The Unscented Kalman Filter for Nonlinear Parameter Identification of Adaptive Cruise Control Systems

This paper develops and investigates a dual unscented Kalman filter (DUKF) for the joint nonlinear state and parameter identification of commercial adaptive cruise control (ACC) systems. Although the core functionality of stock ACC systems, including their proprietary control logic and parameters, is not publicly available, this work considers a car-following scenario with a human-driven vehicle (leader) and an ACC engaged ego vehicle (follower) that employs a constant time-headway policy (CTHP). The objective of the DUKF is to determine the CTHP parameters of the ACC by using real-time observations of space-gap and relative velocity from the vehicle's onboard sensors. Real-time parameter identification of stock ACC systems is essential for assessing their string stability, large-scale deployment on motorways, and impact on traffic flow and throughput. In this regard, $L_2$ and $L_\infty$ string stability conditions are considered. The observability rank condition for nonlinear systems is adopted to evaluate the ability of the proposed estimation scheme to estimate stock ACC system parameters using empirical data. The proposed filter is evaluated using empirical data collected from the onboard sensors of two 2019 SUV vehicles, namely Hyundai Nexo and SsangYong Rexton, equipped with stock ACC systems; and is compared with batch and recursive least-squares optimization. The set of ACC model parameters obtained from the proposed filter revealed that the commercially implemented ACC system of the considered vehicle (Hyundai Nexo) is neither $L_2$ nor $L_\infty$ string stable.Comment: 11 papes, 3 Figure

Multi-Gated Perimeter Flow Control of Transport Networks

This paper develops a control scheme for the multi-gated perimeter traffic flow control problem of urban road networks. The proposed scheme determines optimally distributed input flows (or feasible entrance link green times) for a number of gates located at the periphery of a protected network area. A macroscopic model is employed to describe the traffic dynamics of the protected network. To describe traffic dynamics outside of the protected area, we augment the basic state-space model with additional state variables to account for the queues at store-and-forward origin links at the periphery. We aim to equalise the relative queues at origin links and maintain the vehicle accumulation in the protected network around a desired point, while the system's throughput is maximised. The perimeter traffic flow control problem is formulated as a convex optimal control problem with constrained control and state variables. For real-time control, the optimal control problem is embedded in a rolling-horizon scheme using the current state of the whole system as the initial state as well as predicted demand flows at entrance links. A meticulous simulation study is carried out for a 2.5 square mile protected network area of San Francisco, CA, including fifteen gates of different geometric characteristics. Results demonstrate the efficiency and equity properties of the proposed approach to better manage excessive queues outside of the protected network area and optimally distribute the input flows

Robust Constrained Interpolating Control of Interconnected Systems

This paper presents a decentralised interpolating control scheme for the robust constrained control of uncertain linear discrete-time interconnected systems with local state and control constraints. The control law of each distinct subsystem relies on the gentle interpolation between a local high-gain controller with a global low-gain controller. Both controllers benefit from the computation of separable robust invariant sets for local control design, which overcomes the computational burden of large-scale systems. Another advantage is that for each subsystem both low-and high-gain controllers can be efficiently determined off-line, while the inexpensive interpolation between them is performed on-line. For the interpolation, a new low-dimensional linear programming problem is solved at each time instant. Proofs of recursive feasibility and robust asymptotic stability of the proposed control are provided. A numerical example demonstrates the robustness of decentralised interpolating control against model uncertainty and disturbances. The proposed robust control is computationally inexpensive, and thus it is well suited for large-scale applications

Macroscopic modelling and robust control of bi-modal multi-region urban road networks

The paper concerns the integration of a bi-modal Macroscopic Fundamental Diagram (MFD) modelling for mixed traffic in a robust control framework for congested single- and multi-region urban networks. The bi-modal MFD relates the accumulation of cars and buses and the outflow (or circulating flow) in homogeneous (both in the spatial distribution of congestion and the spatial mode mixture) bi-modal traffic networks. We introduce the composition of traffic in the network as a parameter that affects the shape of the bi-modal MFD. A linear parameter varying model with uncertain parameter the vehicle composition approximates the original nonlinear system of aggregated dynamics when it is near the equilibrium point for single- and multi-region cities governed by bi-modal MFDs. This model aims at designing a robust perimeter and boundary flow controller for single- and multi-region networks that guarantees robust regulation and stability, and thus smooth and efficient operations, given that vehicle composition is a slow time-varying parameter. The control gain of the robust controller is calculated off-line using convex optimisation. To evaluate the proposed scheme, an extensive simulation-based study for single- and multi-region networks is carried out. To this end, the heterogeneous network of San Francisco where buses and cars share the same infrastructure is partitioned into two homogeneous regions with different modes of composition. The proposed robust control is compared with an optimised pre-timed signal plan and a single-region perimeter control strategy. Results show that the proposed robust control can significantly: (i) reduce the overall congestion in the network; (ii) improve the traffic performance of buses in terms of travel delays and schedule reliability, and; (iii) avoid queues and gridlocks on critical paths of the network

Interpolating Constrained Control of Interconnected Systems

This paper presents a decentralised interpolating control scheme for the control of linear discrete-time interconnected systems with local state and control constraints. The control law of each distinct subsystem relies on the gentle interpolation between a local high- gain controller, which satisfies some user-desired performance specifications, with a global low-gain controller. For each subsystem both low- and high-gain controllers can be efficiently determined off-line, while the inexpensive interpolation between them is performed on-line. For the interpolation, a new low-dimensional linear programming formulation is developed, which is computationally less expensive compared to previous works. Therefore, it is appropriate for real- time control of large-scale interconnected systems. Proofs of recursive feasibility and asymptotic stability of the interpolating scheme are given for decoupled as well as interconnected subsystems with coupled state constraints. Two numerical examples show that the proposed decentralised interpolating control outperforms previously proposed interpolating schemes. Finally, it is faster than model predictive control, while their control behaviour and performance is almost identical

Interpolating Control Toolbox (ICT)

Interpolating control toolbox (ICT) is a free and open-source MATLAB toolbox that implements interpolation-based control (IC) for time-invariant and uncertain time-varying linear discrete-time systems with local state and control constraints. The toolbox combines geometrical features to compute robust invariant sets offline and solves a linear programming problem to compute the required IC online. This paper provides an overview on interpolating control and shows how to use ICT to robustly control input centralised and input decentralised interconnected systems. ICT includes some demo files to compare the performance of centralised versus decentralised IC

Robust Stability of Time-varying Polytopic Systems by the Attractive Ellipsoid Method

This paper concerns the robust stabilization of continuous-time polytopic systems subject to unknown but bounded perturbations. To tackle this problem, the attractive ellipsoid method (AEM) is employed. The AEM aims to determine an asymptotically attractive (invariant) ellipsoid such that the state trajectories of the system converge to a small neighborhood of the origin despite the presence of nonvanishing perturbations. An alternative form of the elimination lemma is used to derive new LMI conditions, where the state-space matrices are decoupled from the stabilizing Lyapunov matrix. Then a robust state-feedback control law is obtained by semi-definite convex optimization, which is numerically tractable. Further, the gain-scheduled state-feedback control problem is considered within the AEM framework. Numerical examples are given to illustrate the proposed AEM and its improvements over previous works. Precisely, it is demonstrated that the minimal size ellipsoids obtained by the proposed AEM are smaller compared to previous works, and thus the proposed control design is less conservative

Interpolating Control Toolbox (ICT)

Interpolating control toolbox (ICT) is a free and open-source MATLAB toolbox that implements interpolation-based control (IC) for time-invariant and uncertain time-varying linear discrete-time systems with local state and control constraints. The toolbox combines geometrical features to compute robust invariant sets offline and solves a linear programming problem to compute the required IC online. This paper provides an overview on interpolating control and shows how to use ICT to robustly control input centralised and input decentralised interconnected systems. ICT includes some demo files to compare the performance of centralised versus decentralised IC

Real-Time Estimation of Critical Vehicle Accumulation for Maximum Network Throughput

Perimeter traffic flow control has recently been found to be a practical and efficient control scheme in mitigating traffic congestion in urban road networks. This control scheme aims at stabilising the accumulation of vehicles of the socalled network fundamental diagram near critical accumulation to achieve maximum network throughput. Nevertheless, the maximum throughput in urban road networks may be observed over a range of accumulation-values. In this work, an adaptive perimeter flow control strategy is proposed that allows the automatic monitoring of the critical accumulation to help maintain the accumulation near the optimal range of accumulation-values, while network's throughput is maximised. To this end, we design a Kalman filter-based estimation scheme that utilises real-time measurements of circulating flow and accumulation of vehicles to produce estimates of the currently prevailing critical accumulation. We use real data from an urban area with 70 sensors and show that the area exhibits a network fundamental diagram with low scatter. We demonstrate that the fundamental diagram is reproduced under different days but its shape and critical occupancy depend on the applied semi-real-time signal control and the distribution of congestion in the network. Results from the application of the estimation algorithm to the experimental data indicate good estimation accuracy and performance, and rapid tracking behaviour

Robust disturbance rejection by the attractive ellipsoid method – part I: continuous-time systems

This paper develops sufficient conditions for the constrained robust stabilization of continuous-time polytopic linear systems with unknown but bounded perturbations. The attractive ellipsoid method (AEM) is employed to determine a robustly controllable invariant set, known as attractive ellipsoid, such that the state trajectories of the system asymptotically converge to a small neighborhood of the origin despite the presence of non-vanishing perturbations. To solve the stabilization problem, we employ the Finsler’s lemma and derive new linear matrix inequality (LMI) conditions for robust state-feedback control design, ensuring convergence of state trajectories of the system to a minimal size ellipsoidal set. We also consider the state and control constrained problem and derive extended LMI conditions. Under certain conditions, the obtained LMIs guarantee that the attractive ellipsoid is nested inside the bigger ellipsoids imposed by the control and state constraints. Finally, we extend our AEM approach to the gain-scheduled state-feedback control problem, where the scheduling parameters governing the time-variant system are unknown in advance but can be measured in real-time. Two examples demonstrate the feasibility of the proposed AEM and its improvements over previous works