scholarly journals Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2076
Author(s):  
Haiyue Chen ◽  
Benedikt Haus ◽  
Paolo Mercorelli
Keyword(s):  
Disease Transmission ◽  
Model Simulation ◽  
Herd Immunity ◽  
Compartmental Models ◽  
Lyapunov Theory ◽  
Practical Stability ◽  
Effective Control ◽  
Controlled System ◽  
Control Laws ◽  
The Stability

Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaranteeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission.

scholarly journals A neural network combined with sliding mode controller for the two-wheel self-balancing robot

2021 ◽  
Vol 10 (3) ◽  
pp. 592
Author(s):  
Duc-Minh Nguyen ◽  
Van-Tiem Nguyen ◽  
Trong-Thang Nguyen
Keyword(s):  
Neural Network ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Sliding Mode Controller ◽  
Control Laws ◽  
Noise Compensation ◽  
Simulation Results ◽  
Balancing Robot ◽  
The Stability

This article presents the sliding control method combined with the selfadjusting neural network to compensate for noise to improve the control system's quality for the two-wheel self-balancing robot. Firstly, the dynamic equations of the two-wheel self-balancing robot built by Euler–Lagrange is the basis for offering control laws with a neural network of noise compensation. After disturbance-compensating, the sliding mode controller is applied to control quickly the two-wheel self-balancing robot reached the desired position. The stability of the proposed system is proved based on the Lyapunov theory. Finally, the simulation results will confirm the effectiveness and correctness of the control method suggested by the authors.

scholarly journals Cooperative Visual-SLAM System for UAV-Based Target Tracking in GPS-Denied Environments: A Target-Centric Approach

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 813 ◽  
Author(s):  
Juan-Carlos Trujillo ◽  
Rodrigo Munguia ◽  
Sarquis Urzua ◽  
Antoni Grau
Keyword(s):  
Position Estimation ◽  
Lyapunov Theory ◽  
Fundamental Aspect ◽  
Control Laws ◽  
Position Information ◽  
Practical Applications ◽  
Aerial Robots ◽  
Localization And Mapping ◽  
Flight Formation ◽  
The Stability

Autonomous tracking of dynamic targets by the use of Unmanned Aerial Vehicles (UAVs) is a challenging problem that has practical applications in many scenarios. In this context, a fundamental aspect that must be addressed has to do with the position estimation of aerial robots and a target to control the flight formation. For non-cooperative targets, their position must be estimated using the on-board sensors. Moreover, for estimating the position of UAVs, global position information may not always be available (GPS-denied environments). This work presents a cooperative visual-based SLAM (Simultaneous Localization and Mapping) system that allows a team of aerial robots to autonomously follow a non-cooperative target moving freely in a GPS-denied environment. One of the contributions of this work is to propose and investigate the use of a target-centric SLAM configuration to solve the estimation problem that differs from the well-known World-centric and Robot-centric SLAM configurations. In this sense, the proposed approach is supported by theoretical results obtained from an extensive nonlinear observability analysis. Additionally, a control system is proposed for maintaining a stable UAV flight formation with respect to the target as well. In this case, the stability of control laws is proved using the Lyapunov theory. Employing an extensive set of computer simulations, the proposed system demonstrated potentially to outperform other related approaches.

Position and attitude tracking of uncertain quadrotor unmanned aerial vehicles based on non-singular terminal super-twisting algorithm

2019 ◽  
Vol 234 (3) ◽  
pp. 396-408
Author(s):  
Walid Alqaisi ◽  
Yassine Kali ◽  
Jawhar Ghommam ◽  
Maarouf Saad ◽  
Vahé Nerguizian
Keyword(s):  
Sliding Mode ◽  
Design Procedure ◽  
Lyapunov Theory ◽  
Effective Control ◽  
Attitude Tracking ◽  
Control Scheme ◽  
The Stability ◽  
Terminal Sliding Surface ◽  
Twisting Algorithm ◽  
Twisting Control

This paper proposes an improved non-singular terminal super-twisting control for the problem of position and attitude tracking of quadrotor systems suffering from uncertainties and disturbances. The super-twisting algorithm is a second-order sliding mode known to be a very effective control used to provide high precision and less chattering for uncertain nonlinear electromechanical systems. The proposed method is based on a non-singular terminal sliding surface with new exponent that solves the problem of singularity. The design procedure and the stability analysis of the closed-loop system using Lyapunov theory are detailed for the considered system. Finally, the proposed control scheme is tested in simulations and by experiments on the parrot-rolling spider quadrotor. Moreover, a comparison is made with the standard super-twisting algorithm in the simulation part. The results obtained show adequate performance in trajectory tracking and chattering reduction.

scholarly journals Individual-based modeling of COVID-19 transmission in college communities

2021 ◽  
Author(s):  
Qimin Huang ◽  
Martial Ndeffo-Mbah ◽  
Anirban Mondal ◽  
Sara Lee ◽  
David Gurarie
Keyword(s):  
Risk Reduction ◽  
Disease Transmission ◽  
Herd Immunity ◽  
The United States ◽  
Transmission Risk ◽  
Effective Control ◽  
Social Activities ◽  
Modeling Framework ◽  
Risk Reduction Measures ◽  
And Control

The ongoing COVID-19 pandemic has created major public health and socio-economic challenges across the United States. Among them are challenges to the educational system where college administrators are struggling with the questions of how to reopen in-person activities while prioritizing student safety. To help address this challenge, we developed a flexible computational framework to model the spread and control of COVID-19 on a residential college campus. The modeling framework accounts for heterogeneity in social interactions, activities, disease progression, and control interventions. The relative contribution of classroom, dorm, and social activities to disease transmission were explored. We observed that the dorm has the highest contribution to disease transmission followed by classroom and social activities. Without vaccination, frequent (weekly) random testing coupled with risk reduction measures (e.g. facial mask,) in classroom, dorm, and social activities is the most effective control strategy to mitigate the spread of COVID-19 on college campuses. Moreover, since random screening testing allows for the successful and early detection of both asymptomatic and symptomatic individuals, it successfully reduces the transmission rate such that the maximum quarantine capacity is far lower than expected to further reduce the economic burden caused from quarantine. With vaccination, herd immunity is estimated to be achievable by 50% to 80% immunity coverage. In the absence of herd immunity, simulations indicate that it is optimal to keep some level of transmission risk reduction measures in classroom, dorm, and social activities, while testing at a lower frequency. Though our quantitative results are likely provisional on our model assumptions, extensive sensitivity analysis confirms the robustness of their qualitative nature.

Robust output feedback trajectory tracking for quadrotors

2018 ◽  
Vol 233 (5) ◽  
pp. 1596-1610 ◽  
Author(s):  
Xiling Shi ◽  
Yunqiang Sun ◽  
Xingling Shao
Keyword(s):  
Sliding Mode ◽  
State Observer ◽  
Lyapunov Theory ◽  
Extended State Observer ◽  
Reference Trajectory ◽  
Extended State ◽  
Control Laws ◽  
Virtual Control ◽  
Output Tracking Control ◽  
The Stability

This paper focuses on robust output tracking control for quadrotors exposed to parametric uncertainties and external disturbances. Based on the back-stepping control principle, the quadrotor dynamics is decomposed into translational and rotational subsystems. To handle the limitation of traditional extended state observer that can only be effective for integral-chain systems, a high-order extended state observer with special structure is developed to estimate the unmeasurable states and the lumped disturbances in rotational subsystem simultaneously. To avoid the tedious analysis and repeated differentiation of virtual control laws in the back-stepping technique, a first-order sliding mode differentiator is introduced to compute the derivative of virtual control law at each step in the presence of disturbances. The stability analysis is established using the Lyapunov theory. Simulation results demonstrate the effectiveness of the proposed control scheme in achieving a guaranteed tracking performance with respect to an 8-shaped reference trajectory.

scholarly journals Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: a mathematical modeling study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Xi Huo ◽  
Jing Chen ◽  
Shigui Ruan
Keyword(s):  
Disease Transmission ◽  
Large Scale ◽  
Transmission Rate ◽  
Control Strategies ◽  
Herd Immunity ◽  
Antibody Prevalence ◽  
Screening Process ◽  
Vaccination Programs ◽  
Prevalence Level ◽  
The Impact

Abstract Background The COVID-19 outbreak in Wuhan started in December 2019 and was under control by the end of March 2020 with a total of 50,006 confirmed cases by the implementation of a series of nonpharmaceutical interventions (NPIs) including unprecedented lockdown of the city. This study analyzes the complete outbreak data from Wuhan, assesses the impact of these public health interventions, and estimates the asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan. Methods By taking different stages of the outbreak into account, we developed a time-dependent compartmental model to describe the dynamics of disease transmission and case detection and reporting. Model coefficients were parameterized by using the reported cases and following key events and escalated control strategies. Then the model was used to calibrate the complete outbreak data by using the Monte Carlo Markov Chain (MCMC) method. Finally we used the model to estimate asymptomatic and undetected cases and approximate the overall antibody prevalence level. Results We found that the transmission rate between Jan 24 and Feb 1, 2020, was twice as large as that before the lockdown on Jan 23 and 67.6% (95% CI [0.584,0.759]) of detectable infections occurred during this period. Based on the reported estimates that around 20% of infections were asymptomatic and their transmission ability was about 70% of symptomatic ones, we estimated that there were about 14,448 asymptomatic and undetected cases (95% CI [12,364,23,254]), which yields an estimate of a total of 64,454 infected cases (95% CI [62,370,73,260]), and the overall antibody prevalence level in the population of Wuhan was 0.745% (95% CI [0.693%,0.814%]) by March 31, 2020. Conclusions We conclude that the control of the COVID-19 outbreak in Wuhan was achieved via the enforcement of a combination of multiple NPIs: the lockdown on Jan 23, the stay-at-home order on Feb 2, the massive isolation of all symptomatic individuals via newly constructed special shelter hospitals on Feb 6, and the large scale screening process on Feb 18. Our results indicate that the population in Wuhan is far away from establishing herd immunity and provide insights for other affected countries and regions in designing control strategies and planing vaccination programs.

A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators

1990 ◽  
Vol 112 (4) ◽  
pp. 618-629 ◽  
Author(s):  
Nader Sadegh ◽  
Roberto Horowitz ◽  
Wei-Wen Kao ◽  
Masayoshi Tomizuka
Keyword(s):  
Lyapunov Theory ◽  
Control Input ◽  
Robot Arm ◽  
Unified Approach ◽  
Parameter Adaptation ◽  
Control Laws ◽  
Position Errors ◽  
Adaptive Compensator ◽  
Mechanical Manipulators ◽  
Repetitive Controller

A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

scholarly journals SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY

2012 ◽  
Vol 54 (1-2) ◽  
pp. 23-36 ◽  
Author(s):  
E. K. WATERS ◽  
H. S. SIDHU ◽  
G. N. MERCER
Keyword(s):  
Infectious Disease ◽  
Spatial Heterogeneity ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Epidemic Models ◽  
Final Size ◽  
Infectious Disease Transmission ◽  
Epidemic Dynamics ◽  
Mean Crowding ◽  
Rate Of Movement

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

scholarly journals Long-term O<sub>3</sub>–precursor relationships in Hong Kong: field observation and model simulation

2017 ◽  
Vol 17 (18) ◽  
pp. 10919-10935 ◽  
Author(s):  
Yu Wang ◽  
Hao Wang ◽  
Hai Guo ◽  
Xiaopu Lyu ◽  
Hairong Cheng ◽  
...  
Keyword(s):  
Hong Kong ◽  
Model Simulation ◽  
Ground Level ◽  
Effective Control ◽  
Photochemical Pollution ◽  
Mixing Ratios ◽  
The Past ◽  
Total Volatile Organic Compounds

Abstract. Over the past 10 years (2005–2014), ground-level O3 in Hong Kong has consistently increased in all seasons except winter, despite the yearly reduction of its precursors, i.e. nitrogen oxides (NOx =  NO + NO2), total volatile organic compounds (TVOCs), and carbon monoxide (CO). To explain the contradictory phenomena, an observation-based box model (OBM) coupled with CB05 mechanism was applied in order to understand the influence of both locally produced O3 and regional transport. The simulation of locally produced O3 showed an increasing trend in spring, a decreasing trend in autumn, and no changes in summer and winter. The O3 increase in spring was caused by the net effect of more rapid decrease in NO titration and unchanged TVOC reactivity despite decreased TVOC mixing ratios, while the decreased local O3 formation in autumn was mainly due to the reduction of aromatic VOC mixing ratios and the TVOC reactivity and much slower decrease in NO titration. However, the decreased in situ O3 formation in autumn was overridden by the regional contribution, resulting in elevated O3 observations. Furthermore, the OBM-derived relative incremental reactivity indicated that the O3 formation was VOC-limited in all seasons, and that the long-term O3 formation was more sensitive to VOCs and less to NOx and CO in the past 10 years. In addition, the OBM results found that the contributions of aromatics to O3 formation decreased in all seasons of these years, particularly in autumn, probably due to the effective control of solvent-related sources. In contrast, the contributions of alkenes increased, suggesting a continuing need to reduce traffic emissions. The findings provide updated information on photochemical pollution and its impact in Hong Kong.

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