Fast Finite-time Convergence Research Articles

Dynamic Surface Intelligent Robust Control of Nonlinear Systems With Fixed-Time Sliding-Mode Observer.

The high tracking control precision and fast finite-time convergence for nonlinear systems is a significant challenge due to complex nonlinearity and unknown disturbances. To address this challenge, a dynamic surface intelligent robust control strategy with fixed-time sliding-mode observer (DSIRC-SMO) is proposed to improve the tracking control performance in a finite time. First, adaptive fuzzy neural network based on a predictor (P-AFNN) is designed to imitate the complex nonlinearity. In particular, the weight adaptive law is formulated by utilizing the prediction error information, which improves the accuracy of approximating the nonlinear system. Second, the fixed-time sliding-mode observer (SMO) is integrated into the dynamic surface control technique to deal with unknown disturbances and modeling errors in a fixed time. This integration allows for timely updates the dynamic surface using observation information, thereby enhancing the system's anti-interference capability. Then, the fixed-time convergence of SMO is proven. Third, the proposed DSIRC-SMO can be effectively implemented and the finite-time convergence of DSIRC-SMO is proven in detail based on the fixed-time convergence of SMO. Finally, numerical simulation and actual wastewater treatment processes simulation are conducted to validate the effectiveness of DSIRC-SMO.

Comparative Real-Time Study of Three Enhanced Control Strategies Applied to Dynamic Process Systems

In this study, a comparative analysis of three different control methods for precise, real-time control of a complex dynamic double-tank liquid level process system was performed. Since the system in question has a time-delayed structure, feedforward proportional integral (FF-PI) control and cascaded nonlinear feedforward proportional integral delayed (CNPIR) controllers were tested on the process system. While the FF-PI controller improved the response time of the system, it showed limitations in handling external disturbances and nonlinearities. On the other hand, the CNPIR controller showed better improvements in control accuracy and lower overshoot compared to the FF-PI controller. Since the process system has a nonlinear model and is affected by external disturbances, these two controllers were inadequate in this study when compared to the fractional order adaptive proportional integral derivative sliding mode controller (FO-APIDSMC). The FO-APIDSMC controller provided fairly good performance in both tracking accuracy and disturbance rejection control for non-chattering, fast finite-time convergence, increased robustness, and uncertain dynamic processes. Experimental results reveal that the FO-APIDSMC controller achieves superior minimized tracking error and outperforms the FF-PI and CNPIR controllers by effectively handling uncertainties and external disturbances.

Finite-Time Continuous Nonsingular Terminal Modified Adaptive-Gain Super-Twisting Control: Application to a 2-DOF Planar Robot Manipulator System.

This article proposes finite-time continuous nonsingular terminal modified adaptive-gain super-twisting control (FT-CNT-MAG-STC) for the second-order disturbed systems. Compared with existing sliding-mode controllers, the noteworthy improvements of the proposed framework are the fast finite-time convergence, continuous control signal, ease-of-implementation feature, and relaxation of the assumption related to the information on the bounds of the disturbance and its derivative. In the proposed framework, a fast nonsingular terminal sliding surface is first developed such that the singularity problem is avoided and the convergence rate is improved. Then, we design a continuous modified super-twisting algorithm with an adaptive gain, under which the need for the bounds information of the disturbance and its derivative is relaxed and the performance of the closed-loop system is enhanced. Rigorous analysis is provided to prove the finite-time convergence of the system states to small regions containing the origin. We apply the proposed framework to the position control for a 2-DOF planar robot manipulator system. Various experimental results are illustrated to evaluate the effectiveness of the designed position controller.

Adaptive Event-Triggered Fast Finite-Time Stabilization of High-Order Uncertain Nonlinear Systems and Its Application in Maglev Systems.

This article is concerned with the global fast finite-time adaptive stabilization for a class of high-order uncertain nonlinear systems in the presence of serious nonlinearities and constraint communications. By renovating the technique of continuous feedback domination to the construction of a serial of integral functions with nested sign functions, this article first proposes a new event-triggered strategy consisting of a sharp triggered rule and a time-varying threshold. The strategy guarantees the existence of the solutions of the closed-loop systems and the fast finite-time convergence of original system states while reaching a compromise between the magnitude of the control and the trigger interval. Quite different from traditional methods, a simple logic is presented to avoid searching all the possible lower bounds of trigger intervals. An example of the maglev system and a numerical example are provided to demonstrate the effectiveness and superiority of the proposed strategy.

Fast Finite-Time Super-Twisting Sliding Mode Control with an Extended State Higher-Order Sliding Mode Observer for UUV Trajectory Tracking

This paper proposes a trajectory tracking control scheme consisting of a fast finite-time super-twisting sliding mode control (FSTSMC) approach and an extended state higher-order sliding mode observer (ESHSMO) for unmanned underwater vehicles (UUVs) with external disturbances and model uncertainties. Firstly, an extended state higher-order sliding mode observer with the finite-time convergence is designed based on the higher-order sliding mode technique and the extended state observer technique. Next, on the basis of disturbances and model uncertainties observation, a fast finite-time super-twisting sliding mode control approach is proposed, and the finite time stabilization property of the tracking errors is proved by Lyapunov theory. Finally, through numerical simulation and experiment in a water pool, it has been verified that the proposed control scheme has achieved the high control precision, the smaller chattering, the disturbance compensation and the fast finite-time convergence in UUV trajectory tracking.

Variations in Finite-Time Multi-Surface Sliding Mode Control for Multirotor Unmanned Aerial Vehicle Payload Delivery with Pendulum Swinging Effects

Multi-surface sliding mode control addresses the limitations of traditional sliding mode control by employing multiple sliding surfaces to handle uncertainties, disturbances, and nonlinearities. The design process involves developing sliding surfaces, designing switching logic, and deriving control laws for each surface. In this paper, first, a robust finite-time multi-surface sliding mode controller will be presented and its performance analyzed by applying it to a multirotor subjected to a suspended payload, modeled in the form of a single pendulum, itself defined as a spatial (3D) dynamic model. Next, an adaptive finite-time multi-surface sliding mode controller will be derived—adding a variable adaptive parameter to the existing sliding surfaces of the robust finite-time control—and applied to the same system. It will be shown that the adaptive controller, with an adaptive parameter that adjusts itself based on the present value of the multi-surface sliding mode parameter, creates an improved fast finite-time convergence by obtaining an optimal settling time and minimizing undershoot of the multirotor state vector. Empirical verification of the effectiveness of the adaptive control will be carried out by presenting the control performances against a step response. It is also shown that the control may be utilized to approximate external disturbances—represented by the pendulum—and that with the application of control, the vehicle’s motion may be stabilized and the payload swing suppressed. Lyapunov stability theory-based stability proofs for the controllers’ designs are developed, showing the asymptotic stability of the output and uniform boundedness of the errors in the system dynamics. It is verified that the multi-surface sliding mode control can account for system uncertainties—both matched and mismatched—in addition to changes in internal dynamics and disturbances to the system, where the single pendulum payload is representative of the changes in dynamics that may occur to the system. Numerical simulations and characteristics are presented to validate the performance of the controllers.

Optimal Distributed Finite-Time Fusion Method for Multi-Sensor Networks under Dynamic Communication Weight.

Aiming at the problem of distributed state estimation in sensor networks, a novel optimal distributed finite-time fusion filtering method based on dynamic communication weights has been developed. To tackle the fusion errors caused by incomplete node information in distributed sensor networks, the concept of limited iterations of global information aggregation was introduced, namely, fast finite-time convergence techniques. Firstly, a local filtering algorithm architecture was constructed to achieve fusion error convergence within a limited number of iterations. The maximum number of iterations was derived to be the diameter of the communication topology graph in the sensor network. Based on this, the matrix weight fusion was used to combine the local filtering results, thereby achieving optimal estimation in terms of minimum variance. Next, by introducing the generalized information quality (GIQ) calculation method and associating it with the local fusion result bias, the relative communication weights were obtained and embedded in the fusion algorithm. Finally, the effectiveness and feasibility of the proposed algorithm were validated through numerical simulations and experimental tests.

Reliability improvement of the large-scale wind turbines with actuator faults using a robust fault-tolerant synergetic pitch control

This study addresses the critical issue of enhancing the reliability of large-scale wind turbines in the presence of simultaneous pitch actuator faults. To do this, a fault-tolerant finite-time continuous nonsingular terminal synergetic control manifold is firstly designed and incorporated into the pitch control system to improve precision tracking performance and regulation of the pitch angle for stable power extraction under extreme wind conditions. Besides, the proposed scheme is model-independent, easily accessible, and features fast finite-time convergence. At the same time, the mismatched disturbance observer is designed to attenuate the time-varying perturbations of the wind turbine system (WTS) to achieve robustness and high tracking accuracy. Then, the proposed scheme’s stability conditions and finite-time convergence analysis are derived using the Lyapunov theory. Finally, the simulation and comparative studies are presented to signify the reliable performance of the proposed control method for both a 4.8 MW benchmark WTS and a large-scale 20 MW PMSG-based WTS to verify robustness against simultaneous pitch actuator faults and uncertainties.

Fast terminal synergetic control for morphing quadcopter with time-varying parameters

To enhance flexibility and improve versatility, recent research has focused on the development of variable structure vehicles. In line with this, this paper introduces a morphing quadcopter with time-varying parameters that enables independent rotation of its arms around the main body. This study highlights the influence of these parameters on the geometric properties, dynamics, flight stability, and control of this aerial robot, while considering nonlinear functions, unknown parameters, and external disturbances. The system dynamics are derived using Newton-Euler formalism, and a robust control approach based on synergetic theory is proposed. The distinctive features of this strategy are demonstrated through finite-time convergence, enhanced control accuracy, and effective chattering suppression. In the control aspect, a Synergetic Controller (SC) is initially developed and further improved by incorporating fast finite-time convergence of the state variables. A comparative study is conducted, quantitatively and qualitatively, among four controllers: BackStepping (BS) controller, Sliding Mode Controller (SMC), SC, and Fast Terminal Synergetic Controller (FTSC). The FTSC exhibits numerous advantages, including rapid tracking towards desired states, adaptability to varying system parameters and uncertain external disturbances, as well as suitability for digital implementation. To conduct a significant comparative study, a Genetic Algorithm is employed to select the optimal gains for each control technique. Additionally, to imitate the real situation as much as possible, external disturbances are considered in the performed numerical simulation. Overall, the results demonstrate that the proposed control technique outperforms in terms of accuracy and robustness. It offers superior control performance and effective handling of system variations and external disturbances, making it a promising approach for the morphing quadcopter system.

A Finite-Time Sliding Mode Control Approach for Constrained Euler–Lagrange System

This paper investigates a general control strategy to track the reference trajectory for the constrained Euler–Lagrange system with model uncertainties and unknown external disturbances. Unlike the disturbances assumed to be upper-bounded by a constant in other papers, we consider the disturbances to be bounded by a function of the system states, which are more realistic. First, the nominal controller was designed based on the nonsingular fast terminal sliding mode control, and global fast finite-time convergence to the sliding surface was guaranteed. As the system is state-constrained in this paper, we introduce the control barrier function approach to formulate the constraints and ensure the system does not break the restrictions. The proposed control strategy was numerically assessed on a two-link robot manipulator system, and the simulation results illustrate the effectiveness of the proposed control strategy.

Integral terminal sliding-mode-based singularity-free finite-time tracking control for entry vehicle with input saturation

This paper investigates the finite-time tracking control problem for entry vehicle under input saturation and uncertainty. First, a new integral terminal sliding mode surface is devised, which not only renders fast finite-time convergence, but also presents an explicit estimate of settling time. Subsequently, a singularity-free adaptive integral terminal sliding mode control approach is exploited with application of the designed integral terminal sliding mode surface, anti-windup compensator and adaptive technique, which ensures the superior control performance. By introducing linear and fractional power feedback functions into the adaptation mechanism and anti-windup compensator, the designed controller achieves finite-time convergence of tracking errors and estimation errors, while circumventing the overestimation of control gain. Moreover, the finite-time stability is proved by employing Lyapunov theory and bi-limit homogeneity technique. The results of a Monte Carlo simulation show that the final tracking precision within 3 km of the target is improved about 40% under the developed controller.

ADAPTIVE NONSINGULAR TERMINAL SLIDING MODE CONTROL FOR MANIPULATOR ROBOT

This study presented an improved adaptive nonlinear terminal sliding mode control technique for the manipulator robot to achieve better adaptability and faster finite-time convergence. First, an adaptive self-updating algorithm will be developed to relax the problems of fixed control gain for the main proposed controller. Next, an adaptive neural network estimator is applied by estimating the robot dynamics to increase the tracking control performance. In addition, a compensator-typed robust controller also is designed to guarantee the robustness, continuity, and smoothing properties of the control system. To verify the effectiveness of the proposed method, besides applying the Lyapunov theorem, the comparative numerical simulation results will be provided in more detail.

Fast Finite-Time Tracking Consensus With Applications on Multiple Servo Motors

This article focuses on the fast finite-time tracking consensus for uncertain nonlinear multiagent systems. By gracefully combining the hierarchical decomposition, adding a barrier power integrator and disturbance compensation techniques, a new adaptive fast finite-time controller is proposed. Compared with the existing works, the proposed method has several distinguishing features: 1) It can achieve fast finite-time convergence with full state constraints; 2) it can deal with some fully unknown nonlinearities and state-dependent disturbance. Moreover, the nonlinearities can be related with the states of all the followers; 3) the input of the leader is not required to be zero, meaning a broad class of references signals can be generated; and 4) the controller is computationally simply and ready to be implemented. No fuzzy logic/neural networks are needed. Applications of the proposed method on multiple servo motors are also studied.

Prescribed Performance-Based Finite-Time Consensus Technology of Nonlinear Multiagent Systems and Application to FDPs

This brief focuses on an adaptive bipartite consensus issue for nonlinear multi-agent systems (MASs) over signed digraphs from a new way. A new distributed control algorithm, named finite-time prescribed performance control is designed by applying prescribed performance function (PPF) and a novel first-order filter, which not only guarantees that the bipartite consensus errors converge to a prescribed compact set at a finite time, as well as enables the system to achieve the prescribed performance and fast finite time convergence. Furthermore, the neural networks (NNs) are introduced to deal with the continuous unknown nonlinearity and the effect of non-strict feedback structure that exist in the system, and the dynamic surface control (DSC) mechanism applying a novel first-order filter is used to overcome the “explosion of complexity” problem during a controller design process. Simulation experiment of forced damped pendulums (FDPs) is included to show the feasibility of the theoretical works.

High-order Supper-twisting Based Terminal Sliding Mode Control Applied on Three Phases Permanent Synchronous Machine

Nowadays, research on electric drive control has become popular because hybrid methods to collect the advantages of individual controllers. Moreover, these methods aim to reach better performance and robust control even in the presence of uncertainties and disturbances which are typically evident in high-speed dynamics where the influence of external disturbances and modeling errors are more evident. Therefore, in this paper, a novel hybrid controller is proposed between the super-twisting algorithm based on high order design (HO-STA) and terminal sliding mode control (T-SMC) applied on a permanent magnet synchronous motor PMSM. Whereas, it accounts to deal with the weaknesses of both terminal sliding mode control and super twisting algorithm (STA) and at the same time combining their advantages; furthermore, it provides exceptional characteristics, including fast finite-time convergence, stabilization of the performance and its reaching law developer based on new design which contributes to reducing the chattering problems afflicted by C-SMC. This proposed hybrid technique contributes to gaining robust control under variation between slow, medium, and high speed levels, no matter what load torque is applied or whatever PMSM parameters change. Moreover, it also offers optimum performance characteristics such as smaller settling time and steady state error. Whereas, the control efficiency is demonstrated by Matlab/Simulink simulation to confirm our design parameters.

Continuous Nonsingular Terminal Sliding-Mode Control With Integral-Type Sliding Surface for Disturbed Systems: Application to Attitude Control for Quadrotor UAVs Under External Disturbances

This article proposes a continuous nonsingular terminal sliding-mode control with integral-type sliding surface (CNTSMC-ISS) framework for disturbed systems, in which we consider two types of finite-time controllers: the state feedback CNTSMC-ISS and the disturbance-observer-based CNTSMC-ISS. Compared with the existing sliding-mode controllers, the noteworthy contributions of two finite-time controllers in the proposed CNTSMC-ISS framework are the alleviation of the chattering phenomenon, the fast finite-time stability, and the singularity-free and ease-of-implementation characteristics. In the proposed CNTSMC-ISS framework, we first introduce a nonsingular integral terminal sliding-mode surface (NITSMS) such that the finite-time convergence of the system states to zero in the sliding phase is ensured and the singularity problem is avoided. Besides, a finite-time observer is developed to recover the external disturbance. Then, based on the constructed NITSMS with the supertwisting-like algorithm, the state feedback CNTSMC-ISS and the disturbance-observer-based CNTSMC-ISS are proposed, which generate the continuous control signals and guarantee the fast finite-time convergence of the system states to the designed sliding surface. Rigorous finite-time stability of the closed-loop system under two proposed controllers is provided. Finally, we apply two finite-time controllers in the proposed CNTSMC-ISS framework to the attitude control for quadrotor unmanned aerial vehicles under external disturbances. Extensive simulation and experimental results are illustrated to prove the effectiveness of the proposed attitude controllers.

A Novel Finite-Time Fault Observer for the Actuators of the Industrial Manipulator

A novel fault observer which can accomplish fast finite-time convergence is proposed for the second-order manipulator system with disturbance and actuator faults in this paper. When the degree of actuator fault exceeds the upper bound on the external disturbance, both the fault and disturbance are considered as lumped actuator faults for estimation. A fast finite-time extended fault observer is constructed and demonstrated for estimating the total fault with uniformly and ultimately boundedness. The effiectiveness and superiority of the developed fault observer are illustrated by comparative experiment results on a two-joint manipulator model.

Performance Analysis and Applications of Finite-Time ZNN Models With Constant/Fuzzy Parameters for TVQPEI.

Based on extensive applications of the time-variant quadratic programming with equality and inequality constraints (TVQPEI) problem and the effectiveness of the zeroing neural network (ZNN) to address time-variant problems, this article proposes a novel finite-time ZNN (FT-ZNN) model with a combined activation function, aimed at providing a superior efficient neurodynamic method to solve the TVQPEI problem. The remarkable properties of the FT-ZNN model are faster finite-time convergence and preferable robustness, which are analyzed in detail, where in the case of the robustness discussion, two kinds of noises (i.e., bounded constant noise and bounded time-variant noise) are taken into account. Moreover, the proposed several theorems all compute the convergent time of the nondisturbed FT-ZNN model and the disturbed FT-ZNN model approaching to the upper bound of residual error. Besides, to enhance the performance of the FT-ZNN model, a fuzzy finite-time ZNN (FFT-ZNN), which possesses a fuzzy parameter, is further presented for solving the TVQPEI problem. A simulative example about the FT-ZNN and FFT-ZNN models solving the TVQPEI problem is given, and the experimental results expectably conform to the theoretical analysis. In addition, the designed FT-ZNN model is effectually applied to the repetitive motion of the three-link redundant robot and image fusion to show its potential practical value.

Robust finite-time consensus control for Euler–Lagrange multi-agent systems subject to switching topologies and uncertainties

Euler–Lagrange (EL) system is a typical nonlinear system widely used to model robot systems. Although consensus of EL multi-agent systems has been extensively studied in recent years, how to achieve better consensus performance under constraints such as switching topologies and uncertainties is still an open issue. Aiming at fast convergence and effective disturbance rejection, this paper studies the integral sliding mode control problem for robust finite-time consensus of EL multi-agent systems subject to switching topologies and uncertainties. A basic integral sliding mode control (SMC) scheme is first presented for finite-time consensus of EL multi-agent systems subject to undirected topologies and uncertainties. It is shown that the proposed consensus protocol reaches good disturbance rejection and achieves robust finite-time consensus while avoiding the singularity problem in the existing studies. The proposed integral sliding mode control scheme is further extended to finite-time consensus of EL multi-agent systems subject to directed and switching topologies. Compared with the existing algorithms, faster finite-time convergence is achieved. In the simulation studies, the obtained results demonstrate the effectiveness and efficiency of the proposed algorithm.

Adaptive smooth disturbance observer-based fast finite-time attitude tracking control of a small unmanned helicopter

In this paper, a novel control scheme, which includes an improved fast finite-time adaptive backstepping controller based on a newly designed adaptive smooth disturbance observer, is presented for the attitude tracking of a small unmanned helicopter system subject to lumped disturbances. First, an adaptive smooth disturbance observer (ASDO) is proposed to approximate the lumped disturbances, which owns the characteristics of smooth output, fast finite-time convergence, and adaptability to disturbances. Then, a finite-time backstepping control protocol is constructed to achieve the attitude tracking objective. By virtue of our newly proposed inequality, a singularity-free virtual control law is designed. To tackle the “explosion of complexity” problem, a fast finite-time command filter (FFTCF) is utilized to estimate the virtual control signals and their derivatives. In addition, an auxiliary dynamic system is introduced to attenuate the impact of the errors caused by FFTCF estimation. Moreover, an adaptive law with σ-modification term is developed to compensate the ASDO approximation error. Theoretical analysis proves that all signals of the closed-loop system are fast finite-time bounded, while the attitude tracking errors fast converge to a small region of the origin in finite time. Finally, two contrastive numerical simulations are carried out to validate the effectiveness and superiority of the designed control scheme.