Analysis of global behavior in a diffusive tuberculosis epidemic model structured by ages of latency and infection

This article aims to investigate the neural network (NN) nonsingular fixed-time adaptive consensus control issue for nonlinear multiagent systems (MASs) with parameter uncertainties. By introducing a generalized intermediate-variable-based disturbance observer (IVBDO), a novel distributed fixed-time NN adaptive controller is constructed based on the quartic Lyapunov function method. Under this protocol, the mismatched external disturbances of each agent are real-time online estimated; meanwhile, the singularity phenomenon during the fixed-time design process can be effectively eliminated. The presented control algorithm not only guarantees that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) but also that the distributed output tracking errors converge to an adjustable compact set of the origin within a fixed-time interval. Simulation results are displayed to check the effectiveness of the suggested approach.

In this paper, we introduce a class of stochastic Hopfield neural network with cross-diffusion (SHNNCD), and for the first time, investigate the existence of the ergodic stationary distribution for SHNNCD under time-varying modified Markov switching. In terms of the internal structure, we incorporate cross-diffusion to fully account for the coupling effects between different neuronal states. In terms of the external environment, compared with traditional Markov switching, we consider a class of Markov switching modified by time-varying functions, including periodic, decaying, and random types. Based on these innovations in both internal structure and external environment, we construct a global Lyapunov function for SHNNCD using graph theory under the consideration of cross-diffusion, and derive the criterion for the existence of the ergodic stationary distribution of SHNNCD. Finally, we verify the validity of our theoretical results through numerical simulations.

Investigation the Epidemiological Transition of Ebola Virus under Contagious Population with Sustainable Extended Fractional Operator.

This paper studies the adaptive fuzzy command-filtered backstepping output feedback control for discrete-time nonlinear multi-agent systems. The command filter is used to address the causality contradiction and the error compensation mechanism can remove the filter errors. Fuzzy logic systems are utilised to approximate the unknown nonlinearities of each agent, and the fuzzy state observer is designed to estimate the immeasurable states. Adaptive updating laws are incorporated into both the observer and controller to handle unknown parameters. By constructing weighted Lyapunov functions, the stability of the closed-loop system is rigorously analyzed, proving that all signals are uniformly ultimately bounded. An example of vehicle system is provided to demonstrate the effectiveness of the proposed control strategy.

The study examines the complex processes of intelligent management of energy resilience in modern healthcare facilities during critical situations, large-scale failures, and prolonged outages of the external centralized power supply. The aim is to develop a comprehensive mathematical model and a Safe Deep Reinforcement Learning (Safe DRL) method that ensures guaranteed compliance with the strict physical and operational constraints of hospital energy systems, even during the intensive training phase of a neural network agent. The objectives are: to formalize in detail the decision-making procedure in an energy system in detail by transitioning to the paradigm of Constrained Markov Decision Processes (CMDP); to develop an innovative mathematical model featuring the implementation of a specialized safety layer based on Lyapunov functions; and to ensure high resilience and autonomy of the system through the implementation of a decentralized Edge-Fog data processing architecture. The methods used include: the theory of Constrained Markov Decision Processes (CMDP), deep reinforcement learning methods based on the Actor-Critic architecture, the mathematical apparatus of Lyapunov stability theory for the analytical correction of actions, and methods of simulation modeling for complex dynamic energy systems. The following results were obtained. In the course of the study, a Safe DRL method was proposed and substantiated, which integrates a Lyapunov-based projection directly into the training loop for the immediate correction of the agent’s control actions. This makes it possible to ensure strict theoretical guarantees of maintaining the required State of Charge (SoC) of battery systems and to prevent critical violations of energy system parameters beyond established safety limits, which is crucial for patient life-support. The effectiveness of the proposed approach was confirmed by a series of numerical experiments in the specialized environment, HospitalEnergyEnv. Under a full blackout scenario, the agent demonstrated adaptability and high accuracy in resource management without any violation of the established physical limits during the entire process of autonomous operation. Conclusions. The scientific novelty of the obtained results lies in the following: the existing optimization model for building energy management systems (BEMS) has been improved by introducing an analytical safety projection mechanism, which minimizes the risks of emergency equipment shutdown during the adaptation of artificial intelligence algorithms; further development of decentralized control methods for critical infrastructure based on Edge-Fog computing has been achieved, which significantly increases system fault tolerance in the event of a loss of connection with the global network and ensures obtaining quasi-optimal solutions in high-dimensional problems. The practical value of this work lies in the potential to create highly reliable autonomous energy systems for critical infrastructure facilities.

In wastewater treatment processes (WWTPs), the presence of aeration equipment faults (actuator faults) prevents the desired tracking control effect of the state-constrained dissolved oxygen concentration (DOC). To solve this problem, an adaptive fixed-time fault-tolerant control (AFTFTC) strategy based on the asymmetric integral barrier Lyapunov function (AIBLF) is developed in this article. First, in order to directly consider asymmetric state constraints in the controller design process, an AIBLF is constructed. Second, a fixed-time FTC method is proposed to compensate for the effects of actuator faults on DOC regulation and achieve fast tracking of the DOC setpoint. Specifically, the adaptive compensation term with DOC asymmetric constraint boundaries is used to estimate the unknown boundary of the actuator bias fault (BF). Furthermore, it is proven that the designed controller can ensure the fixed-time stability of the closed-loop system. Finally, the validity of the control strategy is validated on the benchmark simulation model1 (BSM1).

Reaction networks are a general framework widely used in modeling diverse phenomena in different science disciplines. The dynamical process of a reaction network endowed with mass-action kinetics is a mass-action system which is an ODE defined by a directed graph, the so-called "reaction graph". Endotacticity is a graph property used to study persistence and permanence of mass-action systems. In this paper, we provide a detailed characterization of first-order endotactic reaction graphs. Besides, we provide a sufficient condition for endotacticity of reaction networks which are not necessarily of first-order. Such a characterization of a first-order endotactic reaction graph yields the spectral property of the adjacency matrix of the reaction graph. As a consequence, we prove that every first-order endotactic mass-action system as a linear ODE has a weakly reversible deficiency zero realization, and has a unique equilibrium which is exponentially globally asymptotically stable (and is positive) in each (positive) stoichiometric compatibility class. Using a stability result for asymptotically autonomous differential equations, examples are constructed to illustrate that the global stability results can be extended to mass-action systems of higher-order reaction networks modeled by nonlinear ODEs, which are not necessarily endotactic. Different from the classical approaches for proving global asymptotic stability, the proof does not rely on the construction of a Lyapunov function. This paper may serve as a starting point of characterizing higher-order endotactic reaction graphs and studying global stability of mass-action systems in general.

We consider a degenerate quasilinear Kirchhoff equation with a nonlinear strong damping in a bounded domain. The damping involves the p-Laplacian and is modulated by a function of time. We investigate stability issues for this system. In particular, using a Lyapunov function approach, we prove precise polynomial and logarithmic energy decay estimates.

Output-feedback stochastic nonlinear adaptive control against Markovian jump actuator failures.

In this paper, we develop fixed time and uniform fixed time stability theorems for nonlinear time-varying systems. Specifically, we provide Lyapunov and converse Lyapunov theorems for fixed time stability of continuous nonautonomous systems using Lyapunov functions that satisfy scalar differential inequalities. Furthermore, we show that the regularity of the Lyapunov function is inherently linked to that of the system settling time function. As a result, a converse Lyapunov theorem is presented that can guarantee only the existence of continuous Lyapunov functions. Finally, several illustrative numerical examples are provided to highlight some of the nuances between time-invariant and time-varying fixed time stability theory.

This paper proposes a Q-learning-based algorithm to solve the linear quadratic regulator (LQR) problem for unknown dynamic two-dimensional (2D) discrete-time systems. First, based on the value function formulation constructed using the Lyapunov function framework, algebraic Riccati inequality (ARI) and the Bellman inequality for solving the LQR problem are derived. Subsequently, a suboptimal state feedback controller is obtained based on these inequalities, and an offline policy iteration algorithm based on semi-definite programming (SDP) is introduced. On this foundation, by introducing the concept of Q-learning, the objective function and the Bellman inequality are transformed into the Q-function and its corresponding inequality. A Q-learning-based offline policy iteration equation is then derived, and further, an online policy iteration algorithm based on Q-learning is designed. Data are collected online during each iteration to solve the LQR problem for 2D discrete systems with unknown dynamics. Finally, the effectiveness of the proposed control scheme is validated through two examples.

Automated vehicles enhance road safety and efficiency through Advanced Driver Assistance Systems (ADAS) like Adaptive Cruise Control (ACC). However, the reliance on onboard sensors makes ACC vulnerable to False Data Injection (FDI) attacks, which can compromise safety and stability. To address the lack of formal guarantees in conventional systems, this paper proposes a safety-aware, Lyapunov-based ACC framework resilient to FDI attacks. The framework integrates a Lyapunov function with Control Barrier Functions (CBF). The Lyapunov function synthesizes stable control actions by simultaneously capturing tracking dynamics and real-time estimation of both inter-vehicle distance and the FDI attack. Concurrently, the CBF ensures the actual inter-vehicle distance remains above a predefined safety threshold by constraining the control action space. A Quadratic Programming (QP) formulation coordinates these objectives, resolving the trade-off between safety enforcement and stability preservation. Simulation results demonstrate that the proposed framework effectively ensures stability, maintains safety, and accurately mitigates FDI attacks in ACC systems.

Abstract This study explores an encoder/decoder mismatched parameter for input quantization with an algorithmic recipe to construct LF for CT nonlinear systems. The sign‐definiteness of LF determines the decomposition of the state space into attractive and nonattractive segments; a CT sector is constructed, and CLF determines its boundary. Here, quantization parameters exhibit a time‐varying ratio due to nonsynchronous adjustment, which causes quantization discrepancy issues that are attenuated by a hands‐off controller based on On‐Off logic to acquire asymptotic stability. Theoretical research and simulation investigations confirm the efficacy of the technology for input quantization.

Problem: Controlling nonlinearly parameterized systems with unknown disturbances remains challenging because classical adaptive approaches rely on separation-of-variables and reparameterization techniques, leading to increased parameter dimensions, conservative stability bounds, and implementation complexity. Objective: This paper develops a data-driven predictive fuzzy adaptive control (DD-PFAC) framework that eliminates the need for separation techniques while achieving superior tracking performance and formally certified stability. Novelty: The key innovation is a two-layer architecture. Layer 1 provides direct fuzzy approximation of composite nonlinear functions (system dynamics plus disturbance bound) without parameter reparameterization, reducing parameter complexity from O(qn) to O(nN). Layer 2 employs Hankel matrix-based predictive optimization to adaptively tune both control gains ci(k) and adaptation rates γi(k) online using 80–150 recent input–output samples. Methodology: A Lyapunov function augmented with a prediction-error term is used to prove uniform ultimate boundedness of all closed-loop signals. A projection-based recursive least-squares algorithm updates the gain parameters online while guaranteeing ci(k)≥cmin>0 at all times. Results: Comparative simulations demonstrate 31.4% reduction in integral square error, 27.8% reduction in mean absolute error, and 37.4% reduction in steady-state error versus traditional adaptive fuzzy control. A four-group ablation study confirms that adaptive gain scheduling contributes 27.7% and predictive compensation contributes 6.5% to the total MAE improvement. Robustness tests validate consistent 28–32% performance advantage across sinusoidal, pulse, step, and large-disturbance scenarios.

In this article, a novel Lyapunov-based event-trigger mechanism is proposed to reduce the computation cost of model predictive control (MPC) algorithm for discrete-time nonlinear input-affine safety-critical systems. Unlike conventional approaches that require continuous error monitoring, the proposed mechanism leverages the predictive capability of MPC to determine triggering instants directly based on the evolution of the closed-loop Lyapunov function. Safety and stability are enforced by incorporating control barrier functions (CBFs) and control Lyapunov functions (CLFs) as constraints within the MPC optimization. Furthermore, the recursive feasibility of the proposed event-triggered MPC algorithm is rigorously analyzed, with special attention to the potential infeasibility caused by hard CBF constraints. Input-to-state practical stability (ISpS) of the resulting closed-loop system is also established. Simulation results demonstrate that the proposed event-triggered CBF-CLF-MPC algorithm effectively eliminates unnecessary controller updates, reducing computational consumption while maintaining tracking performance comparable to that of a conventional time-triggered MPC algorithm.

A fractional-order mathematical model of the hepatitis B virus (HBV) consisting of eight distinct compartmental classes, is developed and dynamically analysed in this paper. Using the Banach fixed-point theorem, we rigorously establish the existence and uniqueness of the exact solution. The Routh–Hurwitz criteria and Lyapunov functions are employed to demonstrate the local and global stability of the infection-free equilibrium, respectively. A total of 200 iterations are performed using Latin hypercube sampling with partial rank correlation coefficients, taking the basic reproduction number as the response function. In simulations, lowering the fractional order noticeably softened the infection peaks. When the order was reduced to η = 0.75 , the infected groups reached their maximum levels sooner and with much smaller intensities compared to the case η = 1 . This demonstrates how incorporating memory effects into the model can naturally slow the spread of HBV and lessen the severity of outbreaks.

Abstract To enhance the tracking performance and anti-disturbance capability of the Permanent Magnet Synchronous Motor (PMSM) against various disturbances such as parameter mismatch and load torque fluctuation, this paper proposes a sliding mode control method based on an improved disturbance observer. First, an integral terminal sliding mode surface is designed to improve the steady-state control accuracy and ensure the tracking error converges in finite time. On the basis of the exponential reaching law, a variable function gain term based on system state variables and a power term of the sliding mode surface are introduced to increase the convergence speed while suppressing the chattering phenomenon. An improved disturbance observer is developed, in which a new reaching law and a terminal sliding mode surface are incorporated to improve the disturbance observation accuracy and guarantee the finite-time convergence of the observation error.Real-time compensation of disturbances is achieved through a feedforward compensation mechanism. The stability of the proposed control method is proven using the Lyapunov function. The results demonstrate that the proposed control method outperforms other control methods mentioned in this paper in terms of response speed and control accuracy under different operating conditions. It demonstrates stronger robustness under disturbances, boosting speed tracking performance.

Predefined-time control (PTC) is employed to ensure that the system exhibits more definite and predictable behavior in the motor systems. However, as the system ages, sensors may be adversely affected by malfunctions, resulting in performance degradation, even leading to system instability. Thus, to solve this issue, a predefined-time sensor fault-tolerant control (PTSFTC) is developed for motor systems. First, a predefined-time fault compensation scheme is presented to extract the system operational state information. Then, this fault compensation method can judge the sensor fault within a predefined execution time. Second, a Nussbaum technique-based adaptive compensation strategy is introduced in PTSFTC to compensate for the unknown control coefficient. Then, the proposed PTSFTC can achieve safe and stable operation for motor systems with the unknown control gain. Third, the Lyapunov function is constructed to demonstrate the stability of PTSFTC scheme. Then, the comprehensive stability analysis can guarantee the successful application of PTSFTC. Finally, simulation and experiment results demonstrate that the PTSFTC can ensure the motor system exhibits excellent control performance.

Abstract The pressure control system of a pintle solid rocket motor exhibits strong time-varying and nonlinear characteristics and is subject to various disturbances during operation, which adversely affect its regulation performance. To address these issues, this study first derives the mathematical relationship between pressure and pintle displacement based on the zero-dimensional internal ballistic equations and establishes the system transfer function by incorporating the motor model. Subsequently, a nonsingular terminal sliding mode controller is designed, and its stability is proven using a Lyapunov function. The results demonstrate that the proposed nonsingular terminal sliding mode controller offers significant advantages in response speed, accuracy, and robustness, markedly improving the performance of the pressure control system in a pintle solid rocket motor.