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This paper considers the stability of the one-dimensional parabolic system, where one end changes over time and the other is the control end with the external disturbance. Firstly, by the boundary immobilisation method, the displacement change of the system boundary is transferred into the equation so that the original system is transformed into a system with fixed boundaries. Secondly, by combining the backstepping transformation and the sliding mode control method, the feedback control is proposed to compensate the instability of the system itself and reject the matched disturbance. Then, the resulting closed-loop system will be in the form of $ \mathcal{A}+ \mathcal{B}(\tau)+ \mathcal{C} D(\tau) $ A + B (τ) + C D (τ) , where $ \mathcal{A} $ A generates a $ C_0 $ C 0 semigroup, $ \mathcal{B}(\tau) $ B (τ) and $ \mathcal{C} $ C are bounded and unbounded operators respectively, and $ D(\tau) $ D (τ) is the external input. The existence of the generalised solution to the closed-loop system is proved by using the eigenfunction expansion of the system solution. By the Lyapunov method, the closed-loop system is shown to be exponentially stable. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Overhead cranes play a pivotal role in various industrial applications. This paper presents two methodologies for suppressing the payload's swing and completing the accurate positioning. The original crane model is initially transformed into a chained form. Two nonlinear controllers are devised to regulate the trolley's position and achieve the payload's anti-swing control. The first approach utilizes backstepping, extended state observer, and filter technique to effectively estimate system state and disturbance and make the closed-loop system uniformly ultimately bounded. In contrast, the second method involves sliding mode control and finite-time disturbance observer to ensure the finite-time convergence of the resulting closed-loop system and the accurate disturbance estimation. Finally, simulation results are provided to validate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Background and Objectives: The two-axis inertially stabilized platforms (ISPs) face various challenges such as system nonlinearity, parameter fluctuations, and disturbances which makes the design process more complex. To address these challenges effectively, the main objective of this paper is to realize the stabilization of ISPs by presenting a new robust model-free control scheme. Methods: In this study, a robust adaptive fuzzy control approach is proposed for two-axis ISPs. The proposed approach leverages the backstepping method as its foundational design mechanism, employing fuzzy systems to approximate unknown terms within the control framework. Furthermore, the control architecture incorporates a model-free disturbance observer, enhancing the system's robustness and performance. Additionally, novel adaptive rules are devised, and the uniform ultimate boundedness stability of the closed-loop system is rigorously validated using the Lyapunov theorem. Results: Using MATLAB/Simulink software, simulation results are obtained for the proposed control system and its performance is assessed in comparison with related research works across two scenarios. In the first scenario, where both the desired and initial attitude angles are set to zero, the proposed method demonstrates a substantial mean squared error (MSE) reduction: 96.2% for pitch and 86.7% for yaw compared to the backstepping method, and reductions of 75% for pitch and 33.3% for yaw compared to the backstepping sliding mode control. In the second scenario, which involves a 10-degree step input, similar improvements are observed alongside superior performance in terms of reduced overshoot and settling time. Specifically, the proposed method achieves a settling time for the pitch gimbal 56.6% faster than the backstepping method and 58% faster for the yaw gimbal. Moreover, the overshoot for the pitch angle is reduced by 53.5% compared to backstepping and 35.5% compared to backstepping sliding mode control, while for the yaw angle, reductions of 43.6% and 37.6% are achieved, respectively. Conclusion: Through comprehensive simulation studies, the efficacy of the proposed algorithm is demonstrated, showcasing its superior performance compared to conventional control methods. Specifically, the proposed method exhibits notable improvements in reducing maximum deviation from desired angles, mean squared errors, settling time, and overshoot, outperforming both backstepping and backstepping sliding mode control methods. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust regulation of a Planar Vertical Takeoff and Landing (PVTOL) aircraft affected by crosswind disturbances. The proposed approach simultaneously exploits the advantages of passivity-based control and the integral sliding mode (ISM) control technique. We demonstrate that the passivity-based controller accomplishes the PVTOL regulation within a guaranteed stability region. At the same time, the ISM controller can effectively counteract the undesirable disturbances effect from the beginning of the operation since the disturbances are never seen in the measurable output. Using the passivity approach with LaSalle's Invariance Theorem, we construct the required Lyapunov function to establish the closed-loop system stability. The proposed combination of controllers results in a robust system that satisfactorily solves the regulation problem. Numerical simulations are provided to show that the proposed approach allows the tracking of different reference signals: pulse-train shaped trajectory and ellipse-shaped trajectory, considering the presence of perturbations (crosswind). Furthermore, to illustrate the effectiveness of the proposed technique, a comparative analysis considering two robust control strategies is provided. [ABSTRACT FROM AUTHOR]

The traditional second-order sliding mode (SOSM) algorithms can only achieve the finite-time regulation for standard integrator sliding mode systems and the convergence time of which is dependent on the system's initial values and grows as the initial values grow. In this paper, we propose a novel fixed-time SOSM controller whose settling time is bounded by a fixed time independent of the system's initial values. First, a new sliding mode system subjects to a non-vanishing mismatched term is developed to reduce the input uncertainties and relax the well-defined relative degree assumption. Second, a Lyapunov criterion for practical fixed-time stability with a less conservative convergence time estimation is introduced, based on which a practical fixed-time SOSM controller is designed for the new sliding mode system. Finally, a strict Lyapunov analysis demonstrates that the closed-loop system is globally practically fixed-time stable (GPFxTS). Particularly, if the mismatched term is vanishing, global fixed-time convergence of the sliding variable to zero can be achieved. Buck converter is given as an application. [ABSTRACT FROM AUTHOR]

This paper designs an online adjustment strategy for dynamic quantizer parameters and investigates the sliding mode control (SMC) problem for uncertain switched systems under a limited network communication bandwidth. Due to the limitation of the coding length in practical transmission, coding errors can significantly impact the system's ideal performance. To address these issues, a dynamic quantizer is introduced to efficiently encode the system state while minimizing quantization error under the constraint of the finite code length. Additionally, a coding and decoding scheme based on dynamic quantization and a suitable sliding mode controller are designed to obtain a closed-loop switched system. Using Lyapunov functions and the average dwell time method, sufficient conditions are derived to guarantee the reachability of the sliding surface and the exponential ultimate bound (EUB) in the mean square for the closed-loop switched system, even in the presence of coding errors and data loss. The theoretical results are validated through numerical simulations, which demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The major contribution of this study is the feedback design of a finite-time convergence sliding mode control to solve the trajectory-tracking problem in a class of mechanical systems. Some advantages are that the controller presents a continuous signal by integration of the high-frequency switching term. Another benefit is the design and implementation of an uncertainty and disturbance estimator (UDE) to robustify the closed-loop system. We use Lyapunov tools to develop the closed-loop stability analysis and to give an expression of the convergence time t = t through this, we can reduce the convergence time by tuning the gains of the controller. We illustrate the performance of the proposed control structure via numerical simulations conducted for a mass-spring-damper system and experiments developed in a pendular system. [ABSTRACT FROM AUTHOR]

An event-triggered-super twisting sliding mode control (ET-STSMC) with saturation function in reaching law have been designed for a nonlinear Quadcopter model with bounded disturbance and its performance is compared with Event Triggered-Sliding mode control (ET-SMC). Simulation results have been obtained for altitude and attitude tracking, demonstrating the stability of the closed-loop system with the proposed control. The event-triggering conditions are derived based on the Lyapunov method, ensuring non-accumulation of inter-event execution time. Experiments have been performed in real-time to analyse the robustness and computational cost in terms of the number of control updates of the proposed control strategy under normal flight, external disturbances, and parameter uncertainty. Simulation and experimental results show that ET-STSMC can achieves better tracking performance and robustness with reduced computational cost compared to ET-SMC during all flight conditions. [ABSTRACT FROM AUTHOR]

This study introduces a novel control approach for a twin rotor multi-input multi-output system (TRMS), specifically targeting the pitch and yaw movements. The proposed method employs a sliding mode controller (SMC) with variable gains, aiming to overcome limitations like chattering and excessive control effort. Unlike traditional controllers, the gains here dynamically adjust based on the error state, enhancing the robustness of the system against external disturbances and parameter uncertainties. The control algorithm draws inspiration from both first-order and higher-order sliding mode controllers. To rigorously assess the robustness of the controller, Gaussian White noise is incorporated into the model. By dynamically adjusting gains, the proposed approach aims to minimize control effort while mitigating control signal overestimation arising from model uncertainties. Furthermore, stability analysis confirms that the operating point of the closed-loop system converges within a finite time. The effectiveness of this novel controller is validated through simulations using the MATLAB/Simulink environment. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic path following control of underactuated marine vehicles (UMVs) subject to multiple disturbances and constraints. Firstly, the complex marine environment in which UMVs navigate typically contains stochastic components, thus the multiple disturbances are categorized as slow-varying deterministic disturbances and stochastic disturbances. Secondly, a position-constrained line-of-sight (PCLOS) based fractional-order sliding mode stochastic (FSMS) control strategy is established to achieve path following control of UMVs. A PCLOS guidance law based on universal barrier Lyapunov function is proposed to ensure that the position errors remain within the constraint ranges, which is versatile for systems with symmetric constraints or without constraints. An FSMS controller based on fractional-order theory and sliding mode control is designed to improve the dynamic response speed of the system and effectively attenuate chattering phenomenon. A stochastic disturbance observer is developed to estimate the slow-varying deterministic disturbances in the stochastic system, and auxiliary dynamic compensators are used to mitigate the impact of input constraints. Lastly, theoretical analysis indicates that the closed-loop system is stable and the position constraint requirements are satisfied. Comparative simulations illustrate the effectiveness of the proposed control strategy. • The multiple disturbances are categorized as slow-varying deterministic disturbances, and stochastic disturbances. • A novel PCLOS guidance law is designed to ensure that the position errors do not exceed the given constraint ranges. • The fractional-order sliding mode stochastic control method exhibits improved robustness and flexibility compared to traditional integer-order sliding mode control method. [ABSTRACT FROM AUTHOR]

Skid-steer mobile robots (SSMRs) are ubiquitous in indoor and outdoor applications. Their accurate trajectory tracking control is quite challenging due to the uncertainties arising from the complex behavior of frictional force, external disturbances, and fluctuations in the instantaneous center of rotation (ICR) during turning maneuvers. These uncertainties directly disturb velocities, hindering the robot from tracking the velocity command. This paper proposes a nonsingular terminal sliding mode control (NTSMC) based on backstepping for a four-wheel SSMR to cope with the aforementioned challenges. The strategy seeks to mitigate the impacts of external disturbances and model uncertainties by developing an adaptive law to estimate the integrated lumped outcome. The finite time stability of the closed-loop system is proven using Lyapunov's theory. The designed NTSMC input is continuous and avoids noticeable chattering. It was noted in the simulation analysis that the proposed control strategy is strongly robust against disturbance and modeling uncertainties, demonstrating effective trajectory tracking performance in the presence of disturbance and modeling uncertainties. [ABSTRACT FROM AUTHOR]

This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the H ∞ criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control. [ABSTRACT FROM AUTHOR]

This work proposes an adaptive rapid terminal SMC (sliding mode control) approach based on the FFTSO (fast finite-time state observer) for overhead crane trajectory tracking and anti-swing control in the presence of external disturbances and parameter uncertainty. First, the system state observation under the constraint of unknown system parameters is accomplished by designing the FFTSO based on finite-time theory. Next, a parameter-adaptive fast terminal SMC is created for an overhead crane based on the model transformation. This technique can still monitor the intended trajectory and reduce payload swing even in cases when the payload mass and wire rope length are uncertain. Next, the Lyapunov theorem is used to demonstrate the stability of the overhead crane system's positioning and anti-swing angle control mechanism. Lastly, the platform experiments confirm that the suggested closed-loop system control technique is successful. [ABSTRACT FROM AUTHOR]

This paper investigates the control problem of a spacecraft attitude manoeuvrer with external disturbances. Firstly, the spacecraft attitude dynamical model is introduced; then, the tube-based framework is constructed, which includes a nominal system and an error system. Based on that, the control law design would be a two-step process. To start with, the nominal control law is developed via an adaptive dynamic programming technique and a neural network approximation in order to provide a nominal trajectory to the desired attitude. Moreover, based on the nonsingular terminal sliding mode control scheme, the error controller is derived to lead the actual system to track the nominal trajectory and suppress disturbances. The stability of the closed-loop system is analyzed via the Lyapunov approach and the simulation results could verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This work presents a methodology for controlling a quadrotor vehicle in both regulation and trajectory tracking tasks when the system is affected by endogenous and exogenous disturbances. In the proposed approach, the quadrotor is driven by a second-order variable-gain sliding mode controller (VG-SMC), which includes a state-dependent variable-gain that allows enhancing the controller performance against disturbances. Besides, the proposed controller achieves finite-time convergence of the position and orientation error signals and their time derivatives. The performance of the closed-loop system is assessed by comparing it with a standard sliding mode controller whose control objective is to track two optimal smooth reference signals. The comparison between both controllers considers the undisturbed and the perturbed cases. Numerical simulations and experimental results demonstrate that the proposed VG-SMC controller provides better overall closed-loop results than those obtained by a fixed-gain sliding mode controller, despite the presence of disturbances. [ABSTRACT FROM AUTHOR]

In this paper, a learning-based nearly optimal control framework with fault-tolerant capability is designed to tackle the tracking control problem of a flexible-link manipulator in the presence of actuator fault and model uncertainties. Initially, the optimal control law is obtained by adopting the dynamic programming and a critic structure as the solution of Hamilton–Jacobi–Bellman equation for the nominal model. Then, by implementing an integral sliding mode control, the robustness against actuator fault and model uncertainty is guaranteed. The adaptive laws are constructed based on radial basis functions neural networks to estimate the upper bound of uncertainty and the actuator bias fault, satisfying both optimal performance and chattering reduction of the sliding surface. Furthermore, the actuator effectiveness loss is handled. The stability of the closed-loop system is analytically proven, and the performance of the proposed framework is investigated against several practical operating conditions. This incorporates the fidelity assessment of tracking precision and trackability of control signal using performance indices such as the integral absolute error and root-mean-square error. The results of extensive simulation studies confirm the effectiveness and robustness of the proposed control framework. [ABSTRACT FROM AUTHOR]

In this study, we address the trajectory tracking control problem for stratospheric airships, characterized by parameter uncertainties and external disturbances. Initially, a mathematical model of the airship is constructed, from which a trajectory tracking error model is derived. Subsequently, a novel sliding mode control law is formulated to enhance control accuracy and accelerate the convergence rate of the sliding mode. Furthermore, radial basis function neural networks are utilized to estimate and compensate for uncertain system parameters and external disturbances, significantly improving the system's robustness. Lastly, the application of Lyapunov's theory verifies the fixed-time stability of the closed-loop system and ensures the convergence of trajectory tracking error to a near-zero vicinity within fixed time. Simulation results strongly support the efficacy of the proposed control strategy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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This paper studies the straight-line path-following problem on the lateral plane for fixed-wing unmanned aerial vehicles (FWUAVs) which are susceptible to uncertainties. Firstly, based on the natural frame's location on the prescribed reference paths, the command yaw angle (which is the basis for yaw angle control system design) is solved analytically by combining it with the errors of path following, attack angle, sideslip angle, attitude angles, and geometric parameters of the prescribed reference paths. Secondly, by considering complicated dynamic characteristics, a linear extended state observer is designed to estimate uncertainties such as nonlinearities, couplings, and unmodeled dynamics whose estimated values are incorporated into the continuous-time predictive controllers for feedback compensation. Finally, numerical simulations are conducted to demonstrate the advantages of the proposed method, including reduced tracking errors and enhanced robustness in the closed-loop system, as compared to the conventional nonlinear dynamic inversion and sliding mode control approaches. [ABSTRACT FROM AUTHOR]

This paper studies aeroelastic control for a two-dimensional airfoil–flap system with unknown gust disturbances and model uncertainties. Open loop limit cycle oscillation (LCO) happens at the post-flutter speed. The structural stiffness and quasi-steady and unsteady aerodynamic loads of the aeroelastic system are represented by nonlinear models. To robustly suppress aeroelastic vibration within a finite time, a backstepping terminal sliding-mode control (BTSMC) is proposed. In addition, a learning rate (LR) is incorporated into the BTSMC to adjust how fast the aeroelastic response converges to zero. In order to overcome the fact that the BTSMC design is dependent on prior knowledge, a nonlinear disturbance observer (DO) is designed to estimate the variable observable disturbances. The closed-loop aeroelastic control system has proven to be globally asymptotically stable and converges within a finite time using Lyapunov theory. Simulation results of an aeroelastic two-dimensional airfoil with both trailing-edge (TE) and leading-edge (LE) control surfaces show that the proposed DO-BTSMC is effective for flutter suppression, even when subjected to gusts and parameter uncertainties. [ABSTRACT FROM AUTHOR]

An adaptive fractional-order sliding mode control method using a disturbance observer is proposed for position tracking of a quadrotor. The mathematical model of the quadrotor considering disturbance is derived using the Euler–Lagrange equations. The model is divided into two fully actuated and underactuated subsystems. The proposed controller as the result of combining fractional calculus and the sliding mode method is designed for both subsystems separately. Furthermore, a disturbance observer is designed which deals with actuator fault, uncertainty, and wind disturbance. The stability of the closed-loop system is proved using Lyapunov theory and finite-time convergence of the variables to the desired values is guaranteed. In the numerical simulation, position tracking despite the actuator faults and effects of load and wind disturbance are investigated. Finally, the simulation results validate the superior performance and robustness of the proposed controller against actuator fault and wind disturbance and the results of controllers are compared. [ABSTRACT FROM AUTHOR]

Power systems are naturally prone to numerous uncertainties. Power system functioning is inherently unpredictable, which makes the networks susceptible to instability. Rotor-angle instability is a critical problem that, if not effectively resolved, may result in a series of failures and perhaps cause blackouts (collapse). The issue of state feedback sliding mode control (SMC) for the excitation system is addressed in this work. Control is decentralized by splitting the global system into several subsystems. The effect of the rest of the system on a particular subsystem is considered a disturbance. The next step is to build the state feedback controller with the disturbance 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. According to the control architecture, the system motion in the sliding mode is guaranteed to only be minorly affected by mismatched disturbances in power systems. Furthermore, the proposed controllers are expressed in terms of Linear Matrix Inequalities (LMIs) using the Lyapunov theory. Lastly, an IEEE test system is used to illustrate how successful the suggested approach is. [ABSTRACT FROM AUTHOR]

This paper tackles the problem of trajectory tracking for wheeled mobile robots subject to time-varying input delay and bounded external disturbances. First, we establish a dynamic model for a wheeled mobile robot under sliding and skidding conditions, and determine the maximum allowable input delay that maintains system stability using Razumikhin-type stability analysis without prior knowledge of the variation in delay. The proposed adaptive robust controller combined with super-twisting sliding mode control is resilient to disturbances such as input delay, system uncertainty, and parameter variation. The proposed adaptive law enables real-time modification of switching gain based on tracking error without predefined knowledge of uncertainty bounds. Compared with traditional sliding mode control strategies, the super-twisting algorithm can eliminate chattering phenomenon while combined robust methods further reduce modeling uncertainties' influence on system performance. Finally, we select an appropriate Lyapunov function to analyze and prove uniformly ultimately bounded of the closed-loop system. MATLAB simulation comparison results demonstrate that this approach achieves high tracking accuracy, faster response speed, and robustness. [ABSTRACT FROM AUTHOR]

Controlling variable wind speed turbine (VWT) system based on a doubly-fed induction generator (DFIG) is a challenging task. It requires a control law that is both adaptable and robust enough to handle the complex dynamics of the closed control loop system. Sliding mode control (SMC) is a robust control technology that has shown good performance when employed as a passive fault-tolerant control for wind energy systems. To improve the closed control loop of VWT based on DFIG with the aim of improving energy efficiency, even in presence of nonlinearities and a certain range of bounded parametric uncertainties, whether electrically or mechanically, an adaptive passive fault tolerant control (AP-FTC) based on a self-tuning fractional integral sliding mode control law (ST-FISMC) developed from a novel hyperbolic fractional surface is proposed in this paper. ST-FISMC introduces a nonlinear hyperbolic function into the sliding manifold for self-tuning adaptation of control law, while fractional integral of the control law smooths discontinuous sign function to reduce chattering. Additionally, this work introduces an adaptive observer, developed and proved based on a chosen Lyapunov function. This observer is designed to estimate variations in electrical parameters and stator flux, ensuring sensorless decoupling in indirect field-oriented control (SI-FOC) of DFIG. Lyapunov theory is also used to prove stability of states vectors in closed control loop with presence of bounded parameters uncertainties or external disturbances. Simulation results show that the proposed approach offers better performance in capturing optimal wind energy, as well as the ability to regulate active/reactive power and high resilience in presence of occurring parameter uncertainties or external disturbances. [ABSTRACT FROM AUTHOR]

Due to its high power-to-weight ratio, low weight, and silent operation, shape memory alloy (SMA) is widely used as a muscle-like soft actuator in intelligent bionic robot systems. However, hysteresis nonlinearity and multi-valued mapping behavior can severely impact trajectory tracking accuracy. This paper proposes an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) scheme aimed at enhancing position tracking performance in SMA-actuated systems by addressing hysteresis nonlinearity, uncertain dynamics, and external disturbances. Firstly, a simplified third-order actuator model is developed and a variable gain extended state observer (VGESO) is employed to estimate unmodeled dynamics and external disturbances within finite time. Secondly, a novel nonsingular fast terminal sliding mode control (NFTSMC) law is designed to overcome singularity issues, reduce chattering, and guarantee finite-time convergence of the system states. Finally, the ANFTSMC scheme, integrating NFTSMC with VGESO, is proposed to achieve precise position tracking for the prosthetic hand. The convergence of the closed-loop control system is validated using Lyapunov's stability theory. Experimental results demonstrate that the external pulse disturbance error of ANFTSMC is 8.19°, compared to 19.21° for the comparative method. Furthermore, the maximum absolute error for ANFTSMC is 0.63°, whereas the comparative method shows a maximum absolute error of 1.03°. These results underscore the superior performance of the proposed ANFTSMC algorithm. [ABSTRACT FROM AUTHOR]

This study explores the security control challenges encountered in cyber-physical systems when facing unknown nonlinearities and network attacks. It adopts an approach integrating observer-based adaptive sliding mode control and a threshold-changing event-triggered mechanism. Initially, a sliding mode function is formulated utilizing observer state, leading to the derivation of error dynamics and sliding mode dynamics. Subsequently, conditions ensuring stability of the closed-loop system are established through Lyapunov theory, expressed in terms of linear matrix inequalities. To achieve finite-time reaching of the predefined sliding surface, an observer-based adaptive controller is designed. Finally, the effectiveness of the proposed methodology is validated through a practical example. [ABSTRACT FROM AUTHOR]

This paper attempts to develop a unified model predictive control (MPC) method for integrated path planning and trajectory tracking of autonomous underwater vehicles (AUVs). To deal with the computational burden of online path planning, an event-triggered model predictive control (EMPC) method is introduced by using the environmental change as a triggering mechanism. A collision hazard function utilizing the changing rate of hazard as a triggering threshold is proposed to guarantee safety. We further give an illustration of how to calculate this threshold. Then, a Lyapunov-based model predictive control (LMPC) framework is developed for the AUV to solve the trajectory tracking problem. Leveraging a nonlinear integral sliding mode control strategy, we construct the contraction constraint within the formulated LMPC framework, thereby theoretically ensuring closed-loop stability. We derive the necessary and sufficient conditions for recursive feasibility, which are subsequently used to prove the closed-loop stability of the system. In the simulations, the proposed path planning and tracking control are verified separately and integrated and combined with static and dynamic obstacles. [ABSTRACT FROM AUTHOR]

This study investigates the performance of designing a Synergetic Control (SC) approach for angular position tracking control of driven-pendulum systems. SC is one of the popular nonlinear control techniques that contributed in a variety of control design applications. This research shows a unique application of the SC for angular position tracking control of driven-pendulum systems. Initially, the equations of motion of the system are developed. Subsequently, the control law of the SC is established. For the stability analysis of the closed loop control system, the Lyapunov Function (L.F) is used. To guarantee optimal performance, a Sparrow Search Optimization (SSO) based approach is presented in order to search for the optimum designing parameters of the controller. For performance comparison, the classical Sliding Mode Control (SMC) is introduced. The simulation's outcomes of the study have been confirmed that the proposed control algorithm is addressed the tracking problem of the angular position of the system successfully. Besides, when an external disturbance is inherited in the simulation, the SC exhibits a robustness performance. Moreover, the performance of the SC is slightly similar as SMC. However, the distinct difference in the performance is that the control signal of the SMC exhibits chattering problem, while this phenomenon is absent in the SC. All computer simulations are carried out using MATLAB software. [ABSTRACT FROM AUTHOR]

In this paper, an unmanned bicycle (UB) with a reaction wheel is designed, and a second-order mathematical model with uncertainty is established. In order to achieve excellent balancing performance of the UB system, an adaptive controller is designed, which is composed of nominal feedback control, compensating control using extreme learning machine observer and reaching control via integral terminal sliding mode (ITSM) and barrier function (BF)-based adaptive law. Owing to the features of BF-based ITSM (BFITSM), not only any uncertainty or disturbance upper bound is not needed any longer but also the finite-time convergence of the closed-loop system can be ensured with a predefined error bound. Moreover, the BF-based control gain can be adaptively adjusted according to the update of the lumped uncertainty such that the overestimation is removed. The stability analysis of the closed-loop system is given according to Lyapunov theory. Comparable experimental results on an actual UB are carried out to validate the superior balancing performance of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper concentrates on robust attitude control issues for spacecraft formation in gravitational-wave detection missions. Notably, with the large-scale communication delays brought by the million kilometers-scale inter-satellite distance, the exponential convergence of the closed-loop delayed system is firstly achieved via a new delay-dependent nominal attitude coordinated control scheme. Then, a finite-time disturbance observer is deployed to reconstruct the unknown lumped disturbance from internal uncertainties and the external environment. Meanwhile, an integral sliding manifold is embedded in the delay-dependent attitude controller for superior systems' robustness. Finally, two simulation examples illustrate the feasibility and effectiveness of the proposed attitude control strategy for in-orbit gravitational-wave detection spacecraft systems. • Spacecraft formation attitude control in gravitational-wave detection is studied. • Large-scale communication delays (LCD) among formation members are firstly modeled. • An attitude coordinated controller is put forward to handle the LCD. • An integral sliding manifold with disturbance observer is embedded for superior robustness. [ABSTRACT FROM AUTHOR]

This paper describes a new approach to control stall and surge instabilities in the compressor system by using of finite time backstepping-based adaptive sliding mode method. The most important innovation of this study is to provide a finite time adaptive control method to simultaneously prevent the stall and surge instabilities in a compressor system in the presence of disturbance and uncertainty in the compressor characteristic curve as well as the throttle valve. The disturbance and uncertainty issues are covered by a robust sliding mode control and the gain coefficients of this controller as well as the estimation of uncertain terms are obtained by using the adaptive method. The Lyapunov stability criterion is used to evaluate the finite-time stability of the closed-loop system. The performance of the proposed method is compared with other literature methods through simulation in Matlab. The simulation results show that the proposed controller is better than the existing methods in terms of surge preventing and robustness against uncertainty and disturbance. [ABSTRACT FROM AUTHOR]

This paper proposes an output feedback-based control for uncertain electro-hydrostatic systems (EHSs) to satisfy high output tracking precision under the influences of unknown mismatched and matched uncertainties and unstructured dynamical behavior. In this configuration, an extended state observer (ESO) is first employed to obtain unmeasured states and suppress the adverse effect of matched uncertainty. Meanwhile, the influence of unstructured dynamical behavior is approximated by employing a radial basis function neural network (RBFNN)-based technique. With the unmeasured states observed, matched uncertainty, and system dynamics compensated, the robust backstepping sliding mode control is accordingly established and the lumped mismatched uncertainty is then suppressed through disturbance observer-based adaptive law. Interestingly, the proposed control methodology requires only output feedback but can address the whole system dynamics. The stability of the closed-loop system is theoretically proven through a Lyapunov theorem and the effectiveness of the proposed methodology is demonstrated through comparative simulations. [ABSTRACT FROM AUTHOR]

This paper addressed the challenging problem of distributed optimization for nonlinear singular perturbation multi-agent systems. The main focus lies in steering the system outputs toward the optimal points of a globally objective function, which was formed by the combination of several local functions. To achieve this objective, the singular perturbation multi-agent system was initially decomposed into fast and slow subsystems. Compared to traditional methods, robustness in referencetracking signals was ensured through the design of fast-slow sliding mode controllers. Additionally, our method ensured robustness against errors between reference signals and optimal values by employing a distributed optimizer to generate precise reference signals. Furthermore, the stability of the entire closed-loop system was rigorously guaranteed through the application of the small-gain theorem. To demonstrate the efficacy of the proposed approach, a numerical example was presented, providing empirical validation of its effectiveness in practical scenarios. [ABSTRACT FROM AUTHOR]

This article investigates the distributed formation trajectory tracking problem of a homogeneous quadrotor unmanned aerial vehicles (UAVs) system using a leader‐follower consensus protocol in three‐dimensional space. To enable the follower UAVs in the swarm to track a single leader UAV and form a desired formation under undirected topology, a six‐degree‐of‐freedom dynamic model with bounded time‐varying disturbances is established, which is divided into a tracking subsystem and a stabilizing subsystem. A practical sliding mode control (PSMC) based event‐triggered algorithm is proposed to achieve distributed formation control for a leader‐follower quadrotor UAVs system and reduce the network transmission resources. To address the potential issue of inter‐UAVs collisions during formation, an artificial potential field (APF) method is introduced in the tracking subsystem, and an disturbance observer is introduced in the stabilizing subsystem to estimate the unknown external disturbances. The boundedness of signals in the closed‐loop system is demonstrated using Lyapunov stability theory, and the exclusion of Zeno behavior can be ensured by having a positive lower bound on the inter‐event time between two consecutive triggering events. Finally, the effectiveness of the proposed event‐triggered algorithm is validated through simulation examples. [ABSTRACT FROM AUTHOR]

The concurrent existence of model uncertainties, external disturbances, and actuator faults in a nonlinear system such as a robotic manipulator can significantly affect the trajectory tracking performance of these systems. Therefore this study is devoted to proposing a control approach based on fixed‐time control theory to improve the trajectory tracking performance of the robotic manipulator in the presence of lumped disturbance, including uncertainties, external disturbances, and actuator faults. The control approach in this paper is designed based on the integration of a fixed‐time adaptive sliding mode observer and a fixed‐time non‐singular fast terminal sliding mode control design strategy. Firstly, a new fixed‐time adaptive sliding mode observer is designed based on fixed‐time theory and adaptive control theory to estimate the lumped disturbance present in the system. Then, using the information from the disturbance observer, the fixed‐time non‐singular fast terminal sliding mode control is devised based on a non‐singular fixed‐time sliding surface and a fixed‐time reaching approach. Furthermore, in the sense of the Lyapunov theorem, through rigorous analysis, it is demonstrated that the tracking errors of the closed‐loop system converge to a small neighbourhood within a fixed time, regardless of the information about the initial conditions of the states of the system. Finally, extensive comparative simulations are performed using the PUMA560 robot to manifest the feasibility and validity of the proposed control strategy in terms of trajectory tracking accuracy and fast convergence in the presence of uncertainties, disturbances, and actuator faults. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a novel speed‐current single‐loop speed regulation controller for permanent magnet synchronous motor (PMSM) based on model‐assisted cascaded extended state observer (ESO) and sliding mode control (SMC), aimed at simplifying the control structure, increasing dynamic performance, and improving antidisturbance performance. Firstly, a cascaded ESO based on model information is designed for the second‐order model of single‐loop control of PMSM. This approach allows for quick and accurate estimation of disturbance without increasing bandwidth, while also reducing the burden of ESO with model‐assisted information. Next, with the estimation disturbance feedforward compensation, the composite controller is constructed based on SMC, which effectively eliminates residual disturbance and reduces chatterings. The stability of the closed‐loop system under the proposed controller is proved strictly. Finally, simulations and experiments are conducted to validate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: Rock drilling jumbo is an important large construction machine used for tunneling construction, and its automation has an urgent demand in engineering. However, the electro‐hydraulic system of the rock drilling jumbo has strong parameters uncertainties and some dynamics that are hard to model accurately, which causes certain challenges for designing model‐based high‐performance control algorithms. To solve these challenges, a parameter adaptive based neural network sliding mode control algorithm is proposed to enhance control performance of the electro‐hydraulic system. The parameter adaptive law is developed to estimate unknown parameters of the system, the neural network is applied for compensating unmodeled dynamics, and then the final control law is designed by sliding mode control method, and the stability demonstration of the closed‐loop system is given. In the simulations, the effectiveness of the designed parameter adaptive law is verified. Extensive comparison experiments are performed on a real rock drilling jumbo driven by proportional valves, the experimental results demonstrate that the developed control algorithm obviously improves the control precision of hydraulic cylinder of the rock drilling jumbo compared with the traditional sliding mode and PID control algorithm, thus the designed control algorithm can be expanded and applied for general hydraulic servo control mechanism. [ABSTRACT FROM AUTHOR]

A fast trajectory tracking controller is designed for the airship, involving dynamic uncertainties of parameters, capable of guaranteeing the prescribed performance of tracking errors, and fast response of the closed-loop system. To achieve the decoupling of velocity control and attitude control of the airship, a new guidance and control integration framework is proposed first. Then, based on the dynamics model established by the spinor method, the lumped disturbance, caused by unknown aerodynamic parameter uncertainties and exogenous disturbances, is estimated online using a high-order finite-time observer. The control performance, namely, overshoot and steady-state performance of tracking errors, is significantly improved by utilizing the prescribed output performance constraints, while the convergence rate is further enhanced by combining the finite-time convergence property of the fast terminal sliding mode control. Simulation results attest to the effectiveness of the strategy in this paper. Compared with the adaptive fast terminal sliding mode control, the strategy effectively utilizes the capability of the actuator within the allowed range and reduces the convergence time by more than half with similar control inputs. [ABSTRACT FROM AUTHOR]

This paper provides a new sliding mode control (SMC) approach, by which both the nominal and robust stability associated with a trajectory tracking problem for an uncertain robot manipulator are achieved. More precisely, the new control law consists of linear and nonlinear functions of tracking errors, in which the former is for the nominal stability and the latter is to ensure the robust stability of the resulting closed‐loop systems. The nonlinear function can be interpreted as an extended version of conventional SMC approach, and the reaching phase corresponding to a pregiven sliding surface is shown to be completed in a finite time; the tracking errors arrive at the sliding surface in a finite time and do not deviate from it after the arrival. In the sliding phase, the tracking errors are also ensured to converge to the origin. Finally, some simulation results are given to demonstrate both the theoretical validity and practical effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for increasing the precision of high-precision positioning control experiments for a piezoelectric stick–slip actuator system. This is achieved through dynamic sliding mode control with a radial basis function neural network (RBFNN) based on the Lambert W function. The proposed control strategy is divided into two parts: scanning mode control and stepping mode control. For scanning control, a dynamic sliding mode controller was designed to solve the jitter problem in traditional sliding mode control. The introduction of the RBFNN avoids the effects of uncertainty terms and unknown disturbances in the model; reduces the controller gain, which must be adjusted; and improves the robustness of the system to disturbances. The stability of the dynamic sliding mode controller based on the RBFNN was verified through a Lyapunov analysis, and the Lambert W function was introduced to optimize the controller parameters responsible for the time lag in the closed-loop control system. This optimization improved the system's robustness against time delays, which can adversely affect its performance. Simulation and experimental results indicated that the proposed control strategy achieved a positioning control accuracy of <40 nm during the scanning phase and was robust in the presence of a load. In long-distance positioning control experiments, the control strategy achieved a control target of 40 μm while maintaining the positioning control accuracy and reducing the impact of time lag on the system. [ABSTRACT FROM AUTHOR]

The accurate positioning and swing suppression of tower cranes remain open problems, especially when considering unknown payload masses, frictions and wind disturbances, making the controller design more challenging. Therefore, considering the factors, without linearization to 5-DOF tower crane dynamics, an improved non-singular fast terminal sliding mode control (INFTSMC) scheme is proposed, which can drive the trolley, jib and cable to the desired positions accurately within finite time while suppressing payload swings effectively under the unknown payload masses, frictions and wind disturbances. Specifically, an improved sliding mode surface is designed to suppress payload swings; a chattering problem is attenuated by constructing an enhanced convergence law; a payload mass estimation strategy is designed to eliminate the vertical positioning error; adaptive schemes are proposed to counteract the effects of unknown frictions and wind disturbances. The stability of the closed-loop system is proven rigorously by using the Lyapunov principle and LaSalle's invariance theorem. Comparative simulations are implemented to validate the superior control performances and robustness of the proposed method. • Considering the unknown payload masses, frictions and wind disturbances, a 5-DOF tower crane dynamic model without linearization is established. • An improved non-singular fast terminal sliding mode control scheme is proposed to achieve the finite-time convergence of the closed-loop system, accurate payload positioning and effective swing suppression. • The stability and finite-time convergence of the closed-loop system are proved rigorously by using the Lyapunov technique and LaSalle's invariance principle. [ABSTRACT FROM AUTHOR]

This paper investigates the cooperative formation trajectory tracking problem for heterogeneous unmanned aerial vehicle (UAV) and multiple unmanned surface vessel (USV) systems with input quantization performance. Firstly, at the kinematic level, a distributed guidance law based on an extended state observer (ESO) is designed to compensate for the unknown speed of neighbor agents for expected trajectory tracking, and subsequently at the dynamic level, an ESO is utilized to estimate model uncertainties and environmental disturbances. Following that, a linear analytic model is employed to depict the input quantization process, and the corresponding adaptive quantization controller is designed without necessitating prior information on quantization parameters. Based on the input-to-state stability, the stability of the proposed control structure is proved, and all the signals in the closed-loop system are ultimately bounded. Finally, a simulation study is provided to show the efficacy of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper presents an indirect adaptive neural network (NN) control algorithm tailored for flexible joint robots (FJRs), aimed at achieving desired transient and steady-state performance. To simplify the controller design process, the original higher-order system is decomposed into two lower-order subsystems using the singular perturbation technique (SPT). NNs are then employed to reconstruct the aggregated uncertainties. An adaptive prescribed performance control (PPC) strategy and a continuous terminal sliding mode control strategy are introduced for the reduced slow subsystem and fast subsystem, respectively, to guarantee a specified convergence speed and steady-state accuracy for the closed-loop system. Additionally, a composite-learning optimal bounded ellipsoid algorithm (OBE)-based identification scheme is proposed to update the NN weights, where the tracking errors of the reduced slow and fast subsystems are integrated into the learning algorithm to enhance the identification and tracking performance. The stability of the closed-loop system is rigorously established using the Lyapunov approach. Simulations demonstrate the effectiveness of the proposed identification and control schemes. [ABSTRACT FROM AUTHOR]

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods. [ABSTRACT FROM AUTHOR]

We present a novel approach for achieving high-precision trajectory tracking control in an unmanned surface vehicle (USV) through utilization of receding horizon reinforcement learning (RHRL). The control architecture for the USV involves a composite of feedforward and feedback components. The feedforward control component is derived directly from the curvature of the reference path and the dynamic model. Feedback control is acquired through application of the RHRL algorithm, effectively addressing the problem of achieving optimal tracking control. The methodology introduced in this paper synergizes with the rolling time domain optimization mechanism, converting the perpetual time domain optimal control predicament into a succession of finite time domain control problems amenable to resolution. In contrast to Lyapunov model predictive control (LMPC) and sliding mode control (SMC), our proposed method employs the RHRL controller, which yields an explicit state feedback control law. This characteristic endows the controller with the dual capabilities of direct offline and online learning deployment. Within each prediction time domain, we employ a time-independent executive–evaluator network structure to glean insights into the optimal value function and control strategy. Furthermore, we substantiate the convergence of the RHRL algorithm in each prediction time domain through rigorous theoretical proof, with concurrent analysis to verify the stability of the closed-loop system. To conclude, USV trajectory control tests are carried out within a simulated environment. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced and robust tracking control method for the class of uncertain and disturbed affine nonlinear systems. The approach is based on predictive sliding mode control (PSMC) to combine the advantages of sliding mode control (SMC) with those of model predictive control (MPC). The resulting controller offers numerous benefits, including high robustness, quick transient response, finite-time convergence, and robustness against uncertainties and external disturbances. However, a significant limitation of the proposed PSMC is its reliance on prior knowledge of the disturbance and uncertainty bounds. To address this drawback, a sliding mode observer (SMO) is synthesised to identify uncertainties and disturbances. The proposed controller successfully eliminates the chattering effect without compromising robustness and precision. The Lyapunov theory is used to prove the stability of the closed-loop system. The effectiveness of the proposed approach is validated through simulations on a well-known benchmark. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of integrated guidance and control (IGC) design for an unmanned aerial vehicle with an unknown control coefficient, approach angle constraint, and field-of-view limitations. Different from the existing methods, the proposed approach integrates the approach angle and field-of-view requirements into a single reference to satisfy the constraints simultaneously, and meanwhile guarantees the successful mission despite the unknown control coefficient. Based on the established IGC model, a novel sliding mode strategy is generated to ensure that the approach angle and field-of-view constraints can be obeyed once the designed reference is tracked precisely. Then, the IGC issue are transformed into a tracking problem under an unknown control direction, and the periodic sliding mode control technique is introduced to construct the IGC law. The stability of the closed-loop system is analyzed in detail. The effectiveness of the proposed method is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes particle swarm optimization (PSO) and cuckoo search (CS) approaches based on the sliding mode controller (SMC) structure for the unmanned quadrotor's flights. The control law is derived from the Lyapunov theory to guarantee the closed-loop stability. Despite unknown disturbance bounds, the simulation experiments on the nonlinear quadrotor's model prove that these intelligent controllers are very effective for position control, attitude stabilization, automatic take-off and landing, and trajectory tracking missions. Conducted comparisons to the intelligent proportional integral derivative structure through PSO, CS, genetic algorithms, neural networks, fuzzy logic, and some hybrid techniques proposed in previous works of quadrotor control, confirm the superiority of PSO-SMC in terms of robustness and adaptability. [ABSTRACT FROM AUTHOR]

In this paper, a fixed-time sliding mode control scheme is developed to fulfill the trajectory tracking task of a marine surface vehicle with unknown dynamics. To restrain the adverse effects of the unknown dynamics including the parameter inaccuracy and exogenous disturbances, a fixed-time disturbance observer is designed to estimate the lumped uncertainties using the bi-limit homogeneous theory without requiring any knowledge of the model uncertainties. Then, a nominal tracking controller is proposed to stabilize the error dynamic model in the sense of fixed-time Lyapunov stability, based on which a novel integral-type sliding mode manifold with bi-limit homogeneity is constructed to drive tracking error convergence in fixed time. To enhance the robustness of the vessel control system, a disturbance observer–based fixed-time integral sliding mode tracking controller is finally proposed, and the chattering phenomenon is effectively alleviated by direct estimation compensations. The analysis of Lyapunov stability indicates that the closed-loop system is fixed-time stable. Numerical simulations on a model vessel are carried out to validate theoretical results of the proposed control scheme. [ABSTRACT FROM AUTHOR]