This paper presents a novel observer-based approach to detect and isolate faulty sensors in nonlinear systems. The proposed sensor fault detection and isolation (s-FDI) method applies to a general class of nonlinear systems. Our focus is on s-FDI for two types of faults: complete failure and sensor degradation. The key aspect of this approach lies in the utilization of a neural network-based Kazantzis-Kravaris/Luenberger (KKL) observer. The neural network is trained to learn the dynamics of the observer, enabling accurate output predictions of the system. Sensor faults are detected by comparing the actual output measurements with the predicted values. If the difference surpasses a theoretical threshold, a sensor fault is detected. To identify and isolate which sensor is faulty, we compare the numerical difference of each sensor measurement with an empirically derived threshold. We derive both theoretical and empirical thresholds for detection and isolation, respectively. Notably, the proposed approach is robust to measurement noise and system uncertainties. Its effectiveness is demonstrated through numerical simulations of sensor faults in a network of Kuramoto oscillators.

This article provides an overview of the classical and new techniques in traffic flow control and estimations. The overview begins with a description of the most used traffic flow models for estimation and control. Then, it shifts towards using those models for traffic flow estimation using physics-informed machine learning techniques. Lastly, it focuses on traffic flow control describing the most classical techniques and the new advancement in traffic control using autonomous vehicles.

The state reconstruction problem of a heterogeneous dynamic system under sporadic measurements is considered. This system consists of a conversation flow together with a multi-agent network modeling particles within the flow. We propose a partial-state reconstruction algorithm using physics-informed learning based on local measurements obtained from these agents. Traffic density reconstruction is used as an example to illustrate the results and it is shown that the approach provides an efficient noise rejection.

This article investigates the use of a model-based neural network for the traffic reconstruction problem using noisy measurements coming from Probe Vehicles (PV). The traffic state is assumed to be the density only, modeled by a partial differential equation. There exist various methods for reconstructing the density in that case. However, none of them perform well with noise and very few deal with lagrangian measurements. This paper introduces a method that can reduce the processes of identification, reconstruction, prediction, and noise rejection into a single optimization problem. Numerical simulations, based either on a macroscopic or a microscopic model, show good performance for a moderate computational burden. Copyright

This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically stick to the ground. The objective consists of developing numerically tractable conditions ensuring the global asymptotic stability of the unique equilibrium point. The proposed approach merges two intermediate results: The first one relies on the characterization of an attractor around the origin, to which converges the closed-loop trajectories. The second result assesses the regional asymptotic stability of the equilibrium point by estimating its basin of attraction. The main result relies on conditions allowing to ensure that the attractor issued from the first result is included in the basin of attraction of the origin computed from the second result. An illustrative example draws the interest of the approach.

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model used assumes noisy measurements and a partially unknown first-order model. All these considerations make the use of machine learning to reconstruct the state the only applicable solution. We first investigate how the identification and reconstruction processes can be merged and how a sparse dataset can still enable a good identification. Secondly, we propose a pre-training procedure that aids the hyperparameter tuning, preventing the gradient descent algorithm from getting stuck at saddle points. Examples using numerical simulations and the SUMO traffic simulator show that the reconstructions are close to the real density in all cases.

This article deals with the observation problem in traffic flow theory. The model used is the quasiilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the measurements here are obtained from Probe Vehicles (PVs). We propose then a moving dynamic boundary observer whose boundaries are defined by the trajectories of the PVs. The main result of this article is the exponential convergence of the observation error, and, in some cases, its finite-time convergence. Finally, numerical simulations show that it is possible to observe the traffic in the congested, free-flow, and mixed regimes provided that the number of PVs is large enough.

This paper proposes a framework to assess the stability of an Ordinary Differential Equation (ODE) which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are not generated using dissipation inequalities involving the whole state of an infinite-dimensional system, but by using projection coefficients of the infinite-dimensional state. This permits to generalize our robustness result to many other PDEs. The proposed methodology is applied to a time-delay system and numerical results comparable to those in the literature are obtained. 

In this paper we present a numerical study on control and observation of traffic flow using Lagrangian measurements and actuators. We investigate the effect of some basic control and observation schemes using probe and actuated vehicles within the flow. The aim is to show the effect of the state reconstruction on the efficiency of the control, compared to the case using full information about the traffic. The effectiveness of the proposed state reconstruction and control algorithms is demonstrated in simulations. They show that control using the reconstructed state approaches the full-information control when the gap between the connected vehicles is not too large, reducing the delay by more than 60% when the gap between the sensor vehicles is 1.25 km on average, compared to a delay reduction of almost 80% in the full-information control case. Moreover, we propose a simple scheme for selecting which vehicles to use as sensors, in order to reduce the communication burden. Numerical simulations demonstrate that with this triggering mechanism, the delay is reduced by around 65%, compared to a reduction of 72% if all connected vehicles are communicating at all times.

The Gemini South 8-meter telescope's Multi Conjugate Adaptive Optics System GeMS is about to enter a new era of science with an entire new upgrade for its Natural Guide Star wave front sensor (NGS2). With NGS2 the limiting magnitude of the natural guide stars used for tip/tilt sensing is expected to increase from its current limit of 15.4 to 17+ in R-band. This will provide a much greater sky coverage over the current system. NGS2 is a complete replacement of the current Natural Guide Star wave front sensor (NGS). This presents an interesting challenge as the current NGS includes a Slow Focus Sensor (SFS) used to compensate for the sodium layer mean altitude variations. With the new NGS2 setup, this SFS will be removed and a suitable replacement must be found. Within the Gemini environment there exist two facility wave front sensors, Peripheral Wave Front Sensors one and two (PWFS1 and PWFS2), that could act as an SFS. Only one of these (PWFS1) is located optically in front of the GeMS Adaptive Optics (AO) bench (Canopus). We are currently preparing this wave front sensor as the new SFS for GeMS under the NGS2 setup. The results of several nighttime and daytime tests show that PWFS1 will be an adequate SFS for GeMS in the NGS2 setup providing excellent sky coverage without compromising the GeMS Field of View (FoV).