scholarly journals On the Design of Hyperstable Feedback Controllers for a Class of Parameterized Nonlinearities. Two Application Examples for Controlling Epidemic Models

2019 ◽  
Vol 16 (15) ◽  
pp. 2689 ◽  
Author(s):  
Manuel De la Sen
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Linear Part ◽  
Type Inequality ◽  
Epidemic Models ◽  
Time Varying ◽  
Input Output ◽  
Controlled System ◽  
Feed Forward

This paper studies the hyperstability and the asymptotic hyperstability of a single-input single-output controlled dynamic system whose feed-forward input-output dynamics is nonlinear and eventually time-varying consisting of a linear nominal part, a linear incremental perturbed part and a nonlinear and eventually time-varying one. The nominal linear part is described by a positive real transfer function while the linear perturbation is defined by a stable transfer function. The nonlinear and time-varying disturbance is, in general, unstructured but it is upper-bounded by the combination of three additive absolute terms depending on the input, output and input-output product, respectively. The non-linear time-varying feedback controller is any member belonging to a general class which satisfies an integral Popov’s-type inequality. This problem statement allows the study of the conditions guaranteeing the robust stability properties under a variety of the controllers designed for the controlled system and controller disturbances. In this way, set of robust hyperstability and asymptotic hyperstability of the closed-loop system are given based on the fact that the input-output energy of the feed-forward controlled system is positive and bounded for all time and any given initial conditions and controls satisfying Popov’s inequality. The importance of those hyperstability and asymptotic hyperstability properties rely on the fact that they are related to global closed-loop stability, or respectively, global closed-loop asymptotic stability of the same uncontrolled feed-forward dynamics subject to a great number of controllers under the only condition that that they satisfy such a Popov’s-type inequality. It is well-known the relevance of vaccination and treatment controls for Public Health Management at the levels of prevention and healing. Therefore, two application examples concerning the linearization of known epidemic models and their appropriate vaccination and/or treatment controls on the susceptible and infectious, respectively, are discussed in detail with the main objective in mind of being able of achieving a fast convergence of the state- trajectory solutions to the disease- free equilibrium points under a wide class of control laws under deviations of the equilibrium amounts of such populations.

scholarly journals On the Use of Entropy Issues to Evaluate and Control the Transients in Some Epidemic Models

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 534 ◽  
Author(s):  
Manuel De la Sen ◽  
Raul Nistal ◽  
Asier Ibeas ◽  
Aitor J. Garrido
Keyword(s):  
Differential Equation ◽  
Ad Hoc ◽  
Equilibrium Points ◽  
Time Instant ◽  
Equation Model ◽  
Epidemic Models ◽  
Time Varying ◽  
Feedback Information ◽  
First Order ◽  
Log Normal

This paper studies the representation of a general epidemic model by means of a first-order differential equation with a time-varying log-normal type coefficient. Then the generalization of the first-order differential system to epidemic models with more subpopulations is focused on by introducing the inter-subpopulations dynamics couplings and the control interventions information through the mentioned time-varying coefficient which drives the basic differential equation model. It is considered a relevant tool the control intervention of the infection along its transient to fight more efficiently against a potential initial exploding transmission. The study is based on the fact that the disease-free and endemic equilibrium points and their stability properties depend on the concrete parameterization while they admit a certain design monitoring by the choice of the control and treatment gains and the use of feedback information in the corresponding control interventions. Therefore, special attention is paid to the evolution transients of the infection curve, rather than to the equilibrium points, in terms of the time instants of its first relative maximum towards its previous inflection time instant. Such relevant time instants are evaluated via the calculation of an “ad hoc” Shannon’s entropy. Analytical and numerical examples are included in the study in order to evaluate the study and its conclusions.

A Space Function Approach to the Hyperstability and the Average Hyperstability of Distributed Systems With Space-Varying Linear Parts and Time-Varying Gains

1975 ◽  
Vol 97 (4) ◽  
pp. 345-353 ◽  
Author(s):  
G. Jumarie
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
Broad Class ◽  
Linear Part ◽  
Function Approach ◽  
Distributed Parameter ◽  
Time Varying ◽  
Function Concept ◽  
Distributed Transfer Function ◽  
Hyperstability Theory

We propose an extension of the Popov’s hyperstability theory which applies to a class of single-control distributed systems in which the linear part depends explicitely upon the distributed parameter, z. The nonlinearness of these systems is expressed by means of the control. The main features of our results are the following: (i) The hyperstability conditions that we obtain involve specific z-dependent functions which we can consider as being extensions of the transfer function concept; (ii) they also involve integrals with respect to the distributed parameter, which express an averaging effect of this latter. Then systems in which the admissible controls are defined via time-varying conditions are investigated. For such systems, we define the concept of “average hyperstability” in time, and average hyperstability conditions are given. Similar problems are solved for multi-control distributed systems. As an application we show how these results yield a broad class of absolute stability conditions for distributed systems: they are space averaging conditions and they may apply when other criteria are in-applicable. Three examples are given: the last one illustrates how a space-describing function approach can be used to determine the distributed transfer function of the system.

A New Architecture for Set-Point Control of Robotic Manipulators With Time-Varying Input/Output Delays

2011 ◽  
Author(s):  
Yen-Chen Liu ◽  
Nikhil Chopra
Keyword(s):  
Closed Loop ◽  
Rate Of Change ◽  
Time Varying ◽  
Input Output ◽  
Closed Loop System ◽  
Set Point ◽  
Point Control ◽  
Set Point Control ◽  
The Stability ◽  
Two Degree Of Freedom

In this paper we study the classical set-point control problem for rigid robots when there are time-varying delays in the input-output channels. It has been demonstrated earlier that scattering variables together with additional gains can be utilized to stabilize the closed loop system in the presence of time-varying delays. However, this architecture is not able to guarantee asymptotic regulation to the desired configuration, and the stability depends on the maximum rate of change of the time-varying delays in the communication. Hence, in this paper, we present a new architecture where scattering variables and position feedback are utilized to guarantee stability and asymptotic convergence of the regulation error to the origin while simultaneously relaxing a significant assumption on the rate of change of delays. The proposed algorithm is numerically verified on a two-degree-of-freedom manipulator.

Damage Identification Using Sensitivity-Enhancing Control and Identified Models

2005 ◽  
Vol 128 (2) ◽  
pp. 210-220 ◽  
Author(s):  
Jason A. Solbeck ◽  
Laura R. Ray
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Damage Identification ◽  
Structural Models ◽  
Damage Parameter ◽  
Measured Parameter ◽  
Parameter Vector ◽  
Input Output ◽  
Output Data ◽  
Torsional System

This paper investigates a coherence approach for locating structural damage using modal frequencies and transfer function parameters identified from input-output data using Observer/Kalman filter identification (OKID). Autonomous damage identification using such forward methods generally require (i) a structural model by which to relate measured and predicted modal properties induced by damage, and (ii) good sensitivity of modal parameter changes to damage states. Using the coherence approach, a damage parameter vector comprised of a finite set of modal frequencies and transfer function parameters is hypothesized for each damage case using either identified or analytic structural models. Measured parameter vectors are extracted from experimental input-output data for a damaged structure using OKID and are compared to hypotheses to determine the most likely damage state. The richness of the parameter vector set, which is comprised of high-quality frequency measurements and lower-quality transfer function parameters, is evaluated in order to determine the ability to uniquely localize damage. The method is evaluated experimentally using a three-degree-of-freedom torsional system and a space-frame truss. Damage parameter hypotheses are generated from a model of the healthy structure developed by system identification in the torsional system, and an analytic model is used to generate damage hypotheses for the truss structure. Feedback control laws enhance the parameter vectors by including closed-loop modal frequencies in order to reduce noise sensitivity and improve uniqueness of parameter vector hypotheses to each damage case. Results show improvements in damage identification using damage parameter vectors comprised of open- and closed-loop modal frequencies, even when model error exists in structural models used to form damage parameter vector hypotheses.

scholarly journals Realistic Aspects of Simulation Models for Fake News Epidemics over Social Networks

2021 ◽  
Vol 13 (3) ◽  
pp. 76
Author(s):  
Quintino Francesco Lotito ◽  
Davide Zanella ◽  
Paolo Casari
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Simulation Models ◽  
Epidemic Models ◽  
Time Varying ◽  
Fake News ◽  
Network Access ◽  
Spreading Process ◽  
Network Topologies ◽  
Access Patterns

The pervasiveness of online social networks has reshaped the way people access information. Online social networks make it common for users to inform themselves online and share news among their peers, but also favor the spreading of both reliable and fake news alike. Because fake news may have a profound impact on the society at large, realistically simulating their spreading process helps evaluate the most effective countermeasures to adopt. It is customary to model the spreading of fake news via the same epidemic models used for common diseases; however, these models often miss concepts and dynamics that are peculiar to fake news spreading. In this paper, we fill this gap by enriching typical epidemic models for fake news spreading with network topologies and dynamics that are typical of realistic social networks. Specifically, we introduce agents with the role of influencers and bots in the model and consider the effects of dynamical network access patterns, time-varying engagement, and different degrees of trust in the sources of circulating information. These factors concur with making the simulations more realistic. Among other results, we show that influencers that share fake news help the spreading process reach nodes that would otherwise remain unaffected. Moreover, we emphasize that bots dramatically speed up the spreading process and that time-varying engagement and network access change the effectiveness of fake news spreading.

Reliability of nonlinear stochastic controlled systems considering the dynamics of sensors and actuators

2021 ◽  
pp. 107754632110037
Author(s):  
Sun Jiaojiao ◽  
Xia Lei ◽  
Ying Zuguang ◽  
Huan Ronghua ◽  
Zhu Weiqiu
Keyword(s):  
Closed Loop ◽  
First Passage Time ◽  
Hamiltonian Function ◽  
Small Time ◽  
Kolmogorov Equation ◽  
Sensors And Actuators ◽  
First Passage ◽  
Controlled System ◽  
Main Structure ◽  
Controlled Systems

A closed-loop controlled system usually consists of the main structure, sensors, and actuators. The dynamics of sensors and actuators may influence the motion of the main structure. This article presents an analytical study on the first-passage reliability of a nonlinear stochastic controlled system under the consideration of the dynamics of sensors and actuators. The coupled dynamic equations of the controlled systems with sensors and actuators are first given, which are further integrated into a controlled, randomly excited, dissipated Hamiltonian system. By applying the stochastic averaging method for quasi-Hamiltonian systems, a one-dimensional averaged differential equation for the Hamiltonian function is obtained. The backward Kolmogorov equation associated with the averaged equation is then derived for the first-passage reliability analysis, from which the approximate reliability function and probability density of first-passage time are obtained. The accuracy of the proposed procedure is demonstrated by an example. A comparative analysis of the reliability of the system with/without sensors and actuators is carried out, which indicates that ignoring sensors and actuators will make underestimation of the reliability of the closed-loop system with small time. However, when time increases, there appears the opposite trend. Our findings provide a reference for control strategy design.

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