This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by ...This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>展开更多
This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to ha...This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.展开更多
文摘This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>
文摘This paper presents a robust adaptive control scheme for a class of continuous-time linear systems with unknown non-smooth asymmetrical deadzone nonlinearity at the input of the plant. The methodology is applied to handle input deadzone as well as unmeasurable disturbances simultaneously in strictly matched systems. The proposed controller robustly cancels any residual distortion caused by the inaccurate deadzone cancellation scheme. The scheme is shown to successfully cancel the deadzone’s deleterious effect as well as eliminate other unmeasurable disturbances within the span of the input. The new controller ensures the global stability of all states and adaptations, and achieves asymptotic tracking. The asymptotic stability of the closed-loop system is proven by Lyapunov arguments, and simulation results confirm the efficacy of the control methodology.