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This paper presents an observer-based event-triggered boundary control strategy for the one-phase Stefan problem, utilising the position and velocity measurements of the moving interface. The design of the observer and controller is founded on the infinite-dimensional backstepping approach. To implement the continuous-time observer-based controller in an event-triggered framework, we propose a dynamic event triggering condition. This condition specifies the instances when the control input must be updated. Between events, the control input is maintained constant in a Zero-Order-Hold manner. We demonstrate that the dwell-time between successive triggering moments is uniformly bounded from below, thereby precluding Zeno behaviour. The proposed event-triggered boundary control strategy ensures the wellposedness of the closed-loop system and the satisfaction of certain model validity conditions. Additionally, the global exponential convergence of the closed-loop system to the setpoint is established using Lyapunov approach. A simulation example is provided to validate the theoretical findings. 

During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized. 

Abstract The rapid rollout of the COVID-19 vaccine raises the question of whether and when the ongoing pandemic could be eliminated with vaccination and non-pharmaceutical interventions (NPIs). Despite advances in the impact of NPIs and the conceptual belief that NPIs and vaccination control COVID-19 infections, we lack evidence to employ control theory in real-world social human dynamics in the context of disease spreading. We bridge the gap by developing a new analytical framework that treats COVID-19 as a feedback control system with the NPIs and vaccination as the controllers and a computational model that maps human social behaviors into input signals. This approach enables us to effectively predict the epidemic spreading in 381 Metropolitan statistical areas (MSAs) in the US by learning our model parameters utilizing the time series NPIs (i.e., the stay-at-home order, face-mask wearing, and testing) data. This model allows us to optimally identify three NPIs to predict infections accurately in 381 MSAs and avoid over-fitting. Our numerical results demonstrate our approach’s excellent predictive power with R 2  > 0.9 for all the MSAs regardless of their sizes, locations, and demographic status. Our methodology allows us to estimate the needed vaccine coverage and NPIs for achieving R e to a manageable level and how the variants of concern diminish the likelihood for disease elimination at each location. Our analytical results provide insights into the debates surrounding the elimination of COVID-19. NPIs, if tailored to the MSAs, can drive the pandemic to an easily containable level and suppress future recurrences of epidemic cycles. 

Abstract Despite a number of successful approaches in predicting the spatiotemporal patterns of the novel coronavirus (COVID-19) pandemic and quantifying the effectiveness of non-pharmaceutical interventions starting from data about the initial outbreak location, we lack an intrinsic understanding as outbreak locations shift and evolve. Here, we fill this gap by developing a country distance approach to capture the pandemic’s propagation backbone tree from a complex airline network with multiple and evolving outbreak locations. We apply this approach, which is analogous to the effective resistance in series and parallel circuits, to examine countries’ closeness regarding disease spreading and evaluate the effectiveness of travel restrictions on delaying infections. In particular, we find that 63.2% of travel restrictions implemented as of 1 June 2020 are ineffective. The remaining percentage postponed the disease arrival time by 18.56 days per geographical area and resulted in a total reduction of 13,186,045 infected cases. Our approach enables us to design optimized and coordinated travel restrictions to extend the delay in arrival time and further reduce more infected cases while preserving air travel. 

Abstract Temperature control is essential for regulating material properties in laser-based manufacturing. Motion and power of the scanning laser affect local temperature evolution, which in turn determines the a posteriori microstructure. This paper addresses the problem of adjusting the laser speed and power to achieve the desired values of key process parameters: cooling rate and melt pool size. The dynamics of a scanning laser system is modeled by a one-dimensional (1D) heat conduction equation, with laser power as the heat input and heat dissipation to the ambient. Since the model is 1D, length and size are essentially the same. We pose the problem as a regulation problem in the (moving) laser frame. The first step is to obtain the steady-state temperature distribution and the corresponding input based on the desired cooling rate and melt pool size. The controller adjusts the input around the steady-state feedforward based on the deviation of the measured temperature field from the steady-state distribution. We show that with suitably defined outputs, the system is strictly passive from the laser motion and power. To avoid over-reliance on the model, the steady-state laser speed and power are adaptively updated, resulting in an integral-like update law for the feedforward. Moreover, the heat transfer coefficient to the ambient may be uncertain, and can also be adaptively updated. The final form of the control law combines passive error temperature field feedback with adaptive feedforward and parameter estimation. The closed-loop asymptotical stability is shown using the Lyapunov arguments, and the controller performance is demonstrated in a simulation.