scholarly journals Travel-blocking Optimal Control Policy on Borders of a Chain of Regions Subject to SIRS Discrete Epidemic Model

2018 ◽  
pp. 1-12
Author(s):  
Sara Bidah ◽  
Mostafa Rachik ◽  
Omar Zakary ◽  
Hamza Boutayeb ◽  
Ilias Elmouki
Keyword(s):  
Optimal Control ◽  
Control Policy ◽  
Discrete Version ◽  
Discrete Time System ◽  
Modeling Framework ◽  
Control Approach ◽  
Discrete Epidemic Model ◽  
Travel Restrictions ◽  
A Chain ◽  
Spread Of Infection

With thousands of people moving from one area to another day by day, in a chain of regions tightly more interconnected than other regions in a given large domain, an epidemic may spread rapidly around it from any point of borders. It might be sometimes urgent to impose travel restrictions to inhibit the spread of infection. As we aim to protect susceptible people of this chain to contact infected travelers coming from its neighbors, we follow the so-called travel-blocking vicinity optimal control approach with the introduction of the notion of patch for representing our targeted group of regions when the epidemic modeling framework is in the form of a Susceptible-Infected-Removed-Susceptible (SIRS) discrete-time system to study the case of the removed class return to susceptibility because of their short-lived immunity. A discrete version of the Pontryagin’s maximum principle is employed for the characterization of the travel-blocking optimal control. Finally, with the help of discrete progressive-regressive iterative schemes, we provide cellular simulations of an example of a domain composed with 100 regions and where the targeted chain includes 7 regions.

scholarly journals Disease-dependent interaction policies to support health and economic outcomes during the COVID-19 epidemic

2020 ◽  
Author(s):  
Guanlin Li ◽  
Shashwat Shivam ◽  
Michael E. Hochberg ◽  
Yorai Wardi ◽  
Joshua S Weitz
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Return To Work ◽  
Serological Test ◽  
Control Policy ◽  
Disease Status ◽  
Serological Tests ◽  
Control Policies ◽  
Control Approach ◽  
Dependent Interaction

Lockdowns and stay-at-home orders have partially mitigated the spread of Covid-19. However, the indiscriminate nature of mitigation - applying to all individuals irrespective of disease status - has come with substantial socioeconomic costs. Here, we explore how to leverage the increasing reliability and scale of both molecular and serological tests to balance transmission risks with economic costs involved in responding to Covid-19 epidemics. First, we introduce an optimal control approach that identifies personalized interaction rates according to an individual's test status; such that infected individuals isolate, recovered individuals can elevate their interactions, and activity of susceptible individuals varies over time. Critically, the extent to which susceptible individuals can return to work depends strongly on isolation efficiency. As we show, optimal control policies can yield mitigation policies with similar infection rates to total shutdown but lower socioeconomic costs. However, optimal control policies can be fragile given mis-specification of parameters or mis-estimation of the current disease state. Hence, we leverage insights from the optimal control solutions and propose a feedback control approach based on monitoring of the epidemic state. We utilize genetic algorithms to identify a 'switching' policy such that susceptible individuals (both PCR and serological test negative) return to work after lockdowns insofar as recovered fraction is much higher than the circulating infected prevalence. This feedback control policy exhibits similar performance results to optimal control, but with greater robustness to uncertainty. Overall, our analysis shows that test-driven improvements in isolation efficiency of infectious individuals can inform disease-dependent interaction policies that mitigate transmission while enhancing the return of individuals to pre-pandemic economic activity.

scholarly journals Optimal Pressure Boundary Control of Steady Multiscale Fluid-Structure Interaction Shell Model Derived from Koiter Equations

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 149
Author(s):  
Andrea Chierici ◽  
Leonardo Chirco ◽  
Sandro Manservisi
Keyword(s):  
Optimal Control ◽  
Solid Wall ◽  
Fluid Structure Interaction ◽  
Computational Cost ◽  
Robin Boundary Condition ◽  
Design Parameters ◽  
Fluid Structure ◽  
Control Approach ◽  
Structure Interaction ◽  
Fluid Boundary

Fluid-structure interaction (FSI) problems are of great interest, due to their applicability in science and engineering. However, the coupling between large fluid domains and small moving solid walls presents numerous numerical difficulties and, in some configurations, where the thickness of the solid wall can be neglected, one can consider membrane models, which are derived from the Koiter shell equations with a reduction of the computational cost of the algorithm. With this assumption, the FSI simulation is reduced to the fluid equations on a moving mesh together with a Robin boundary condition that is imposed on the moving solid surface. In this manuscript, we are interested in the study of inverse FSI problems that aim to achieve an objective by changing some design parameters, such as forces, boundary conditions, or geometrical domain shapes. We study the inverse FSI membrane model by using an optimal control approach that is based on Lagrange multipliers and adjoint variables. In particular, we propose a pressure boundary optimal control with the purpose to control the solid deformation by changing the pressure on a fluid boundary. We report the results of some numerical tests for two-dimensional domains to demonstrate the feasibility and robustness of our method.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

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