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In this dissertation we develop systematic procedures for the control and analysis of general nonlinear systems with delays and of nonlinear PDE systems. We design predictor feedback laws (i.e., feedback laws that use the future, rather than the current state of the system) for the compensation of delays (i.e., after the control signal reaches the system for the first time, the system behaves as there were no delay at all) that can be time-varying or state-dependent, on the input and on the state of nonlinear systems. We also provide designs of predictor feedback laws for linear systems with constant distributed delays and known or unknown plant parameters, and for linear systems with simultaneous known or unknown constant delays on the input and the state. Moreover, we introduce infinite-dimensional backstepping transformations for each particular problem, which enables us to construct Lyapunov -Krasovskii functionals. With the available Lyapunov- Krasovskii functionals we study stability, as well as, robustness of our control laws to plant uncertainties. We deal with coupled PDE-ODE systems. We consider nonlinear systems with wave actuator dynamics, for which we design a predictor inspired feedback law. We study stability of the closed-loop system either by constructing Lyapunov functionals, or using arguments of explicit solutions. We also consider linear systems with distributed actuator and sensor dynamics governed by diffusion or wave PDEs, for which we design stabilizing feedback laws. We study stability of the closed-loop systems using Lyapunov functionals that we construct with the introduction of infinite-dimensional transformations of forwarding type. Finally, we develop a control design methodology for coupled nonlinear first-order hyperbolic PDEs through an application to automotive catalysts

Summarization: We develop a predictor-based adaptive cruise control design with integral action (based on a nominal constant time-headway policy) for the compensation of large actuator and sensor delays in vehicular systems utilizing measurements of the relative spacing as well as of the speed and the short-term history of the desired acceleration of the ego vehicle. By employing an input-output approach, we show that the predictor-based adaptive cruise control law with integral action guarantees all of the four typical performance specifications of adaptive cruise control designs, namely, 1) stability, 2) zero steady-state spacing error, 3) string stability, and 4) non-negative impulse response, despite the large input delay. The effectiveness of the developed control design is shown in simulation considering various performance metrics. Presented on: IEEE Transactions on Intelligent Transportation Systems

Nikolaos Bekiaris-Liberis was supported by the funding from the European Commission’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 747898, project PADECOT. Claudio Roncoli and Markos Papageorgiou were supported by the funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. [321132], project TRAMAN21. Summarization: A model-based traffic state estimation approach is developed for per-lane density estimation as well as on-ramp and off-ramp flows estimation for highways in presence of connected vehicles. Three are the basic ingredients of the developed estimation scheme: (1) a data-driven version of the conservation-of-vehicles equation (in its time- and space-discretized form); (2) the utilization of position and speed information from connected vehicles’ reports, as well as total flow measurements obtained from a minimum number (sufficient for the observability of the model) of fixed detectors, such as, for example, at the main entry and exit of a given highway stretch; and (3) the employment of a standard Kalman filter. Furthermore, necessary and sufficient conditions for the (strong) structural observability of the introduced model are established (properties, which are rarely studied in the literature on traffic estimation), which yield the fixed detectors requirements needed for the proper operation of the developed estimation scheme. The performance of the estimation scheme is evaluated for various penetration rates of connected vehicles utilizing real microscopic traffic data collected within the Next Generation SIMulation (NGSIM) program. It is shown that the estimation performance is satisfactory, in terms of a suitable metric, even for low penetration rates of connected vehicles. The sensitivity of the estimation performance to variations of the model parameters (two in total) is also quantified, and it is shown that, overall, the estimation scheme is little sensitive to the model parameters. Presented on: Transportation Research Part B: Methodological

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 321132, project TRAMAN21. Summarization: This study presents a thorough microscopic simulation investigation of a recently developed model-based approach for per-lane density estimation, as well as on-ramp and off-ramp flow estimation, for highways in the presence of connected vehicles. The estimation methodology is mainly based on the assumption that a certain percentage of vehicles is equipped with Vehicle Automation and Communication Systems (VACS), which provide the necessary measurements used by the estimator, namely vehicle speed and position measurements. In addition, a minimum number of conventional flow detectors is needed. In the investigation, a calibrated and validated, with real data, microscopic multi-lane model is employed, which concerns a stretch of motorway A20 from Rotterdam to Gouda in the Netherlands. It is demonstrated that the proposed methodology provides satisfactory estimation performance even for low penetration rates of connected vehicles. Παρουσιάστηκε στο: IEEE 20th International Conference on Intelligent Transportation Systems

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 321132, project TRAMAN21. Summarization: We propose a feedback control strategy for lane assignment at bottleneck locations, assuming that a percentage of vehicles, equipped with Vehicle Automation and Communication Systems (VACS), are capable of receiving and executing specific lane-changing orders or recommendations. Starting from a previously proposed optimal control strategy, based on a simplified multi-lane motorway traffic flow model and formulated as a linear quadratic regulator, we design a feedback control problem aiming at maximising the throughput at bottleneck locations while distributing, according to a given policy, the total density at the bottleneck area among the different lanes, via optimal lane assignment of vehicles upstream of the bottleneck. The feedback control decisions are based on real-time measurements of the traffic state and inflow. The proposed strategy is tested on a nonlinear first-order macroscopic multi-lane traffic flow model, which also accounts for the capacity drop phenomenon. Παρουσιάστηκε στο: 96th Annual Meeting of the Transportation Research Board

International audience; — We consider the problems of trajectory generation and tracking for general 2 × 2 systems of first-order linear hyperbolic PDEs with anti-collocated boundary input and output. We solve the trajectory generation problem via backstepping. The reference input, which generates the desired output, incorporates integral operators acting on advanced and delayed versions of the reference output with kernels which were derived by Vazquez, Krstic, and Coron for the backstepping stabilization of 2×2 linear hyperbolic systems. For tracking the desired trajectory we employ a PI control law on the tracking error of the output. We prove exponential stability of the closed-loop system, under the proposed PI control law, when the parameters of the plant and the controller satisfy certain conditions, by constructing a novel " non-diagonal " Lyapunov functional.