WP5: Testing.

Besides the introduction of the fundamental control design and analysis tools, PADECOT aims at the validation and implementation of the developed control/estimation algorithms. WP5 includes activities for the numerical implementation and testing of the proposed control/estimation algorithms as well as for the validation of the algorithms utilizing traffic data. The activities of WP5 can be organized in the following tasks.

Task 5.1: Development of a software tool for implementing numerically the developed control and estimation algorithms.

A1. Utilizing the software Matlab, a code is developed that implements the traffic state estimation algorithm developed in Task 2.2.A of WP2.

A2. A code is developed for solving numerically the model as well as for implementing the control algorithm developed in Task 3.2.A1 of WP3.

A3. Utilizing the software Matlab a code is developed, which implements the control algorithm developed in Task 2.1.A1 of WP2 as well as solves numerically the models considered in Task 2.1.A1 of WP2.

A4. Utilizing the software Matlab a code is developed, which implements the control and estimation algorithm introduced in Task 2.3.A of WP2 as well as solves numerically the considered PDE models.

A5. A code is developed, which implements the ACC algorithm introduced in Task 3.2.A2 of WP3 as well as solves numerically the considered models.

A6. A code is developed, which implements the control algorithm introduced in Task 3.2.A3 of WP3 as well as solves numerically the proposed model.

Task 5.2: Simulation-based testing of the proposed algorithms, employing the developed software tool, using fictitious traffic data.

A1. In this task, to illustrate the control design framework proposed in Task 2.1.A1 of WP2, the developed control algorithm is tested based on data produced by a traffic flow model, which accounts for the traffic flow dynamics at bottleneck areas, (i.e., areas that feature a significantly smaller capacity due to the presence of, for example, curvature, tunnel, narrowing, etc.) located far downstream from the actuation point (where, e.g., an on-ramp is located). Specifically, we consider a scenario where the flow at the bottleneck area, which may impose a reduction in flow capacity as high as 50%, is to be regulated at a desired set-point, via manipulating the inflow at an on-ramp located far upstream. Due to the long distance (delay) between the location of the actuated on-ramp and the bottleneck area, the performance of nominal (i.e., which do not take into account this delay), ramp metering feedback laws, such as, e.g., a proportional controller, may deteriorate. In particular, our testings show that, while the developed predictor-feedback ramp metering strategy regulates the flow at the desired equilibrium point, in contrast, when the uncompensated, nominal feedback law is applied, the density of the bottleneck area eventually exceeds the critical density (and thus, the traffic system falls into congestion).

  • N. Bekiaris-Liberis and M. Krstic, Compensation of actuator dynamics governed by quasilinear hyperbolic PDEs,,Automatica, vol. 92, pp. 29--40, 2018.
  • N. Bekiaris-Liberis and M. Krstic, Control of nonlinear systems with actuator dynamics governed by quasilinear first-order hyperbolic PDEs, European Control Conference, 2018.

    • A2. The control and estimation methodologies introduced in Task 2.3.A are illustrated here via application to a model for the dynamics of the cumulative number of vehicles, which also includes the effect of drivers’ look-ahead ability. In particular, it is shown that the developed bilateral feedback control strategies are able to robustly regulate the density, at a given highway stretch, to a desired reference profile with a specified convergence rate and for various initial profiles. Moreover, the bilateral boundary control design is compared to the unilateral case, in which, a full-state feedback law is employed only at the one boundary of the highway, while, at the other end, only a static, collocated output feedback control law is employed. Our testings show that the unilateral control design results in larger control effort, although the convergence rate of the closed-loop system would be identical to the bilateral case. Thus, although in both cases actuation is applied at both ends, the proposed bilateral control design results in a feedback law that utilizes more efficiently both the available actuators and the available measurements. It should be also noted that, from a traffic flow control perspective, such large control values may lead to practically unrealistic ordered values for flows or speeds.

  • N. Bekiaris-Liberis and R. Vazquez, Nonlinear bilateraloutput-feedback control for a class of viscous Hamilton-Jacobi PDEs, Automatica, vol. 101, pp. 223--231, 2019.
  • N. Bekiaris-Liberis and R. Vazquez, Nonlinear bilateral full-state feedback trajectory tracking for a class of viscous Hamilton-Jacobi PDEs, IEEE Conference on Decision and Control, 2018.

    • A3. The performance of the developed ACC algorithm in Task 3.2.A2 is verified in simulation and compared with a nominal, existing ACC strategy considering seven different performance indices that provide quantitative performance measures for four common physical requirements of ACC designs, namely, (1) tracking error, (2) safety, (3) fuel consumption, and (4) comfort. It is shown that the predictor-based ACC law with integral action achieves better performance in all metrics. This is attributed to the fact that the nominal ACC strategy, in contrast to the proposed predictor-based ACC law, cannot guarantee string stability in the presence of long actuator/sensor delays.

  • N. Bekiaris-Liberis, C. Roncoli, and M. Papageorgiou, Predictor-based adaptive cruise control design with integral action, IFAC Symposium on Control in Transportation Systems, 2018.

    • A4. The control algorithm developed in Task 3.2.A1 of WP3 is tested using data produced by the model developed in Task 3.2.A. of WP3, for the particular case of the so-called ``Underwood" fundamental diagram. The numerical experiments show that the fully congested equilibrium attracts the solution of the open-loop system. In contrast, the solution of the closed-loop system under the proposed feedback law converges to the desired equilibrium profile.

  • I. Karafyllis, N. Bekiaris-Liberis, and M. Papageorgiou, Feedback control of nonlinear hyperbolic PDE systems inspired by traffic flow models, IEEE Transactions on Automatic Control, vol. 64, pp. 3647--3662, 2019.
  • I. Karafyllis, N. Bekiaris-Liberis, and M. Papageorgiou, Traffic flow inspired analysis and boundary control for a class of 2x2 hyperbolic systems, European Control Conference, 2018.

    • A5. The benefits in traffic flow of employing the proposed strategy from Task 3.2.A3 are illustrated in simulation, also including the quantification of the performance improvement in terms of various indices, measuring total travel time, fuel consumption, and comfort level.

  • N. Bekiaris-Liberis and A. Delis, PDE-based feedback control of freeway traffic flow via time-gap manipulation of ACC-equipped vehicles, IEEE Transactions on Control Systems Technology, provisionally accepted, 2019.
  • N. Bekiaris-Liberis and A. Delis, Feedback control of freeway traffic flow via time-gap manipulation of ACC-equipped vehicles: A PDE-based approach, IFAC Workshop on Control of Transportation Systems, 2019.

    • A6. The method introduced in Task 2.1.A4 is evaluated in simulation experiments, performed on a first-order, multi-lane, macroscopic traffic flow model, also featuring the capacity drop phenomenon, which allows to demonstrate the effectiveness of the developed methodology and to highlight the improvement in terms of the generated congestion. In particular, it is shown that significant improvement may be achieved with the proposed control approach, in terms of TTS (Total Time Spent).

  • F. Tajdari, C. Roncoli, N. Bekiaris-Liberis, and M. Papageorgiou, Integrated ramp metering and lane-changing feedback control at motorway bottlenecks, European Control Conference, 2019.

    • Task 5.3: Testing of the control/estimation schemes with real traffic data, employing the developed software tool, if the algorithms in Task 5.2 show good performance, if not, the software library is refined.

    A. The performance of the estimation scheme developed in Task 2.2.A. of WP2 is evaluated for various penetration rates of connected vehicles utilizing real microscopic traffic data collected within the Next Generation SIMulation (NGSIM) program. The data concern a 400-meter long stretch, which includes an on-ramp, in the northbound direction of I-80 in Emeryville, California, recorded from 4:00 pm to 4:15 pm on April 13, 2005. The anonymized data set utilized is a pre-processed version of the original data set, which is available online.

    Overall, it is shown that the estimation performance is satisfactory, in terms of a suitable metric, even for low penetration rates of connected vehicles and for both congested as well as free-flow conditions. Specifically, the following investigations are performed: i) Performance evaluation for a baseline scenario, ii) performance comparison with a simple ad hoc estimation scheme, iii) sensitivity analysis to variations of the estimator's parameters, and iv) sensitivity analysis to variations of the model's parameters.

  • N. Bekiaris-Liberis, C. Roncoli, and M. Papageorgiou, Highway traffic state estimation per lane in the presence of connected vehicles, Transportation Research Part B, vol. 106, pp. 1--28, 2017.
  • I. Papamichail, N. Bekiaris-Liberis, A. I. Delis, D. Manolis, K.-S. Mountakis, I. K. Nikolos, C. Roncoli, & M. Papageorgiou, Motorway traffic flow modelling, estimation and control with vehicle automation and communication systems, Annual Reviews in Control, to appear, 2019.