Asymptotic Stability Research Articles

Brayton-Moser passivity based controller for constant power load with interleaved boost converter.

A DC microgrid with renewable energy sources can achieve reduced current ripple, higher efficiency, faster dynamics, high voltage gain, and less operational stress by interfacing with an interleaved boost converter (IBC). The stability of an IBC linked to a DC microgrid supplying a constant power load (CPL) can be imperceptibly guaranteed by a conventional controller. A tightly regulated CPL with nonlinear and negative incremental impedance characteristics will lead to stability issues. Uncertainties such as load and line variations will further affect the stability of the system. A nonlinear passivity-based control algorithm requires more attention than a traditional controller to achieve the stability of power converters. This article explains the Brayton-Moser (BM) passivity-based controller (PBC) for a 2-level interleaved boost converter (IBC) interfaced DC microgrid with CPL. The suggested controller can achieve high signal stability by injecting a series-connected virtual impedance. The stability of the proposed controller has been assessed using the Lyapunov stability approach. A BM passivity-based controller for a 2-level IBC with CPL has been derived and investigated under various operating modes using MATLAB and Simulink. It was also observed that the proposed system achieves at least improvement in efficiency and reduction in current ripple. To evaluate the performance of BM Passivity-based controller, a comparative analysis was performed between the suggested controller and the traditional PI controller, which is also included in this paper.

An active queue management method for multiple bottleneck networks based on distributed average tracking

The active queue management (AQM) is a key technology for the information infrastructure and the Internet. The AQM for multiple bottleneck networks is especially challenging than that for single-bottleneck networks because the stability analysis of multiple bottleneck networks is more complex. In this paper, the active queue management problem for multiple bottleneck networks is considered. A novel random early detection algorithm is designed based on distributed average tracking technology, which is used to estimate the global queue length and improve the network's performance. Sufficient conditions for global asymptotic stability of the closed-loop active queue management system are presented, and some simulation results with NS-2 are given. Compared with the RED algorithm, simulation results show that the presented algorithm has smaller oscillations at routers, which highlights its effectiveness.

The Stability of a Predator–Prey Model with Cross-Dispersal in a Multi-Patch Environment

This paper investigates the stability of predator–prey models within multi-patch environments, with a particular focus on the influence of cross-dispersion across patches. We apply Kirchhoff’s matrix tree theorem and Liapunov’s method to derive criteria related to the cross-dispersion topology, thus solving the challenge of determining global asymptotic stability conditions. The method incorporates realistic ecological interactions and spatial heterogeneity, offering a framework for stability analysis. Our findings demonstrate that an appropriate level of cross-dispersion can effectively mitigate oscillations and foster convergence toward equilibrium. Two numerical examples validate these theoretical results and demonstrate the feasibility and effectiveness of the model across multiple patches.

ELLIPSOIDAL DESIGN OF SLIDING MODE CONTROL FOR CAR ACTIVE SUSPENSION SYSTEM

The issue of state feedback sliding mode control (SMC) for a particular kind of active quarter-car suspension system is discussed in this work. The suspension systems' dynamic system is built with the three control objectives of maximal actuator control force, suspension deflection, and ride comfort in mind. The next step is to build the state-feedback controller with the disturbance (vibration) attenuation level in mind to guarantee the asymptotic stability of the closed-loop system. The algorithm for SMC design is introduced. It is predicated on choosing the sliding surface correctly using the invariant ellipsoid approach. The system motion in the sliding mode is guaranteed to be little affected by mismatched disturbances according to the control architecture. Furthermore, the presence of admissible controllers is articulated in terms of LMIs through the use of Lyapunov theory and the linear matrix inequality (LMI) technique. The objective is to create a desired dynamic state-feedback controller when these requirements are met. Lastly, a quarter-car model is used to illustrate how successful a suggested approach is.

Mathematical modeling of an articulated flying vehicle for precise control analysis in grasping highly oscillatory objects

In this research work, a detailed mathematical modeling approach has been taken in order to develop a complete package for the investigation of phenomena associated with the flight dynamics and control of an articulated aerial robot in grasping high weight oscillatory objects such as living creatures. To this end, the origin of forces and moments generated by a moving target is analyzed and the nonlinear differential equations of the system are derived. Then, the model is verified and the effect of target oscillations on the whole system dynamics is investigated. In the next step, due to the nonlinear nature of this under-actuated system and the presence of the force-generating target with unknown dynamics and model parametric and non-parametric uncertainties, two versions of adaptive sliding mode control (A-SMC) are designed to enable the system follows the nominal trajectories in a desirable way without needing to know the upper bounds of the time-varying forces and uncertainties. In this regard, the stability of closed-loop systems is proved based on Lyapunov theory. The performance and robustness of the designed controllers are evaluated and compared through numerical and Monte Carlo simulations with some standard criteria. At the end, the conclusion of this work is presented.

A Control Method for Path Following of AUVs Considering Multiple Factors Under Ocean Currents

To improve the path-following performance of autonomous underwater vehicles (AUVs) under ocean currents, a control method based on line-of-sight with fuzzy controller (FLOS) guidance and the fuzzy sliding mode controller (FSMC) is proposed. This method considers multiple factors affecting guidance and adaptively determines the optimal heading angle through the fuzzy controller to enhance guidance capability. Additionally, a novel FSMC based on Lyapunov stability theory is designed to suppress the influence of model uncertainty and external disturbances on the control system. Simulations and experiments of the proposed control method demonstrate that it can maintain precise tracking under disturbances, improving path-following performance metrics by more than 15%.

Event‐Triggered Adaptive Neural Network Control for 4WS4WD Wheeled Mobile Robot

ABSTRACTIn this article, an event‐triggered adaptive neural network controller based on threshold band is designed for a four wheels independently steered and four wheels independently driven (4WS4WD) mobile robot. The 4WS4WD mobile robot is attracting attention for its excellent motion performance such as manipulation versatility and posture flexibility. However, its control difficulty is increased due to its characteristics of being controlled by eight motors for steering and driving respectively. Also, since the robot itself has limited computing and communication resources, real‐time control cannot be guaranteed. To copy with that, the kinematic and dynamics models are first introduced for the 4WS4WD mobile robot. Second, an adaptive neural network controller with low‐frequency learning rate is utilized to control the mobile robot since there are unknown perturbations in the model. It can maintain system stability while handing unidentified model perturbations. The stability of the controller is demonstrated by Lyapunov stability analysis. An event‐triggered based on threshold band is suggested to lessen the amount of computation in the control process. Finally, the simulation outcomes further demonstrate how the suggested approach can greatly lessen the computational and communication cost while maintaining control performance.

A Generalised Difference Equation and Its Dynamics and Solutions

Rational difference equations have a wide range of applications in various fields of science. To illustrate, the equation xn+1=a+bxnc+dxn,n=0,1,..., known as the Riccati difference equation, has been applied in the field of optics. In this study, the global asymptotic stability of the difference equation xn+1=Axn−2k+j+1B+Cxn−(k+j)xn−2k+j+1,n=0,1,..., is proved. The solutions of this difference equation are obtained by applying the standard iteration method, and the periodicity of these solutions is determined. Furthermore, this difference equation represents a generalisation of the results obtained in previous studies.

Fixed-time adaptive sliding mode-based active rollover prevention control of automated guided vehicles via improved super-twisting observer

As an important component of automated guided vehicle (AGV) active safety systems, the active rollover prevention (ARP) control has been widely studied. In this paper, a fixed-time adaptive sliding mode (FTASM) control strategy based on nested adaptive law (NAL) and improved super-twisting observer (ISTO) is developed for the AGV. Firstly, the lateral and roll motion dynamics of AGV are established, and the ARP problem is transformed into the yaw stability control with constraints. Subsequently, a faster fixed-time stable system-based FTASM composite controller is proposed to guarantee a fixed and faster convergence time of the yaw rate tracking error, such that the rollover stability will reach a region of permissible risk. The adoption of NAL enables the adaptive controller to automatically search the minimum switching gain satisfying the reaching condition of sliding mode, thus the conservative assumption constraint of the disturbance upper bound is released. In addition, an ISTO is developed to estimate the unknown disturbance to further improve the control robustness and attenuate the control chattering. The closed-loop stability analysis is rigorously given by Lyapunov theory. Finally, the performance of the proposed control strategy is validated by hardware-in-loop simulations with Adams and Matlab software and an actual steer-by-wire plant.

Constrained Control of Autonomous Underwater Gliders Based on Disturbance Estimation and Tracking Back Calculation

ABSTRACTThis article presents an anti‐disturbance constrained control scheme for the pitch channel of autonomous underwater gliders subject to internal and external disturbances, as well as actuator saturation. First, the integral control technique is employed to develop a disturbance observer to estimate the overall effect of possible uncertainties and disturbances on the nominal vehicle model, which is referred to as the mismatched lumped disturbance. Then, a disturbance rejection control law is constructed based on the disturbance observer. Following that, a straightforward anti‐windup modification is proposed to handle potential input constraints by using the tracking back calculation technique. Specifically, the difference between saturated and unsaturated control input signals is utilized to create a feedback signal that addresses the disturbance observer input, thereby alleviating system windup during actuator saturation events. Furthermore, the stability of the overall closed‐loop system is established in term of the Lyapunov stability theorem, demonstrating that the tracking error is ultimately bounded. Compared with some existing anti‐windup control schemes, the suggested approach offers intuitive design guidelines, resulting in a simple controller that can be easily implemented. Finally, the effectiveness and robustness of the proposed control scheme are verified through simulation results.

Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

This paper examines a stochastic SEIS epidemic model motivated by Black–Karasinski process. First, it is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption compared with existing stochastic modeling methods. By analyzing the diffusion structure of the model and solving the relevant Kolmogorov–Fokker–Planck equation, a complete characterization for explicitly approximating the stationary density function near some quasi-positive equilibria is provided. Then for the deterministic model, the basic reproduction number and related asymptotic stability are studied. Finally, several numerical examples are given to substantiate our theoretical findings.

Internal Model‐Based Anti‐Disturbances Low‐Level Control for Drones Considering Actuator Dynamics

ABSTRACTLow‐level control plays a critical role in the overall flight performance of drones. Despite some progress, existing methods do not adequately consider the complex electromechanical characteristics of actuators and aerodynamic disturbances of propellers, which deteriorates low‐level control performance. To tackle these issues, we propose a new nonlinear low‐level controller for higher precision control. First, a high‐precision low‐level model that integrates the actuator dynamics and angular velocity dynamics is presented. Based on this model, a dynamic compensator is designed using the internal model method to handle aerodynamic disturbances. Next, a high‐gain observer is designed to estimate the actuator states without adding new sensors, and an observer‐based low‐level controller is proposed through a recursive design process. Finally, the local asymptotic stability of the closed‐loop system is analyzed. The effectiveness and superiority of the proposed method are validated through simulations and physical experiments.

A Finite-Time Disturbance Observer for Tracking Control of Nonlinear Systems Subject to Model Uncertainties and Disturbances

In this study, a finite-time disturbance observer (FTDOB) with a new structure is originally put forward for the motion tracking problem of a class of nonlinear systems subject to model uncertainties and exogenous disturbances. Compared to existing disturbance estimator designs in the literature, in which the estimation error only converges to the origin asymptotically under assumptions that the first and/or second derivatives are vanishing, the suggested DOB is able to estimate the disturbance exactly in finite time. Firstly, uncertainties (parametric and unstructured uncertainties), unknown dynamics, and external disturbances in system dynamics are lumped into a generalized disturbance term that is subsequently estimated by the proposed DOB. Based on this, a DOB-based backstepping controller is synthesized to ensure high-accuracy tracking performance under various working conditions. The stability analysis of not only the DOB but also the overall closed-loop system is theoretically confirmed by the Lyapunov stability theory. Finally, the advantages of the proposed FTDOB and the FTDOB-based controller over other DOBs and existing DOB-based controllers are explicitly simultaneously demonstrated by a series of numerical simulations on a second-order mechanical system and comparative experiments on an actual DC motor system.

Dynamic event-triggered fault-tolerant control for nonaffine systems with asymmetric error constraint

This paper focuses on the problem of dynamic event-triggered fault-tolerant control (FTC) for nonaffine systems with unmeasurable state and asymmetric error constrain. At first, an adaptive failure compensation observer is designed to calculate unpredictable state of the nonaffine systems. Then, a dynamic event triggering strategy (DETS) is constructed to adjust the control signal and make it more flexible in transmission. Next, a new error-dependent conversion function (EDCF) is designed to confine tracing error, which can ensure that the designed Lyapunov function is always positive definite, and extend the symmetric constraint boundary to the asymmetric constraint boundary. The tracking performance and stability of closed-loop systems are proven through Lyapunov stability analysis. Finally, the availability of this method is verified by simulation experiments.

Asymptotic stability in a predator-prey system with density-dependent diffusion and indirect pursuit-evasion interaction in 2D

This paper deals with a predator-prey system with density-dependent diffusion and indirect pursuit-evasion interaction under homogeneous Neumann boundary conditions. By providing appropriate conditions, the asymptotic stability of solution is investigated.

Synchronization Analysis of Coupled Fitzhugh Nagumo Dynamical Systems

Synchronization plays a pivotal role in understanding various natural events. Understanding this concept with reference to a biologically inspired dynamical model of a neuron is also essential. It is basically a rhythm adjustment phenomenon and a consequence of the coupling between the individual units. In the present work, we aim to derive sufficient conditions for the synchronization of coupled Fitzhugh Nagumo Dynamics using Lyapunov stability analysis. In particular, a non-smooth Lyapunov function based upon the geodesic distance between respective states of coupled systems has been chosen as the Lyapunov function, and the concept of upper Dini-derivative has been utilized to calculate the derivative of the Lyapunov function along the error dynamics. The negative definiteness of the derivative of the Lyapunov function gives sufficient coupling gain for synchronization. The findings are verified on the Matlab simulation platform. The results should help to enhance the knowledge of neural dynamics.

On the Global Existence of Solution and Lyapunov Asymptotic Practical Stability for Nonlinear Impulsive Caputo Fractional Derivative via Comparison Principle

This paper examines the existence of maximal solution of the comparison differential system and also establishes sufficient conditions for the asymptotic practical stability of the trivial solution of a nonlinear impulsive Caputo fractional differential equations with fixed moments of impulse using the vector Lyapunov functions. First, it was discovered that the vector form of the Lyapunov function was majorized by the maximal solution of the comparison system. From the results obtained, it was also established that the main system is asymptotically practically stable in the sense of Lyapunov.

Robust Distributed Load Frequency Control for Multi-Area Power Systems with Photovoltaic and Battery Energy Storage System

The intermittent power generation of renewable energy sources (RESs) interrupts the balance between power generation and demand load due to the increased frequency fluctuation, which challenges the frequency stability analysis and control synthesis of power generation systems. This paper proposes a robust distributed load frequency control (DLFC) scheme for multi-area power systems. Firstly, a multi-area power system is constructed by integrating photovoltaic (PV) and battery energy storage systems (BESSs). Then, by employing the linear matrix inequality (LMI) technique, the sufficient condition capable of ensuring that the proposed controller satisfies H∞ robust performance in the sense of asymptotic stability is derived. Finally, testing is conducted on a four-area renewable power system, and results verify the strong robustness of the proposed controller against load disturbance and intermittence of RESs.

The impact of obesity on chronic diseases: type 2 diabetes, heart disease, and high blood pressure

Obesity is a risk factor for several chronic diseases, including type 2 diabetes, heart disease, and high blood pressure. Developing models of obesity and its complications allows for close monitoring of these epidemics, informing the creation of effective control strategies. This research focuses on presenting an endemic model of obesity and its health complications, taking into account, social factors and relationships among people in society. The term epidemic is related to the influence of the health lifestyle of obese people on healthy individuals. The transmission of obesity and its complications is through peer pressure to consume fast food and acquire bad eating habits from relatives and friends. So, in our model, the effect of these factors is expressed with parameters β i . We demonstrate theoretically the asymptotic local stability of disease-free equilibrium and the asymptotic local stability of endemic equilibrium, proving the existence and uniqueness of the solution to the obesity model and its complications. To confirm the model's theoretical results, we conduct numerical simulations to study the impact of variation in social factor parameters on the diseases studied.

Reinforcement learning-adaptive fault-tolerant IGC method for a class of aircraft with non-affine characteristics and multiple uncertainties

Abstract In this paper, a brand-new adaptive fault-tolerant non-affine integrated guidance and control method based on reinforcement learning is proposed for a class of skid-to-turn (STT) missile. Firstly, considering the non-affine characteristics of the missile, a new non-affine integrated guidance and control (NAIGC) design model is constructed. For the NAIGC system, an adaptive expansion integral system is introduced to address the issue of challenging control brought on by the non-affine form of the control signal. Subsequently, the hyperbolic tangent function and adaptive boundary estimation are utilised to lessen the jitter due to disturbances in the control system and the deviation caused by actuator failures while taking into account the uncertainty in the NAIGC system. Importantly, actor-critic is introduced into the control framework, where the actor network aims to deal with the multiple uncertainties of the subsystem and generate the control input based on the critic results. Eventually, not only is the stability of the NAIGC closed-loop system demonstrated using Lyapunov theory, but also the validity and superiority of the method are verified by numerical simulations.