated and compared to other existing approach by using simulation environment.

Similarity state transformations between equivalent State-Space (SS) representations of discrete-time Linear Parameter-Varying (LPV) systems are investigated. Based on previous results, it is known that to characterize all equivalent LPV-SS representations, the statetransformation matrix must depend dynamically on the scheduling variable. However, preserving static dependence of a LPV-SS representation, i.e. characterizing all equivalent SS representation with static dependence, has primary importance both in control and identication. Therefore, rst, the state transformation problem is investigated from an algebraic (behavior) point of view, then conditions are developed to guarantee preservation of the static dependence in similarity state transformations. Additional geometric interpretation of the obtained results, together with computational approach to synthesize state-transformations are also developed. An illustrative example is provided to demonstrate the validity of the obtained results.

The paper investigates the problem of uncertainty modeling and constrained robust control of urban traffic. Linear polytopic approach is used by state-space representations to describe the uncertain network system. In order to handle model mismatches, robust and infinite horizon model predictive control (MPC) method is proposed. The control strategy is an efficient method to reduce travel time and improve homogeneous traffic flow under changing model conditions. Centralized numerical solution has been carried out as a solution of Linear Matrix Inequalities (LMI) by using semidefinite programming (SDP). Closed-loop control results were tested in simulation environment taking alternative model uncertainty levels into account.

In the paper a novel non-linear modeling formalism is suggested for freeway traffic flow. A second-order macroscopic model has been transformed into a Linear Parameter Varying (LPV) model. The paper proposes two LPV descriptions for traffic modeling: the first one covers completely the non-linear macroscopic dynamics, while the second one is an approximate description. Real test field topology and measurement data are used for validating the proposed modeling methodology. Simulation examples are given to compare real detector measurements, non-linear and the parameter-dependent responses.

Using induced L2-norm minimization, a robust controller was developed for insulin delivery in Type I diabetic patients. The high-complexity nonlinear diabetic patient Sorensen-model was considered and Linear Parameter Varying methodology was used to develop open loop model and robust controller. Considering the normoglycemic set point (81.1 mg/dL), a polytopic set was created over the physiologic boundaries of the glucose-insulin interaction of the Sorensen-model. In this way, Linear Parameter Varying model formalism was defined. The robust control was developed considering input and output multiplicative uncertainties with two additional uncertainties from those used in the literature: sensor noise and worst case design for meal disturbance (60 g carbohydrate).

The paper shows an interpolation-based control solution asapossible technique to formulate the constrained H∞ control problem for discrete-time linear parameter varying (LPV) systems. The control policy is constructed by interpolating amongapriori designed, unconstrained, constant, state feedback controllers. Invariant set theory is used to introduce the measure of the domain of applicability. It is shown that the `trade-off' between the performance and the size of the domain of applicability can be significantly reduced by controller interpolation. Hence, the interpolation-based controller becomes applicable overamuch larger region than any other single state feedback. The proposed method gives stabilizing solution not only under hard constraints, but also allows the online modification of the induced L² norm from the generalized disturbance input to the predefined performance output. Moreover, the suggested method can be applied in real-time environment.

In this paper, we present the application of a novel Linear Parameter-Varying (LPV) system identification approach on a DC motor setup with an unbalanced disc. This setup is used as a real-life application of the closed-loop LPV subspace identification technique described in van Wingerden and Verhaegen [2009], this work demonstrates the identification procedure and the effectiveness of the algorithm in identifying nonlinear models using real data.

This paper presents a new Fault detection and Identification approach Connected to Subspace Identification (FICSI) for a special class of nonlinear system casted to Linear but Parametrically Varying (LPV) form. The model based algorithm utilizes the specific nonlinear nature of the LPV system along the past horizon to construct the output predictor. Similar with its LTI counterpart in a companion paper ([Dong and Verhaegen (2008)]), the FICSI-LPV avoids projecting the residual vector onto the parity space of the extended observability matrix, and hence produces residuals more sensitive to faults than the parity space approach (PSA) for LPV systems does. Asymptotically unbiased condition and algorithm are also proposed for fault estimation. The difference of FICSI from the existing fault detection and estimation approaches based on PSA or moving horizon estimation (MHE) can also be attributed to the fact that FICSI does not require an LPV state space model, but a sequence of Markov parameters mapping the I/O measurements and the scheduling parameters to the residual, which can be estimated in closed-loop.

The paper investigates the reconfigurable features of the Subspace Predictive Control scheme for Linear Parameter Varying Systems (SPC LPV). This model independent predictive approach combines the predictor based subspace identification and (constrained) predictive control for affine LPV systems. By means of using recursive update of the identified closed loop Markov parameters, the SPC LPV can be used for Fault Tolerant Control. The proposed algorithm is implemented and applied in a rotation speed tracking for a nonlinear DC motor.

The paper presents a method for the constrained Moving Horizon Estimation of origin-destination (OD) matrices for traffic networks. In traffic systems split ratios are important parameters for OD estimation and for control problems as well. The paper treats the general constrained Moving Horizon Estimation problem for traffic systems modelled in terms of linear time varying system and solves the split rate estimation process. The estimation is subjected to equality and inequality constraints. A numerical example is solved to demonstrate the Moving Horizon Estimation of split variables.

The paper examines the conditions for isolating the unknown input detection from the effects of the measurements noise in the important family of positional control problems. The study is motivated by the need of improving the homing performance of interceptor missiles against randomly maneuvering targets. The required isolation is possible if, in addition to noisy relative position measurements, noise-free measurement of the line of slight rate or the relative lateral velocity is available. Although with noisy measurement of line of slight rate the isolation of the input is not possible, the detection filter designed for the noise-free case succeeds to provide a satisfactory estimate of target acceleration, which is needed for an improved homing performance.

In this article the disturbance attenuation problem arising in Failure Detection and Identification (FDI) using detection filters is discussed. The filter is designed using the general Fundamental Problem of Residual Generator(FPRG) algorithm and it is assumed that decoupling the failure modes from the deterministic disturbance is not possible. The disturbance attenuation is achieved by applying H ∞ filtering concepts. Numerical example is shown to demonstrate the effect, of the worst case disturbance rejection on residuals that are sensitive to failure directions.