Optimized fast non-singular integral terminal sliding mode control of immune response and HCMV infection of renal transplant recipient.

Kidneys are the most commonly transplanted organs, and renal transplant is the best treatment for patients with advanced stages of renal disease. Immunosuppressive drugs are used after renal transplant to prevent the body from rejecting the transplanted kidney and ensure its proper kidney functioning. However, suppression of the immune system increases the risk of viral infections and other complications. Therefore, careful monitoring and management of immunosuppressive and antiviral drugs are essential for the success of the transplants. This article presents a hybrid fast non-singular integral terminal sliding mode control technique to adjust the efficacies of these drugs in renal transplant recipients, ensuring successful transplants and preventing viral infections. The proposed strategy tracks system trajectories to reference values and adjusts the treatment plan accordingly. The Lyapunov stability theorem is used to prove the asymptotic stability of the closed-loop system. Several simulation studies are conducted in MATLAB/Simulink environment to evaluate the performance of the proposed control technique in maintaining a balance between over-suppression and under-suppression. Genetic Algorithm is used to optimize the gain values to further improve the performance of the proposed control technique. Its performance is compared with two other variants of terminal sliding mode controllers to demonstrate its effectiveness against them.

Computational investigation of stochastic Zika virus optimal control model using Legendre spectral method.

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. For R 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while for R 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios.

Backstepping based intelligent control of tractor-trailer mobile manipulators with wheel slip consideration.

In this research, a new hybrid backstepping control strategy based on a neural network is proposed for tractor-trailer mobile manipulators in the presence of unknown wheel slippage and disturbances. To minimize the negative impacts of wheel slippage, the desired velocities of the tractor's wheels are computed with a proposed kinematic control model with an adaptive term. As the system's dynamical model contains unavoidable uncertainties, model-based backstepping control technique is unable to effectively manage these systems. Hence, the proposed controller blends a radial basis function neural network with the merits of a dynamical model-based backstepping approach. The neural networks are employed to approximate the non-linear unknown smooth function. To minimize the impact of external disturbances, and network reconstruction error an adaptive term is added to the control law. The Lyapunov theorem and Barbalat's lemma are employed to guarantee the stability of the control method. The tracking error is shown to be bounded and to rapidly converge to zero with the proposed method. To demonstrate the efficacy and validity of the control mechanism, comparison simulation results are presented.

Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

Stability analysis of a metapopulation model for the dynamics of malaria's spread including climatic factors.

Eradicating malaria remains a big challenge for computer scientists, mathematicians, epidemiologists, entomologists, physicians and many others. Their approaches range from recovering patients to eradicating the disease. However, collaboration, not always efficient between all these scientists, leads to the implementation of incomplete prototypes or to an under-exploitation of their results. Environmental and climatic factors are part of these elements that are usually omitted by computer scientists and mathematicians in the modelling of the malaria spread dynamic. Tropical countries, most affected by the disease are also mostly underdeveloped or developing countries, and therefore, statistical data are often lacking or difficult to access. Populations are constantly in motion over ecosystems with different environmental and climatic conditions, from a region to another. In this paper, we analyse the global asymptotic stability at the disease-free equilibrium of a metapopulation model including climatic factors.

Tube-based model predictive control for linear systems with bounded disturbances and input delay.

This paper proposes a tube-based model predictive control strategy for linear systems with bounded disturbances and input delay to ensure input-to-state stability. Firstly, the actual disturbed system is decomposed into a nominal system without disturbances and an error system. For the nominal system, solving an optimization problem, where the delayed control input is set as an optimization variable, yields a nominal control law that enables the nominal state signal to approach to zero. Then, for the error system, the Razumikhin approach is used to identify a robust control invariant set. Using the set invariance theorem, an ancillary control law is developed to confine the error state signal in the invariant set. Combining the two results, we obtain a control law that enables the state signal to remain within a robustly invariant tube. Finally, the effectiveness of the developed control strategy is validated by simulations.

Mathematical analysis of a modified Volterra-Leslie chemostat Model.

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.

What are the key stability challenges in high-bandwidth, non-minimum phase systems with time-varying, and non-smooth delays?

The analysis and control of stability in high-bandwidth systems characterized by non-minimum phase delays represent a formidable challenge within the realm of control theory and engineering. This research aims to address the pivotal question of whether it is feasible to enhance the stability of such intricate systems. These systems inherently possess uncertain and swiftly changing delay characteristics, rendering them exceptionally demanding to control effectively. In the course of this investigation, we embark on a comprehensive exploration of the theoretical underpinnings of the stability of high-bandwidth, non-minimum phase delay systems. This encompassing inquiry encompasses a meticulous consideration of both derivative-delay and piecewise continuous delay components. To underpin our analysis, we judiciously incorporate feedback mechanisms, drawing upon mathematical tools such as the Jensen inequality and Lyapunov-based methodologies to rigorously establish stability conditions. Furthermore, our exploration extends to encompass the concept of input-output stability and complements it with the notion of asymptotic stability, thereby ensuring that the systems in question exhibit uniform stability across diverse temporal domains. The outcomes of our investigation furnish compelling evidence that by harnessing the power of discrete-time Lyapunov-Krasovskii functionals, it becomes conceivable to circumscribe the maximum delay within predefined thresholds. This achievement holds the promise of enhancing stability in non-minimum phase delay systems characterized by high bandwidth. These findings have far-reaching implications, profoundly influencing the design and control paradigms across a spectrum of engineering applications. Notably, this impact extends to areas such as communication networks, real-time control systems, and robotics, where the mitigation of instability due to non-minimum phase delays has been an enduring challenge.

Design of robust fuzzy iterative learning control for nonlinear batch processes.

In this paper, a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes is proposed. By employing the local-sector nonlinearity method, the nonlinear batch process is represented by a 2D uncertain T-S fuzzy model with non-repetitive disturbances. Then, the feedback control is integrated with the ILC scheme to be investigated under the constructed model. Sufficient conditions for robust asymptotic stability and 2D $ H_\infty $ performance requirements of the resulting closed-loop fuzzy system are established based on Lyapunov functions and some matrix transformation techniques. Furthermore, the corresponding controller gains can be derived from a set of linear matrix inequalities (LMIs). Finally, simulations on the three-tank system and the highly nonlinear continuous stirred tank reactor (CSTR) are carried out to prove the feasibility and efficiency of the proposed approach.

Dynamic analysis of a bacterial resistance model with impulsive state feedback control.

Bacterial resistance caused by prolonged administration of the same antibiotics exacerbates the threat of bacterial infection to human health. It is essential to optimize antibiotic treatment measures. In this paper, we formulate a simplified model of conversion between sensitive and resistant bacteria. Subsequently, impulsive state feedback control is introduced to reduce bacterial resistance to a low level. The global asymptotic stability of the positive equilibrium and the orbital stability of the order-1 periodic solution are proved by the Poincaré-Bendixson Theorem and the theory of the semi-continuous dynamical system, respectively. Finally, numerical simulations are performed to validate the accuracy of the theoretical findings.

Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay.

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established. Next, the global asymptotic stability for the system around the positive equilibrium is gained by applying the functional differential equation theory and constructing a proper Lyapunov function. Last, some numerical examples verify the validity and feasibility of previous theoretical results.

Modeling and analysis of the transmission dynamics of cystic echinococcosis: Effects of increasing the number of sheep.

A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.

Novel results on asymptotic stability and synchronization of fractional-order memristive neural networks with time delays: The 0<뫲1 case.

This paper investigates the asymptotic stability and synchronization of fractional-order (FO) memristive neural networks with time delays. Based on the FO comparison principle and inverse Laplace transform method, the novel sufficient conditions for the asymptotic stability of a FO nonlinear system are given. Then, based on the above conclusions, the sufficient conditions for the asymptotic stability and synchronization of FO memristive neural networks with time delays are investigated. The results in this paper have a wider coverage of situations and are more practical than the previous related results. Finally, the validity of the results is checked by two examples.

A New Decomposition of the Graph Laplacian and the Binomial Structure of Mass-Action Systems.

We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible core matrix, the vector of tree constants, and the incidence matrix of an auxiliary graph, representing an order on the vertices. Depending on the particular order, the core matrix has additional properties. Our results are graph-theoretic/algebraic in nature. As a first application, we further clarify the binomial structure of (weakly reversible) mass-action systems, arising from chemical reaction networks. Second, we extend a classical result by Horn and Jackson on the asymptotic stability of special steady states (complex-balanced equilibria). Here, the new decomposition of the graph Laplacian allows us to consider regions in the positive orthant with given monomial evaluation orders (and corresponding polyhedral cones in logarithmic coordinates). As it turns out, all dynamical systems are asymptotically stable that can be embedded in certain binomial differential inclusions. In particular, this holds for complex-balanced mass-action systems, and hence, we also obtain a polyhedral-geometry proof of the classical result.

Dynamics of consumer-resource reaction-diffusion models: single and multiple consumer species.

A consumer-resource reaction-diffusion model with a single consumer species was proposed and experimentally studied by Zhang et al.(Ecol Lett 20:1118-1128, 2017). Analytical study on its dynamics was further performed by He et al.(J Math Biol 78:1605-1636, 2019). In this work, we completely settle the conjecture proposed by He et al.(J Math Biol 78:1605-1636, 2019) about the global dynamics of the consumer-resource model for small yield rate. We then study a multi-species consumer-resource model where all the consumer species compete with each other through depression of the limited resources by consumption and there is no direct competition between them. We show that in this case, all consumer species persist uniformly, which implies that "competition exclusion" phenomenon will never happen. We also clarify its dynamics in both homogeneous and heterogeneous environments under various circumstances.

$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay.

This paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the considered MNN. A criterion on the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability is proposed using a Lyapunov functional, the Bessel-Legendre inequality, and the convex combination inequality. Then, a linear matrix inequalities-based design scheme for the required output-feedback controller is developed by decoupling nonlinear terms. Finally, two examples are presented to verify the proposed $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability criterion and design method.

Modelling the impact of vaccination and environmental transmission on the dynamics of monkeypox virus under Caputo operator.

In this study, we examine the impact of vaccination and environmental transmission on the dynamics of the monkeypox. We formulate and analyze a mathematical model for the dynamics of monkeypox virus transmission under Caputo fractional order. We obtain the basic reproduction number, the conditions for the local and global asymptotic stability for the disease-free equilibrium of the model. Under the Caputo fractional order, existence and uniqueness solutions have been determined using fixed point theorem. Numerical trajectories are obtained. Furthermore, we explored some of the sensitive parameters impact. Based on the trajectories, we hypothesised that the memory index or fractional order could use to control the Monkeypox virus transmission dynamics. We observed that if the proper vaccination is administrated, public health education is given, and practice like personal hygiene and proper disinfection spray, the infected individuals decreases.

Asymptotic stabilization of a transformed quadrotor model using energy-shaping method: Theory and experiments.

This note presents a new passivity-based controller that ensures asymptotic stability for quadrotor position without solving partial differential equations or performing a partial dynamic inversion. After a resourceful change of coordinates, a pre-feedback controller, and a backstepping stage on the yaw angle dynamic, it is possible to identify new quadrotor cyclo passive outputs. Then, a simple proportional-integral controller of these cyclo-passive outputs completes the design. The cyclo-passive outputs allow the construction of an energy-based Lyapunov function that includes five out of six quadrotor degrees of freedom and guarantees asymptotic stability of the desired equilibrium. Moreover, the constant velocity reference tracking problem is solved with a slight modification to the proposed controller. Finally, the approach is validated through simulations and real-time experimental results.

Global stability of a continuous bioreactor model under persistent variation of the dilution rate.

In this work, the global stability of a continuous bioreactor model is studied, with the concentrations of biomass and substrate as state variables, a general non-monotonic function of substrate concentration for the specific growth rate, and constant inlet substrate concentration. Also, the dilution rate is time varying but bounded, thus leading to state convergence to a compact set instead of an equilibrium point. Based on the Lyapunov function theory with dead-zone modification, the convergence of the substrate and biomass concentrations is studied. The main contributions with respect to closely related studies are: i) The convergence regions of the substrate and biomass concentrations are determined as function of the variation region of the dilution rate (D) and the global convergence to these compact sets is proved, considering monotonic and non-monotonic growth functions separately; ii) several improvements are proposed in the stability analysis, including the definition of a new dead zone Lyapunov function and the properties of its gradient. These improvements allow proving convergence of substrate and biomass concentrations to their compact sets, while tackling the interwoven and nonlinear nature of the dynamics of biomass and substrate concentrations, the non-monotonic nature of the specific growth rate, and the time-varying nature of the dilution rate. The proposed modifications are a basis for further global stability analysis of bioreactor models exhibiting convergence to a compact set instead of an equilibrium point. Finally, the theoretical results are illustrated through numerical simulation, showing the convergence of the states under varying dilution rate.

Global dynamics and pattern formation for predator-prey system with density-dependent motion.

In this paper, we concern with the predator-prey system with generalist predator and density-dependent prey-taxis in two-dimensional bounded domains. We derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the Lyapunov functionals. In addition, by linear instability analysis and numerical simulations, we conclude that the prey density-dependent motility function can trigger the periodic pattern formation when it is monotone increasing.