Search Results (15)

Considering the anti-swing control and output constraint problems of shipboard cranes, a nonlinear anti-swing controller based on asymmetric barrier Lyapunov functions (BLFs) is designed. First, model transformation mitigates the explicit effects of ship roll on the desired position and payload fluctuations. Then, a newly constructed BLF is introduced into the energy-based Lyapunov candidate function to generate nonlinear displacement and angle constraint terms to control the rope length and boom luffing angle. Among these, constraints with positive bounds are effectively handled by the proposed BLF. For the swing constraints of the unactuated payload, a carefully designed relevant constraint term is embedded in the controller by constructing an auxiliary signal, and strict theoretical analysis is provided by using a reductio ad absurdum argument. Additionally, the auxiliary signal effectively couples the boom and payload motions, thereby improving swing suppression performance. Finally, the asymptotic stability is proven using LaSalle’s invariance principle. The simulation comparison results indicate that the proposed method exhibits satisfactory performance in swing suppression control and output constraints. In all simulation cases, the payload swing angle complies with the 3° constraint and converges to the desired range within 6 s. This study provides an effective solution to the control challenges of shipboard crane systems operating in confined spaces, offering significant practical value and applicability. Full article

This study develops a modified SIR model (Susceptible–Infected–Recovered) to analyze the dynamics of the COVID-19 pandemic. In this model, infected individuals are categorized into the following two classes: $I_a$, representing asymptomatic individuals, and $I_s$, representing symptomatic individuals. Moreover, accounting for the psychological impacts of COVID-19, the incidence function is nonlinear and expressed as $Sg(I_a,I_s)={\displaystyle \frac{\beta S(I_a+I_s)}{1+\alpha (I_a+I_s)}}$. Additionally, the model is based on a symmetry hypothesis, according to which individuals within the same compartment share common characteristics, and an asymmetry hypothesis, which highlights the diversity of symptoms and the possibility that some individuals may remain asymptomatic after exposure. Subsequently, using the next-generation matrix method, we compute the threshold value ($R_0$), which estimates contagiousness. We establish local stability through the Routh–Hurwitz criterion for both disease-free and endemic equilibria. Furthermore, we demonstrate global stability in these equilibria by employing the direct Lyapunov method and La-Salle’s invariance principle. The sensitivity index is calculated to assess the variation of $R_0$ with respect to the key parameters of the model. Finally, numerical simulations are conducted to illustrate and validate the analytical findings. Full article

We propose a within-host mathematical model for the dynamics of Usutu virus infection, incorporating Crowley–Martin functional response. The basic reproduction number ${\mathfrak{R}}_0$ is found by applying the next-generation matrix approach. Depending on this threshold, parameter, global asymptotic stability of one of the two possible equilibria is also established via constructing appropriate Lyapunov functions and using LaSalle’s invariance principle. We present numerical simulations to illustrate the results and a sensitivity analysis of ${\mathfrak{R}}_0$ was also completed. Finally, we fit the model to actual data on Usutu virus titers. Our study provides new insights into the dynamics of Usutu virus infection. Full article

Exploration of Venus is recently driven by the interest of the scientific community in understanding the evolution of Earth-size planets, and is leading the implementation of missions that can benefit from new design techniques and technology. In this work, we investigate the possibility to implement a microsatellite exploration mission to Venus, taking advantage of (i) weak capture, and (ii) nonlinear orbit control. This research considers the case of a microsatellite, equipped with a high-thrust and a low-thrust propulsion system, and placed in a highly elliptical Earth orbit, not specifically designed for the Earth-Venus mission of interest. In particular, to minimize the propellant mass, phase (i) of the mission was designed to inject the microsatellite into a low-energy capture around Venus, at the end of the interplanetary arc. The low-energy capture is designed in the dynamical framework of the circular restricted 3-body problem associated with the Sun-Venus system. Modeling the problem with the use of the Hamiltonian formalism, capture trajectories can be characterized based on their state while transiting in the equilibrium region about the collinear libration point L1. Low-energy capture orbits are identified that require the minimum velocity change to be established. These results are obtained using the General Mission Analysis Tool, which implements planetary ephemeris. After completing the ballistic capture, phase (ii) of the mission starts, and it is aimed at driving the microsatellite toward the operational orbit about Venus. The transfer maneuver is based on the use of low-thrust propulsion and nonlinear orbit control. Convergence toward the desired operational orbit is investigated and is proven analytically using the Lyapunov stability theory, in conjunction with the LaSalle invariance principle, under certain conditions related to the orbit perturbing accelerations and the low-thrust magnitude. The numerical results prove that the mission profile at hand, combining low-energy capture and low-thrust nonlinear orbit control, represents a viable and effective strategy for microsatellite missions to Venus. Full article

Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle’s invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number $R_{\rho }$ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19. Full article

In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method. Full article

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses which infect the same target, CD$4^{+}$ T cells. This type of cell is considered the main component of the immune system. Since both viruses have the same means of transmission between individuals, HIV-1-infected patients are more exposed to the chance of co-infection with HTLV-I, and vice versa, compared to the general population. The mathematical modeling and analysis of within-host HIV-1/HTLV-I co-infection dynamics can be considered a robust tool to support biological and medical research. In this study, we have formulated and analyzed an HIV-1/HTLV-I co-infection model with humoral immunity, taking into account both latent HIV-1-infected cells and HTLV-I-infected cells. The model considers two modes of HIV-1 dissemination, virus-to-cell (V-T-C) and cell-to-cell (C-T-C). We prove the nonnegativity and boundedness of the solutions of the model. We find all steady states of the model and establish their existence conditions. We utilize Lyapunov functions and LaSalle’s invariance principle to investigate the global stability of all the steady states of the model. Numerical simulations were performed to illustrate the corresponding theoretical results. The effects of humoral immunity and C-T-C transmission on the HIV-1/HTLV-I co-infection dynamics are discussed. We have shown that humoral immunity does not play the role of clearing an HIV-1 infection but it can control HIV-1 infection. Furthermore, we note that the omission of C-T-C transmission from the HIV-1/HTLV-I co-infection model leads to an under-evaluation of the basic HIV-1 mono-infection reproductive ratio. Full article

In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Based on this study, an optimal strategy is proposed to decrease the number of infected cells. Finally, some numerical simulations are presented to illustrate the theoretical findings. Full article

In this paper, a rumor-spreading model with Holling type III functional response was established. The existence of the equilibrium points was discussed. According to the Routh–Hurwitz criteria, the locally asymptotic stability of the equilibrium points was analyzed. The global stability of the equilibrium points was proven based on Lasalle’s invariance principle and generalized Bendixson–Dulac theorem. Numerical simulations were carried out to illustrate the impact of different parameters on the spread of rumors. When the stifling rate $\lambda$ increases, or the predation capacity $\beta$ or the system coming rate $k$ decreases, the number of rumor-spreaders is reduced to extinction. The results provide theory, method and decision support for effectively controlling the spread of rumors. Full article

In this article, we examine the dynamics of a Chikungunya virus (CHIKV) infection model with two routes of infection. The model uses four categories, namely, uninfected cells, infected cells, the CHIKV virus, and antibodies. The equilibrium points of the model, which consist of the free point for the CHIKV and CHIKV endemic point, are first analytically determined. Next, the local stability of the equilibrium points is studied, based on the basic reproduction number (${\mathcal{R}}_0$) obtained by the next-generation matrix. From the analysis, it is found that the disease-free point is locally asymptotically stable if ${\mathcal{R}}_0\le 1$, and the CHIKV endemic point is locally asymptotically stable if ${\mathcal{R}}_0>1$. Using the Lyapunov method, the global stability analysis of the steady-states confirms the local stability results. We then describe our design of an optimal recruitment strategy to minimize the number of infected cells, as well as a nonlinear optimal control problem. Some numerical simulations are provided to visualize the analytical results obtained. Full article

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number ${\mathcal{R}}_0$ using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population. Full article

By using differential equations with discontinuous right-hand sides, a dynamic model for vector-borne infectious disease under the discontinuous removal of infected trees was established after understanding the transmission mechanism of Huanglongbing (HLB) disease in citrus trees. Through calculation, the basic reproductive number of the model can be attained and the properties of the model are discussed. On this basis, the existence and global stability of the calculated equilibria are verified. Moreover, it was found that different $I_0$ in the control strategy cannot change the dynamic properties of HLB disease. However, the lower the value of $I_0$, the fewer HLB-infected citrus trees, which provides a theoretical basis for controlling HLB disease and reducing expenditure. Full article

This paper studies the consensus problem for heterogeneous multi-agent systems with output saturations. We consider the agents to have different dynamics and assume that the agents are neutrally stable and that the communication graph is undirected. The goal of this paper is to achieve the consensus for leaderless and leader-following cases. To solve this problem, we propose the observer-based distributed consensus algorithms, which consists of three parts: the nonlinear observer, the reference generator, and the regulator. Then, we analyze the consensus based on the Lasalle’s Invariance Principle and the input-to-state stability. Finally, we provide numerical examples to demonstrate the validity of the proposed algorithms. Full article

In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 ${}^{+}$ T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium $E{P}_0$ and endemic equilibrium $E{P}_1$ . We derive the basic reproduction number $R_0$ , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle’s invariance principle. We prove that if $R_0<1$ , then $E{P}_0$ is globally asymptotically stable, and if $R_0>1$ , then $E{P}_1$ is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication. Full article

A new two-stage model for assessing the effect of basic control measures, quarantine and isolation, on a general disease transmission dynamic in a population is designed and rigorously analyzed. The model uses the Holling II incidence function for the infection rate. First, the basic reproduction number ( ${\mathcal{R}}_0$ ) is determined. The model has both locally and globally asymptotically stable disease-free equilibrium whenever ${\mathcal{R}}_0<1$ . If ${\mathcal{R}}_0>1,$ then the disease is shown to be uniformly persistent. The model has a unique endemic equilibrium when ${\mathcal{R}}_0>1.$ A nonlinear Lyapunov function is used in conjunction with LaSalle Invariance Principle to show that the endemic equilibrium is globally asymptotically stable for a special case. Full article