scholarly journals Identification of System with Bouc-Wen Hysteresis

2019 ◽  
Vol 224 ◽  
pp. 01003
Author(s):  
Nikolay Karabutov
Keyword(s):  
Adaptive System ◽  
Adaptive Algorithms ◽  
Identification System ◽  
Model Parameters ◽  
Adaptive Identification ◽  
Identification Of Parameters ◽  
Adaptive Observers ◽  
The Stability ◽  
Lyapunov Second Method ◽  
Lyapunov Vector

A method of adaptive identification of parameters for a system with Bouc-Wen hysteresis has been developed. The method is based on the use of adaptive observers and resolves the problem of stability of the identification system. Adaptive algorithms of identification were obtained using the Lyapunov second method. The stability proof of the adaptive system is based on the application of Lyapunov vector functions. Adaptive algorithms for adjusting model parameters were developed obtained and finiteness of trajectories in the adaptive system was pointed out.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

ADAPTIVE IDENTIFICATION ALGORITHMS FOR AR SYSTEM DRIVEN BY CHAOTIC SEQUENCE

2003 ◽  
Vol 13 (04) ◽  
pp. 963-972 ◽  
Author(s):  
BAO-YUN WANG ◽  
T. W. S. CHOW ◽  
K. T. NG
Keyword(s):  
Communication System ◽  
Adaptive Algorithms ◽  
Chaotic Sequence ◽  
Estimation Accuracy ◽  
Chaotic Communication ◽  
Adaptive Identification ◽  
System Parameters ◽  
Chaotic Sequences ◽  
Simulation Results ◽  
Typical Method

In this article the identification of AR system driven by chaotic sequences is addressed. This problem emerges in chaotic communication system, in which chaos-modulated signal passes through a channel described as an AR system. Two adaptive algorithms are presented to tackle this problem. Compared with the existing algorithms such as MPSV and MNPE, the proposed algorithms have very low computational complexities and can be used to track the system parameters in a slowly time-variant environment. The obtained simulation results illustrate that the proposed scheme can offer a better estimation accuracy than the conventional typical method in the high SNR case.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

Observer-Based Fault Diagnosis of Satellite Systems Subject to Time-Varying Thruster Faults

2006 ◽  
Vol 129 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Wen Chen ◽  
Mehrdad Saif
Keyword(s):  
Fault Diagnosis ◽  
Estimation Error ◽  
Fault Estimation ◽  
Time Varying ◽  
Satellite Systems ◽  
Adaptive Observers ◽  
Error Dynamics ◽  
The Stability ◽  
Estimation Of Time ◽  
Identification Strategy

This paper presents a novel fault diagnosis approach in satellite systems for identifying time-varying thruster faults. To overcome the difficulty in identifying time-varying thruster faults by adaptive observers, an iterative learning observer (ILO) is designed to achieve estimation of time-varying faults. The proposed ILO-based fault-identification strategy uses a learning mechanism to perform fault estimation instead of using integrators that are commonly used in classical adaptive observers. The stability of estimation-error dynamics is established and proved. An illustrative example clearly shows that time-varying thruster faults can be accurately identified.

scholarly journals Using the LIST model to Estimate the Effects of Contact Tracing on COVID-19 Endemic Equilibria in England and its Regions

2020 ◽  
Author(s):  
Rosalyn J. Moran ◽  
Alexander J. Billig ◽  
Maell Cullen ◽  
Adeel Razi ◽  
Jean Daunizeau ◽  
...  
Keyword(s):  
Endemic Equilibrium ◽  
Contact Tracing ◽  
Model Parameters ◽  
Infection Rates ◽  
Stable States ◽  
Medium Term ◽  
The Stability ◽  
Lower Death Rate ◽  
The Impact ◽  
List Model

AbstractGovernments across Europe are preparing for the emergence from lockdown, in phases, to prevent a resurgence in cases of COVID-19. Along with social distancing (SD) measures, contact tracing – find, track, trace and isolate (FTTI) policies are also being implemented. Here, we investigate FTTI policies in terms of their impact on the endemic equilibrium. We used a generative model – the dynamic causal ‘Location’, ‘Infection’, ‘Symptom’ and ‘Testing’ (LIST) model to identify testing, tracing, and quarantine requirements. We optimised LIST model parameters based on time series of daily reported cases and deaths of COVID-19 in England— and based upon reported cases in the nine regions of England and in all 150 upper tier local authorities. Using these optimised parameters, we forecasted infection rates and the impact of FTTI for each area—national, regional, and local. Predicting data from early June 2020, we find that under conditions of medium-term immunity, a ‘40%’ FTTI policy (or greater), could reach a distinct endemic equilibrium that produces a significantly lower death rate and a decrease in ICU occupancy. Considering regions of England in isolation, some regions could substantially reduce death rates with 20% efficacy. We characterise the accompanying endemic equilibria in terms of dynamical stability, observing bifurcation patterns whereby relatively small increases in FTTI efficacy result in stable states with reduced overall morbidity and mortality. These analyses suggest that FTTI will not only save lives, even if only partially effective, and could underwrite the stability of any endemic steady-state we manage to attain.

Modeling the Vibratory Drilling Process

1999 ◽  
Author(s):  
Stephen A. Batzer ◽  
Alexander M. Gouskov ◽  
Sergey A. Voronov
Keyword(s):  
Rotational Velocity ◽  
Time Lag ◽  
Chip Thickness ◽  
Cutting Conditions ◽  
Model Parameters ◽  
Drilling Process ◽  
Workpiece Material ◽  
Velocity Amplitude ◽  
The Stability

Abstract The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the entrance of the cutting tool into workpiece material and exit. Model parameters include the actual rigidity of the tool and workpiece, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. The stability conditions of excited vibrations are also investigated. Calculated bifurcation diagrams make it possible to derive the domain of system parameters along with the determination of optimal cutting conditions.

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