scholarly journals CoSIR: Managing an Epidemic via Optimal Adaptive Control of Transmission Policy

2020 ◽  
Author(s):  
Harsh Maheshwari ◽  
Shreyas Shetty ◽  
Nayana Bannur ◽  
Srujana Merugu
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Transmission Rate ◽  
Analytical Framework ◽  
Sir Model ◽  
Practical Implementation ◽  
Stable Equilibrium Point ◽  
Transmission Control ◽  
Susceptible Population ◽  
Predator Prey Model

AbstractShaping an epidemic with an adaptive contact restriction policy that balances the disease and socioeconomic impact has been the holy grail during the COVID-19 pandemic. Most of the existing work on epidemiological models [40, 11, 17, 7] focuses on scenario-based forecasting via simulation but techniques for explicit control of epidemics via an analytical framework are largely missing. In this paper, we consider the problem of determining the optimal policy for transmission control assuming SIR dynamics [28], which is the most widely used epidemiological paradigm. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model [8]. The modified SIR system (LVSIR) has a stable equilibrium point, an “energy” conservation property, and exhibits bounded cyclic behaviour similar to an LV system. This mapping permits a theoretical analysis of the control problem supporting some of the recent simulation-based studies [16, 29] that point to the benefits of periodic interventions. We use a control-Lyapunov approach to design adaptive control policies (CoSIR) to nudge the SIR model to the desired equilibrium that permits ready extensions to richer compartmental models. We also describe a practical implementation of this transmission control method by approximating the ideal control with a finite, but a time-varying set of restriction levels and provide simulation results to demonstrate its efficacy.

scholarly journals Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

2021 ◽  
Author(s):  
Jayanta Kumar Ghosh ◽  
Prahlad Majumdar ◽  
Uttam Ghosh
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Logistic Growth ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Susceptible Population ◽  
Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

Analysis of a predator–prey model with herd behavior and disease in prey incorporating prey refuge

2019 ◽  
Vol 12 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Sangeeta Saha ◽  
G. P. Samanta
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Herd Behavior ◽  
Prey Refuge ◽  
Free System ◽  
Susceptible Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Disease Free

In this work, we have introduced an eco-epidemiological model of an infected predator–prey system. Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption. Moreover, to make the model more realistic to the environment, we have introduced strong Allee effect in the susceptible population. Boundedness and positivity of the solution have been established. Local stability conditions of the equilibrium points have been found with the help of Routh–Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease, then both the prey (susceptible and infected) and predator cannot survive simultaneously in the system for any parametric values. The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics. For different values of these two key parameters, we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Disturbance compensation-based output feedback adaptive control for shape memory alloy actuator system

2021 ◽  
Vol 18 (1) ◽  
pp. 172988142199399
Author(s):  
Xiaoguang Li ◽  
Bi Zhang ◽  
Daohui Zhang ◽  
Xingang Zhao ◽  
Jianda Han
Keyword(s):  
Adaptive Control ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Control Method ◽  
Control Law ◽  
Reference Trajectory ◽  
Disturbance Compensation ◽  
Comparison Results ◽  
Control Scheme ◽  
Actuator System

Shape memory alloy (SMA) has been utilized as the material of smart actuators due to the miniaturization and lightweight. However, the nonlinearity and hysteresis of SMA material seriously affect the precise control. In this article, a novel disturbance compensation-based adaptive control scheme is developed to improve the control performance of SMA actuator system. Firstly, the nominal model is constructed based on the physical process. Next, an estimator is developed to online update not only the unmeasured system states but also the total disturbance. Then, the novel adaptive controller, which is composed of the nominal control law and the compensation control law, is designed. Finally, the proposed scheme is evaluated in the SMA experimental setup. The comparison results have demonstrated that the proposed control method can track reference trajectory accurately, reject load variations and stochastic disturbances timely, and exhibit satisfactory robust stability. The proposed control scheme is system independent and has some potential in other types of SMA-actuated systems.

scholarly journals A Novel Adaptive Control Approach Based on Available Headroom of the VSC-HVDC for Enhancement of the AC Voltage Stability

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3222
Author(s):  
Duc Nguyen Huu
Keyword(s):  
Adaptive Control ◽  
Voltage Stability ◽  
Reactive Power ◽  
Control Method ◽  
Offshore Wind ◽  
Voltage Source ◽  
Long Distance ◽  
Control Approach ◽  
Hvdc System ◽  
Voltage Support

Increasing offshore wind farms are rapidly installed and planned. However, this will pose a bottle neck challenge for long-distance transmission as well as inherent variation of their generating power outputs to the existing AC grid. VSC-HVDC links could be an effective and flexible method for this issue. With the growing use of voltage source converter high-voltage direct current (VSC-HVDC) technology, the hybrid VSC-HVDC and AC system will be a next-generation transmission network. This paper analyzes the contribution of the multi VSC-HVDC system on the AC voltage stability of the hybrid system. A key contribution of this research is proposing a novel adaptive control approach of the VSC-HVDC as a so-called dynamic reactive power booster to enhance the voltage stability of the AC system. The core idea is that the novel control system is automatically providing a reactive current based on dynamic frequency of the AC system to maximal AC voltage support. Based on the analysis, an adaptive control method applied to the multi VSC-HVDC system is proposed to realize maximum capacity of VSC for reactive power according to the change of the system frequency during severe faults of the AC grid. A representative hybrid AC-DC network based on Germany is developed. Detailed modeling of the hybrid AC-DC network and its proposed control is derived in PSCAD software. PSCAD simulation results and analysis verify the effective performance of this novel adaptive control of VSC-HVDC for voltage support. Thanks to this control scheme, the hybrid AC-DC network can avoid circumstances that lead to voltage instability.

Anti-noise model-free adaptive control and its application in the circulating fluidized bed boiler

2020 ◽  
pp. 095965182097937
Author(s):  
Na Dong ◽  
Wenjin Lv ◽  
Shuo Zhu ◽  
Donghui Li
Keyword(s):  
Adaptive Control ◽  
Complete Convergence ◽  
Circulating Fluidized Bed ◽  
Control Method ◽  
Noise Model ◽  
Good Resistance ◽  
Industrial Systems ◽  
Noise Interference ◽  
Model Free ◽  
Tracking Differentiator

Model-free adaptive control has been developed greatly since it was proposed. Up to now, model-free adaptive control theory has become mature and tends to be an effective solution for complex unmodeled industrial systems. In practical industrial processes, most control systems are inevitably accompanied by noise that will result in indelible error and may further cause inaccurate feedback to the output. In order to solve this kind of problem with model-free technique, this article incorporates an improved tracking differentiator into model-free adaptive control. After that, the anti-noise model-free adaptive control method with complete convergence analysis is proposed. Meanwhile, numerical simulation proves that the improved control method can quickly track a given signal with good resistance to noise interference. Finally, the effectiveness and practicability of the proposed algorithm are verified by experiments through the control of drum water level of circulating fluidized.

Multimode Adaptive Control for Tank Gun Control System Based on Tracking Differentiator

2011 ◽  
Vol 383-390 ◽  
pp. 79-85
Author(s):  
Dong Yuan ◽  
Xiao Jun Ma ◽  
Wei Wei
Keyword(s):  
Adaptive Control ◽  
Control System ◽  
High Speed ◽  
Control Method ◽  
Reference Model ◽  
Gun Control ◽  
Math Model ◽  
Tracking Differentiator ◽  
Switch Control ◽  
Model Reference Adaptive

Aiming at the problems such as switch impulsion, insurmountability for influence caused by nonlinearity in one tank gun control system which adopts double PID controller to realize the multimode switch control between high speed and low speed movement, the system math model is built up; And then, Model Reference Adaptive Control (MRAC) method based on nonroutine reference model is brought in and the adaptive gun controller is designed. Consequently, the compensation of nonlinearity and multimode control are implemented. Furthermore, the Tracking Differentiator (TD) is affiliated to the front of controller in order to restrain the impulsion caused by mode switch. Finally, the validity of control method in this paper is verified by simulation.

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