Asymptotic Stability Research Articles

Real-sea validation of a model predictive controller's inherent robustness for medium-scale unmanned trimaran heading

The development of medium-to large-scale and high-performance unmanned surface vehicles (USVs) is a burgeoning trend in intelligent marine systems. The heading controller is crucial for USVs to execute diverse missions, especially given their inherent underactuation characteristics and constraints. Recent efforts have focused on enhancing the robustness of controllers against external disturbances and employed two main strategies: one converges the control error to a bounded residual set through robust modifications, while the other eliminates the error by modelling disturbances. Notably, these enhancements have primarily catered to small USVs, where disturbances significantly impact their manoeuvrability, necessitating such robust control strategies. This focus has somewhat overshadowed the inherent robustness of closed-loop control systems. Compared with small USVs, medium-to large-scale USVs are less affected by external disturbances, despite undertaking more complex missions. Leveraging the intrinsic robustness of controllers presents an opportunity to simplify controller design, thereby reallocating computational resources towards enhancing mission capabilities. Model Predictive Control (MPC) has attracted significant attention recently, and its receding horizon and optimality theoretically provides a new level of inherent robustness, which remains under-explored in real sea. This paper focuses on the inherent robustness of MPC in managing the heading of a medium-scale unmanned trimaran subjected to the thrust angle and angular velocity constraints. A model predictive controller considering the constraints is designed based on the identified Nomoto model and the asymptotic stability is ensured with a terminal cost. Conducted real-sea experiments and comparative analyses with a Proportional-Integral-Derivative (PID) controller, the most widespread and dominant control algorithm in practical USV engineering, underscore the superiority of MPC in maintaining satisfactory closed-loop performance. Furthermore, the MPC controller is also successfully applied to real-sea path-following missions and demonstrated good tracking performance in various sea conditions ranging from level 3 to 5 and wind speeds spanning from level 6 to 8. This validation opens up new avenues for motion control strategies in the evolving landscape of larger-scale USVs.

Formation tracking control for networked heterogeneous MSV systems with actuator faults: A distributed optimal event-triggered fixed-time sliding mode fault-tolerant control approach

This paper studies the formation tracking problem in networked heterogeneous marine surface vessel systems (NHMSVs) subject to model perturbations, marine environmental disturbances, and actuator faults. A distributed optimal event-triggered fixed-time sliding mode fault-tolerant control (EFSMFC) method is proposed, which can achieve formation tracking within a fixed time that is only related to the control parameters. At the same time, a distance-based Floyd distributed optimization method is used to reduce the high communication cost caused by the redundancy of the network communication topology. In addition, an event-triggered strategy is integrated into the design of the controller to reduce the update frequency of control signals and reduce waste of communication resources. Finally, using Lyapunov stability theory, the global fixed-time convergence of system errors is proved. The simulation results demonstrate the feasibility of the proposed method, exhibiting superior robustness and speed compared to existing control methods.

Optimized triangular observer based adaptive supertwisting sliding mode control for wind turbine system

This paper presents a modified adaptive supertwisting sliding mode controller (AST-SMC) that dynamically adjusts control settings without prior knowledge of uncertainty limits, thereby removing chattering and putting reliability first while maintaining the original benefits of sliding mode control (SMC). First, we model and build the wind turbine system using three different controllers: the AST-SMC, the supertwisting sliding mode controller (ST-SMC), and the first-order sliding mode controller (FOSMC). A second comparison is necessary. Only the rotor speed is available to the control law because of concealed state information, which makes use of the full system state. In order to minimize observing errors over time, an asymptotic observer triangle is used to estimate the unknown rotor acceleration. By improving AST-SMC's control law, particle swarm optimization finds the most effective controller. The stability of AST-SMC over a finite time is shown via the Lyapunov stability theorem. Based on simulation findings, it is proven to be more effective than traditional SMC in wind turbine system control. It excels in settling time, tracking accuracy, energy consumption, and control input smoothness.

Discrete-time Luenberger observer design for Lithium-ion battery state-of-charge with stability guarantee

State-of-charge (SOC) estimation is particularly important as it provides information about the remaining energy capacity of the battery, allowing for better planning and utilization. Accurate SOC estimation is challenging because it cannot be directly measured from the battery. Instead, it is estimated by analyzing measurable variables such as current and voltage. To address this challenge, a discrete-time observer-based SOC estimation approach is proposed in this paper. This approach utilizes a second-order equivalent circuit model and a piecewise linear approximation to represent the relationship between SOC and open circuit voltage (OCV). The proposed observer-based approach utilizes these models to estimate the SOC with assured asymptotic stability under specific assumptions to simplify the design process. Simulations in Python are conducted to evaluate the performance of the designed observer. In the simulations, the SOC estimation under various conditions, such as model uncertainty, disturbances, and measurement noise, is also covered. In addition, three different observer gains are considered in the simulations. Lastly, simulation studies indicate that the estimated SOC values converge to the real SOC values, with some different behavior depending on the regarded situations.

Synchronous behavior in directed networks of heterogeneous piecewise linear oscillators

In this paper, we investigate the onset of synchronous behavior on strongly connected directed networks of heterogeneous piecewise linear (PWL) oscillators. Each oscillator is composed of a linear part, which is assumed to be identical for all oscillators, and a commutation function, which is different for each oscillator, creating in this way the heterogeneity in the whole network. Due to this heterogeneity, the oscillators do not achieve perfect or complete synchronization but instead, practical synchronization emerges. The stability properties of the practical synchronous solution in the network are analyzed using standard Lyapunov theory for systems with nonvanishing perturbations and the concept of disagreement vectors. Our results provide an ultimate bound on the norm of the disagreement vector and also a maximal bound on the synchronization error, such that a relationship between the disagreement bound and practical synchronization is established. Additionally, we provide numerical simulations to illustrate the theoretical results.

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.