Prognosticating the spread of covid-19 pandemic based on optimal arima estimators

2020 ◽  
Vol 20 ◽  
Author(s):  
Venuka Sandhir ◽  
Vinod Kumar ◽  
Vikash Kumar
Keyword(s):  
South Africa ◽  
Statistical Analysis ◽  
Moving Average ◽  
Arima Model ◽  
Information Criterion ◽  
Stable Case ◽  
Johns Hopkins University ◽  
Modelling Techniques ◽  
Auto Regressive ◽  
Global Threat

Background: COVID-19 cases have been reported as a global threat and several studies are being conducted using various modelling techniques to evaluate patterns of disease dispersion in the upcoming weeks. Here we propose a simple statistical model that could be used to predict the epidemiological extent of community spread of COVID-19from the explicit data based on optimal ARIMA model estimators. Methods: Raw data was retrieved on confirmed cases of COVID-19 from Johns Hopkins University (https://github.com/CSSEGISandData/COVID-19) and Auto-Regressive Integrated Moving Average (ARIMA) model was fitted based on cumulative daily figures of confirmed cases aggregated globally for ten major countries to predict their incidence trend. Statistical analysis was completed by using R 3.5.3 software. Results: The optimal ARIMA model having the lowest Akaike information criterion (AIC) value for US (0,2,0); Spain (1,2,0); France (0,2,1); Germany (3,2,2); Iran (1,2,1); China (0,2,1); Russia (3,2,1); India (2,2,2); Australia (1,2,0) and South Africa (0,2,2) imparted the nowcasting of trends for the upcoming weeks. These parameters are (p, d, q) where p refers to number of autoregressive terms, d refers to number of times the series has to be differenced before it becomes stationary, and q refers to number of moving average terms. Results obtained from ARIMA model showed significant decrease cases in Australia; stable case for China and rising cases has been observed in other countries. Conclusion: This study tried their best at predicting the possible proliferate of COVID-19, although spreading significantly depends upon the various control and measurement policy taken by each country.

scholarly journals Modified Vector Field Path-Following Control System for an Underactuated Autonomous Surface Ship Modelin the Presence of Static Obstacles

2021 ◽  
Vol 9 (6) ◽  
pp. 652
Author(s):  
Haitong Xu ◽  
Miguel A. Hinostroza ◽  
C. Guedes Guedes Soares
Keyword(s):  
Control System ◽  
Vector Field ◽  
Path Following ◽  
Field Method ◽  
Integrated System ◽  
Ship Model ◽  
Surface Ship ◽  
Path Following Control ◽  
Exponentially Stable ◽  
Vector Field Method

A modified path-following control system using the vector field method for an underactuated autonomous surface ship model is proposed in the presence of static obstacles. With this integrated system, autonomous ships are capable of following the predefined path, while avoiding the obstacles automatically. It is different from the methods in most published papers, which usually study path-following and obstacle collision avoidance, separately. This paper considers the coupled path following and collision avoidance task as a whole. Meanwhile, the paper also shows the heading control design method in the presence of static obstacles. To obtain a strong stability property, a nonlinear autopilot is designed based on the manoeuvring tests of the free-running ship model. The equilibrium point of the controller is globally exponentially stable. For the guidance system, a novel vector field method was proposed, and the proof shows the coupled guidance and control system is uniform semi-global exponentially stable (USGES). To prevent the obstacles near the predefined path, the proposed guidance law is augmented by integrating the repelling field of obstacles so that it can control the ship travel toward the predefined path through the obstacles safely. The repelling field function is given considering the obstacle shape and collision risk using the velocity obstacle (VO) algorithm. The simulations and ship model test were performed to validate the integrated system of autonomous ships.

Robust Stability Analysis of Delay-Dependence for a Class of Switched Uncertain Systems with Time Delay

2013 ◽  
Vol 415 ◽  
pp. 139-142
Author(s):  
Chi Jo Wang ◽  
Juing Shian Chiou
Keyword(s):  
Time Delay ◽  
Stability Margin ◽  
Uncertain System ◽  
Switching Law ◽  
Delay Dependence ◽  
Robust Stability Analysis ◽  
Exponentially Stable ◽  
Delay Dependent ◽  
Interval Systems ◽  
Delay Dependent Stability

Some new criteria of delay-dependent stability for the switched time-delay uncertain system are deduced by employing time-switched method and the comparison theorem in this paper. The total activation time ratio of the switching law can be determined to guarantee the switched time-delay uncertain system is exponentially stable with stability margin . Finally, this method can be extended to switched interval systems with time-delay. Some examples are exploited to illustrate the proposed schemes..

scholarly journals Exponential Stability of Stochastic Differential Equation with Mixed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Xinfeng Ruan ◽  
Zhao Zhao
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Stochastic Differential Equation ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Martingale Inequality ◽  
Mixed Delay ◽  
Exponentially Stable ◽  
Theoretical Results

This paper focuses on a class of stochastic differential equations with mixed delay based on Lyapunov stability theory, Itô formula, stochastic analysis, and inequality technique. A sufficient condition for existence and uniqueness of the adapted solution to such systems is established by employing fixed point theorem. Some sufficient conditions of exponential stability and corollaries for such systems are obtained by using Lyapunov function. By utilizing Doob’s martingale inequality and Borel-Cantelli lemma, it is shown that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. In particular, our theoretical results show that if stochastic differential equation is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic differential equation with mixed delay will remain exponentially stable. Moreover, time delay upper limit is solved by using our theoretical results when the system is exponentially stable, and they are more easily verified and applied in practice.

Perturbations in Networked Control Systems

2001 ◽  
Author(s):  
Octavian Beldiman ◽  
Linda G. Bushnell ◽  
Gregory C. Walsh ◽  
Hua O. Wang ◽  
Yiguang Hong
Keyword(s):  
Control System ◽  
Control Systems ◽  
Networked Control Systems ◽  
Networked Control System ◽  
Networked Control ◽  
Asymptotically Stable ◽  
Networked System ◽  
External Perturbations ◽  
Exponentially Stable

Abstract In this paper we study the effect of external perturbations on a networked control system. We start by assuming that the non-networked system without perturbation is exponentially stable. Then, for fast enough networks we show that if the perturbation is bounded the networked system is ultimately bounded and if the perturbation is vanishing then the networked system is asymptotically stable. We conclude the paper with simulations verifying the results.

Nonlinear dynamic image-based visual servoing of a quadrotor

2015 ◽  
Vol 3 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Geoff Fink ◽  
Hui Xie ◽  
Alan F. Lynch ◽  
Martin Jagersand
Keyword(s):  
Visual Servoing ◽  
Lateral Position ◽  
Control Law ◽  
Stationary Target ◽  
Dynamic Image ◽  
Change Of State ◽  
Dependent Change ◽  
Exponentially Stable ◽  
Aerial Vehicle ◽  
Error Dynamics

This paper proposes a dynamic image-based visual servoing (IBVS) control law for a quadrotor unmanned aerial vehicle (UAV) equipped with a single fixed on-board camera facing downward. The motion control problem is to regulate the relative lateral position of the vehicle to a stationary target located on the ground. The control law is termed dynamic as it is based on the dynamics and kinematics of the vehicle. The proposed design uses a nonlinear input-dependent change of state coordinates and its error dynamics are proven to be locally exponentially stable with an estimate provided for the region of attraction. Experimental and simulation results demonstrate the method's ease of on-board implementation, performance, and robustness. The simulation and experimental results include a comparison with an established dynamic IBVS method. This comparison shows the proposed method can provide similar performance with the benefit of reduced complexity.

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