Asymptotic Stability Research Articles

ADP-based adaptive control of ship course tracking system with prescribed performance

In this paper, an adaptive dynamic programing (ADP)-based adaptive control problem is studied for the ship course tracking system with prescribed performance. Firstly, the complex sea conditions will bring difficulty to ship course tracking when unmanned ship sailing on sea. In order to overcome this difficulty, a prescribed performance feedforward term is designed in the controller to improve the course tracking ability of ship. Secondly, by defining a cost function, an ADP technology is exploited to achieve an optimal control of ship course tracking system. Finally, the stability of the closed loop system is turned out by Lyapunov stability theory and all signals are uniformly ultimately bounded (UUB). Simulation results validate the effectiveness of the proposed method.

Adaptive vibration control for stabilisation of the Euler–Bernoulli beam with an unknown payload

In this paper, an adaptive boundary controller is designed to solve the boundary control problem of Euler–Bernoulli beams with an unknown payload. Therefore, a boundary controller with an adaptive law is designed to compensate for the parameter uncertainty of the system. Partial Differential Equations (PDEs) are used to describe the Euler–Bernoulli beam system. The well-posedness of the system under the action of an adaptive boundary controller is proved by using the linear operator semigroup method. Meanwhile, the asymptotic stability of the closed-loop system is derived from the extended Krasovskii–LaSalle invariance principle. The effectiveness and superiority of the proposed method are illustrated by simulation in comparison with the existing results.

Compensation Function Observer-Based Backstepping Sliding-Mode Control of Uncertain Electro-Hydraulic Servo System

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding-mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of a backstepping sliding-mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of the Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is respectively improved by 94.86% and 88.19% under the influence of large external load forces and disturbances.

Finite-time optimal control for a class of nonlinear systems with performance constraints via critic-only ADP: Theory and experiments

This paper addresses the optimal control problem within the framework of adaptive dynamic programming (ADP) for a class of nonlinear systems subjected to performance constraints. A new finite-time optimal control scheme is developed to stabilize the system by using the critic-only neural network ADP method. Compared with the existing ADP-based optimal control methods with uniformly ultimately bounded stability, the provided control scheme ensures that the controlled system's state and neural network weight estimation error are finite-time stable. It can ensure optimality, prescribed performance, and finite-time stability of the closed-loop control system simultaneously through an integration of ADP, the prescribed performance control technique, and Lyapunov theory. The designed adaptive neural network weight update law can relax the persisting excitation condition. The proposed control scheme is implemented on a robotic experiment platform to achieve trajectory tracking and verify its effectiveness.

Stability and Bifurcation Analysis of a Symmetric Fractional-Order Epidemic Mathematical Model with Time Delay and Non-Monotonic Incidence Rates for Two Viral Strains

This study investigates a symmetric fractional-order epidemic model with time delays and non-monotonic incidence rates, considering two viral strains. By confirming the existence, uniqueness, and boundedness of the system’s solutions, the research ensures the model’s well-posedness, guaranteeing its mathematical soundness and practical relevance. The study calculates and evaluates the equilibrium points and the basic reproduction numbers R01 and R02 to understand the dynamic behavior of the model under different parameter settings. Through the application of the Lyapunov method, the research examines the asymptotic global stability of the system, determining whether it will converge to a particular equilibrium state over time. Furthermore, Hopf bifurcation theory is employed to investigate potential periodic solutions and bifurcation scenarios, highlighting how the system might shift from stability to periodic oscillations under certain conditions. By utilizing the Adams-Bashforth-Moulton numerical simulation method, the theoretical results are validated, reinforcing the conclusions and demonstrating the model’s applicability in real-world contexts. It emphasizes the importance of fractional-order models in addressing epidemiological issues related to time delays (τ), individual heterogeneity (m, k), and memory effects (θ), offering greater accuracy compared with traditional integer-order models. In summary, this research provides a theoretical foundation and practical insights, enhancing the understanding and management of epidemic dynamics through fractional-order epidemic models.

Dynamic output feedback robust MPC hybrid fault-tolerant control for discrete uncertain systems: a switching control strategy

To guarantee the control performance of the discrete system under unmeasurable state and partial actuator failure, a robust dynamic output feedback predictive fault-tolerant control method derived from switching strategy is developed. A new iterative error switching model is established, which both ensures tracking performance and lays the foundation for the development of the next switching controller. Based on this model, output feedback switching fault-tolerant controller is developed. Compared with conventional fault-tolerant control methods, the designed controller can be used under the case of unmeasurable states, and it is more fault tolerant and less conservative. According to the Lyapunov stability theory, the robust stability analysis is carried out under normal and fault conditions, respectively. Then, depending on the findings of the stability analysis, sufficient conditions to guarantee the stability of the closed-loop normal and faulty system are derived. Finally, the suggested method's efficacy is confirmed using the injection moulding process as an example.

Enhanced control of grid-connected multi-machine wind power generation systems using fuzzy backstepping approaches

This research paper presents an approach for enhancing the performance of a multi-machine wind power generation system (WPGS) through the combination of nonlinear and intelligent control techniques. The suggested approach focuses on optimizing the WPGS, which utilizes permanent magnet synchronous generators (PMSGs) interconnected with the grid. To enable grid connection, a back-to-back configuration is employed for both the rectifier and inverter in a fifteen-switch configuration, with control achieved through pulse width modulation. The designed control algorithm is designed to effectively regulate the system and reduce the active and reactive power ripples. Initially, the WPGS model is provided. Subsequently, the fuzzy backstepping control (FBC) law is detailed, incorporating the Lyapunov stability technique. Fuzzy logic is used to adapt the gains in the backstepping approach, ensuring the control system can accommodate disturbances and system variations. As a result, this adaptive control approach enables optimal effusiveness of the entire system in both static and dynamic operational regimes. Experimental tests were conducted using MATLAB to compare the efficacy of the designed strategy against the traditional backstepping control approach. The obtained results demonstrated the robustness and effective reference tracking capabilities of the designed FBC approach, along with the complete elimination of speed overshoot across diverse wind conditions. These findings validate the designed control approach's effectiveness and superiority over the BC approach under varying conditions.

The role of asymptomatic cattle for leptospirosis dynamics in a herd with imperfect vaccination

Leptospirosis is an emerging zoonotic disease with high health and economic damage. In this study, we developed a deterministic mathematical model that describes the dynamics of leptospirosis transmission within a cattle herd, incorporating asymptomatic infected and vaccinated compartments. The study examined the transmission role of asymptomatic cattle that contaminate herds without farmers’ knowledge. We proved the well-posedness of the proposed model and found the basic reproduction number using the next-generation matrix. Analytically, we demonstrated that the disease-free equilibrium point is locally and globally asymptotically stable when R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr {R}}_0$$\\end{document} is less than unity and is otherwise unstable. Graphically, we further established the local asymptotic stability of disease-free and endemic equilibria. Sensitivity analysis showed that the contact rate with asymptomatic infected cattle, βA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _A$$\\end{document}, is the most sensitive parameter in the stated model, followed by the recovery rate of asymptomatic infected cattle, σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document}, and the vaccination rate of susceptible cattle, τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}. Numerical simulations revealed that a reduction in contact rate with asymptomatic infected cattle significantly reduced pathogen Leptospira transmission in the herd. In addition, fostering the recovery rate of asymptomatic infected cattle can significantly reduce new infections in the herd. Furthermore, augmenting the vaccination rate among susceptible cattle resulted in a notable decrease in disease prevalence within the herd. Findings of this study underscore the remarkable importance of targeted interventions, such as reducing contact rates with asymptomatic infected cattle, increasing recovery rates using proper treatments, and enhancing vaccination efforts to manage leptospirosis transmission in cattle herds.

System modeling and fuzzy adaptive PI sliding-mode control of a novel ship-mounted cable-based bulkhead cleaning robot

Ship cleaning poses significant risks and consumes considerable time, primarily due to the irregular hull surface geometry and the unpredictable ship motion induced by wave excitation. To address this challenge and achieve efficient, autonomous cleaning, a spatial variable structure cable-based bulkhead cleaning robot (SC-R) is proposed. Unlike traditional cable-driven parallel mechanisms (CDPMs), SC-R operates in a non-inertial frame, whereby its motion is subject to continuous and unpredictable ship motion. Consequently, SC-R exhibits intricate dynamic characteristics, posing a significant hurdle for controller design. To solve this problem, a sliding-mode controller is proposed for SC-R. Specifically, the dynamic model of SC-R, which includes ship motion and various disturbing forces, is systematically established using the Newton-Euler method. Furthermore, a fuzzy adaptive PI sliding-mode controller (FAPI-SMC) is specifically proposed to enhance the convergence speed and robustness of SC-R. The stability of the closed-loop system is analyzed using Lyapunov theory, and the tracking error is proved to be eventually bounded. Finally, the availability of this theory is confirmed by simulation and experiment. It is shown that FAPI-SMC can achieve a satisfactory control effect in practice.

Development and experimental validation of high-order sliding mode control for quadratic boost converters in fuel cell electric vehicles

The global energy evolution is at a critical juncture, necessitating an urgent transition towards clean and sustainable energy sources, notably green hydrogen, to combat climate change and the inevi-table depletion of fossil fuels. This transition is underscored by the emergence of fuel cell electric vehicles (FCEVs) as a promising solution for clean transportation, demanding advanced DC-DC power converter technologies to ensure their efficiency and reliability. This paper addresses the topic of control for the Quadratic Boost Converter, which presents a challenge due to its non-minimum phase characteristic and nonlinear nature. To tackle this, a nonlinear controller is developed using dual-loop control employing STA-SMC and Lyapunov theory as the control ap-proach. Simulation and experimental validation evaluate the controller's performance, testing ro-bustness against varying load currents and under time-varying reference voltages to assess its ef-fectiveness.

Flatness-based control in successive loops for dual-arm robotic manipulators

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping and lifting, or assembling tasks. In this article, a multi-loop flatness-based controller is proposed for the dynamic model of a dual-arm robot. In the considered application, the dual-arm robotic system has to lift and transfer an object under synchronized motion of its two end-effectors while it has also to compensate for the grasping forces between the two end-effectors and the object. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. The control problem for this robotic system is solved with the use of a flatness-based control approach which is implemented in successive loops. To apply the multi-loop flatness-based control method, the state-space model of the dual-arm robotic manipulator is separated into subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. The state variables of the preceding i-th subsystem become virtual control inputs for the subsequent ( i + 1)-th subsystem. In turn, real control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The multi-loop flatness-based control approach is an exact nonlinear control scheme which (i) does not use approximate linearization of the dynamic model of the controlled system and (ii) does not need changes of state variables and complicated state-space model transformations.

Barrier function–based adaptive STSMC for steering feel feedback of SBW vehicle with uncertainty

As an essential component of human–computer interaction in steer-by-wire (SBW) vehicles, the steering feel feedback system provides drivers with accurate steering feel by precisely controlling the output torque of the steering feel motor. Meanwhile, the existence of uncertainties makes the accurate control of steering feel feedback torque become an acknowledged challenging issue. This article proposes an adaptive super-torque sliding mode control strategy based on barrier functions for the steering feel feedback system of SBW vehicles with highly complex dynamics in the presence of uncertainties. First, to achieve intelligent modeling under the influence of uncertainty factors, a dynamic system with unknown uncertainty based on adaptive fuzzy logic system (FLS) is proposed. In the framework of this model, the uncertainty factors introduced by unknown external disturbance, parameter uncertainty, and model couplings are considered as a lumped uncertainty function. Furthermore, the membership functions of the FLS are dynamically adjusted based on nearest neighbor clustering, aiming to enhance the modeling accuracy beyond traditional fuzzy modeling. To further offset the system uncertainty and FLS approximation error, an adaptive super-twisting sliding mode control (STSMC) method based on barrier function is proposed. This algorithm retains the advantages of traditional sliding mode control (SMC) methods in dealing with systems with uncertainty and eliminates the need for a priori knowledge of the upper bound of uncertainties by introducing the adaptive law based on barrier function, avoiding the use of complex identification algorithms. Moreover, it eliminates the gain of overestimation and significantly reduces chattering phenomenon in traditional sliding mode control. Finally, based on Lyapunov stability theory, this article proves the proposed system can achieve convergence within a finite time. Compared with STSMC, traditional SMC and proportional–integral–derivative (PID) control, the results verify the effectiveness of the proposed control method. The proposed strategy provides a new solution to reduce the steering feel feedback torque error under the influence of uncertain factors.

Design of Neural Network-Based Multi-Fault Tolerant Control System for Unmanned Aerial Vehicles

Actuator failure seriously threatens the flight safety of unmanned helicopters. Considering the problem of multiple faults such as actuator bias and failure in unmanned helicopters, a composite fault-tolerant flight control algorithm is proposed. For actuator bias fault, a nonlinear fault observer is designed to estimate it in real time; for actuator failure fault, a same-dimensional auxiliary system is constructed and processed by neural network technology. The composite fault-tolerant flight controller of the unmanned helicopter is designed by backstepping method, and the Lyapunov stability theory is used to prove that the error signals of the closed-loop system are bounded and convergent. Simulation results show that the proposed control algorithm can improve the fault tolerance of the unmanned helicopter when multiple actuator faults occur, ensuring its safe flight.

Stability and computational analysis of Influenza-A epidemic model through double time delay

Delay factors demonstration has a significant role in controlling a strain of infectious disease instead of a pharmaceutical strategy. According to the World Health Organization (WHO), 3–5 million cases are reported annually and approximately 290,000 to 650,000 respiratory deaths annually. So, in the present study, we develop a delayed mathematical model based on delay differential equations (DDEs) for the influenza epidemic using a deterministic approach by introducing double delay parameters. The four distinct sub-populations are considered susceptible, exposed, infected, and recovered. For the rigorous analysis, the fundamental properties of the model like positivity, boundedness, existence, and uniqueness, were studied. The influenza-free equilibrium (IFE) and influenza-existing equilibrium (IEE), are the two nonnegative equilibrium points that the model demonstrates. Both locally and globally, the asymptotic stability of the equilibrium points of the model is established and shown under specific situations of reproduction number. Additionally, investigated the model's parameter sensitivity and determined the relative sensitivity of each parameter. Both standard and nonstandard methods—such as Euler, Runge-Kutta, and nonstandard finite difference with a delayed sense—are presented to make computational analysis support a dynamical analysis and the best visualization of results. The stability of the non-standard finite difference scheme is thoroughly analyzed around the steady states of the model. Additionally, the results show that the nonstandard finite difference approximation is an efficient, cost-effective method, independent of time step size, to solve such highly nonlinear and complex real-world problems.

A Lyapunov Theory-Based SEIG–STATCOM Voltage Regulation Control Strategy

To improve the voltage regulation of asynchronous generators during load switching, a Lyapunov-based control strategy has been proposed to stabilize the generator’s voltage by connecting a static synchronous compensator. By constructing a Lyapunov function from the mathematical model, the error tracking problem is transformed into a global asymptotic stability problem of the Lyapunov function at the equilibrium point. The outer loop linearizes the direct current (DC) voltage control process, while the inner loop replaces integral terms with differential terms. The proposed Lyapunov method achieves linearized voltage control with a quadratic outer loop structure and the inner loop differential structure exhibits a shorter transient process, outperforming traditional methods. Simulation and experimental tests were then used, where the latter was a down-scale laboratory prototype experiment. Compared to traditional (voltage-oriented control) VOC, the outer loop (Lyapunov-function-based control) LBC reduces the DC voltage transient processes by approximately 9.4 milliseconds, while the inner loop LBC reduces both alternating current (AC) and DC voltage transient processes by approximately 2.6 ms and 8.7 ms, respectively.

Gait coordination control of bipedal modular reconfigurable robot based on adaptive neural network

This paper proposed an adaptive neural network (NN) control method to track the desired trajectory of a bipedal modular reconfigurable robot (MRR), which can solve the gait coordination problem of bipedal MRR. The leg dynamic model and the body dynamic model of bipedal MRR are established based on the Newton–Euler iterative method, and the global dynamic model is subsequently established. Aiming at the gait coordination problem between double support phase (DSP) and single support phase (SSP), the desired trajectory is generated based on the zero-moment point (ZMP) method. The adaptive NN controller is designed to track the generated desired trajectory, which also compensates interconnected dynamic coupling (IDC) effects of the bipedal MRR. The stability of bipedal MRR system is proved by Lyapunov theory. In the end, the effectiveness of the control method is verified by comparative simulation. The simulation results show that the proposed adaptive NN method reduces the position tracking error by [Formula: see text] and the control torque by [Formula: see text] compared with the existing control methods.

Command filter‐based adaptive finite‐time control of fractional‐order nonlinear constrained systems with input saturation

AbstractIn this article, the command filter‐based finite‐time tracking control issue is explored for fractional‐order nonlinear constrained systems (FONCSs) with saturated input. Firstly, a novel fractional‐order Lyapunov stability lemma is put forward, thereby offering a reliable strategy for finite‐time convergence of FONCSs. By employing an improved error compensation system and introducing auxiliary signal, a new finite‐time command filtered backstepping technique is developed. The proposed control strategy guarantees the finite‐time convergence characteristic of filtering signals, in addition to alleviate the impacts produced by saturated input. After that, a modified nonlinear state‐dependent function (NSDF) is developed to solve the state constraint problem while fulfilling the concavity condition. In comparison to the existing constrained control techniques in FONCSs, this approach not only ensures finite‐time convergence of the tracking error but also gets rid of feasibility demands. Ultimately, two simulation scenarios are supplied to illustrate the feasibility and usefulness of the suggested strategy.

Iterative Dissipativity of Partial Difference Equation Dynamics in Open-Loop Iterative Learning Control Mode

Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach.

Bounded Kukles Systems of Degree Three

One of the most important tasks in the qualitative theory of differential equations in the plane is the study of global asymptotic stability: an equilibrium point that is globally attractive. It is known that if an equilibrium point of a planar vector field is globally asymptotically stable, then the vector field is bounded. A planar vector field is said to be bounded if the forward orbit of every point enters and remains in a compact set. In this paper, we study cubic Kukles systems that are bounded which is the first step toward the characterization of cubic Kukles systems that are globally asymptotically stable. We emphasize that these systems form a seven-parameter family of polynomial differential systems. We obtain a total of 25 cubic Kukles sub-systems that are bounded and we provide 11 phase portraits of such sub-systems in a neighborhood of infinity.

An Adaptive Controller with Disturbance Observer for Underwater Vehicle Manipulator Systems

Dynamic control of underwater vehicle manipulator systems (UVMSs) is the key part of underwater intervention tasks. In this paper, we propose an adaptive controller with a disturbance observer that mainly consists of two parts: the first part is the adaptive control law that estimates the changes in the center of mass (COM) and the center of buoyancy (COB) of the vehicle, and the second part is the nonlinear disturbance observer that estimates the external disturbance and model uncertainties. To attenuate the overestimation problem, a damping term is introduced to the adaptive law. The stability of the proposed method is proven on the basis of Lyapunov theory. We develop three scenarios on the Simurv platform and illustrate the effectiveness of the proposed method with a short response time and high tracking performance.