GLOBAL STABILIZATION OF LINEAR SYSTEMS WITH BOUNDED CONTROLS USING STATE-DEPENDENT SATURATION FUNCTIONS

By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach.

Saturation functions of non-linear standing waves

All harmonics of the non-linear standing wave tend to saturate when the excitation is strong enough. In the present work, saturation functions are found from the experimental laws of saturation, so that the physical significance thereof may be investigated

The Influence of Saturated and Bilinear Incidence Functions on the Dynamical Behavior of HIV Model Using Galerkin Scheme Having a Polynomial of Order Two

Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications.Mathematical modelling has been widely used in order to better understand the transmission,treatment,and prevention of infectious diseases.Herein,we study the dynamics of a human immunodeficiency virus(HIV)infection model with four variables:S(t),I(t),C(t),and A(t)the susceptible individuals;HIV infected individuals(with no clinical symptoms of AIDS);HIV infected individuals(under ART with a viral load remaining low),and HIV infected individuals with two different incidence functions(bilinear and saturated incidence functions).A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of themodel.The influence of different clinical parameters on the dynamical behavior of S(t),I(t),C(t)and A(t)is described and analyzed.All the results are depicted graphically.On the other hand,we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation,heat flux,hall impact,variable heat source,and nanomaterial.The flow is considered to be 2D,boundary layer,viscous,incompressible,laminar,and unsteady.Sufficient transformations turn governing connected PDEs intoODEs,which are solved using the proposed scheme.To justify the envisaged problem,a comparison of the current work with previous literature is presented.

Multi-level gait transition model for a new type of arthropod robot

To realize the continuous and variable gait transition for a new type of arthropod robot, a multi-level gait transition model is studied in this paper. The model is composed of central pattern generator （CPG） and saturation function. The CPG consists of four pairs of oscillators which can ex- hibit rhythmic activity when given stimulation signal S that lies in the range of saturation function. All oscillators receive the same S, but each pair of oscillators has different saturation functions. Multi- level gait transition can be realized when S changes regularly, as the oscillators start or stop oscilla- ting at different times. After computer simulation, the gait transition model is implemented in the ar- thropod robot. The experimental results show that ideal gait transition for the arthropod robot can be realized with the multi-level gait transition model.

Fluid substitution in NMR T_(2)distribution and resistivity independent saturation computation using synthetic capillary pressure data

Petrophysicists and reservoir engineers utilise the capillary pressure and saturation-height function for calculating the water saturation of any reservoir,at a given height above the free water level.The results have a big impact on reserve estimation.The majority of capillary pressure studies are carried out in labs with core data.Cores,on the other hand,are usually altered from their original state before being delivered to laboratories.Moreover,the accuracy of discrete sets of core data in describing entire reservoir parameters,is still up for debate.Prediction of the capillary pressure curve in reservoir condition is an important subject that is challenging to perform.The use of nuclear magnetic resonance(NMR)logs for oil and gas exploration has grown in popularity over the last few decades.However,most of the time the utilization of the data is limited for evaluating porosity-permeability,distributions and computation of irreducible water saturation.After the advent of fluid substitution methods,NMR T_(2)distributions may now be used to synthesize core equivalent capillary pressure curves.Using fluid substitution workflow,our study introduces a better approach for obtaining capillary pressure curves from the NMR T_(2)distribution.The available core data has been used to calculate calibration parameters for better saturation height modelling.The workflow introduces a novel approach in resistivity independent saturation computation.In the exploratory wells of our study area,computed water saturation derived from the saturation height function exhibits encouraging agreement with resistivity based water saturation from multi-mineral model.The NMR based saturation height modelling approach has been included in study area for the first time so far.

DYNAMICS OF SIS EPIDEMIC MODEL WITH THE STANDARD INCIDENCE RATE AND SATURATED TREATMENT FUNCTION

An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the popula- tion over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov-Takens bifurca- tion. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions, Numerical simulations are consistent with our obtained results in the- orems, which show that improving the efficiency and capacity of treatment is important for control of disease.

Transmission dynamics of onchocerciasis with two classes of infection and saturated treatment function

A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.