Search for: All records

For population systems modeled by age‐structured hyperbolic partial differential equations (PDEs), we redesign the existing feedback laws, designed under the assumption that the dilution input is directly actuated, to the more realistic case where dilution is governed by actuation dynamics (modeled simply by an integrator). In addition to the standard constraint that the population density must remain positive, the dilution dynamics introduce constraints of not only positivity of dilution, but possibly of given positive lower and upper bounds on dilution. We present several designs, of varying complexity, and with various measurement requirements, which not only ensure global asymptotic (and local exponential) stabilization of a desired positive population density profile from all positive initial conditions, but do so without violating the constraints on the dilution state. To develop the results, we exploit the relation between first‐order hyperbolic PDEs and an equivalent representation in which a scalar input‐driven mode is decoupled from input‐free infinite‐dimensional internal dynamics represented by an integral delay system.

 

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. 

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.