Finite-time Error Convergence Research Articles

Trajectory tracking control of autonomous space-based simulators for the on-orbit assembly of large space optical telescopes

To enhance the precision of on-orbit assembly for large space optical telescopes, the control of attitude motion in the Autonomous Space-based Simulator (ASS) is imperative. This paper presents a robust finite-time trajectory tracking control method aimed at improving the position and attitude tracking performance of ASS. Considering the dynamic characteristics inherent in ASS, we introduce an improved non-singular fast terminal sliding mode controller (INFTSMC) incorporating an adaptive fuzzy mechanism to attain finite-time error convergence and robust control. The adaptive fuzzy logic control (AFLC) method yields an equivalent gain, eliminating discontinuous switching in terminal sliding mode control (TSMC). This reduction minimizes chattering in control inputs and compensates for uncertainties and time-varying disturbances within the dynamic model. The proposed method’s effectiveness is validated through comprehensive simulation and experimental studies.

Distributed Dynamic Task Allocation for Moving Target Tracking of Networked Mobile Robots Using k -WTA Network.

Tasks allocation plays a pivotal role in cooperative robotics. This study proposes a novel fully distributed task allocation method for target tracking, by which mobile robots only need to share state information with communication neighbors. The proposed method adopts a distributed k winners-take-all ( k -WTA) network to select the k mobile robots closest to the moving target to perform the target tracking task. In addition, an innovative robot control law is designed, incorporating speed feedback and nonlinear activation functions to achieve finite-time error convergence. Unlike previous approaches, our distributed task allocation method yields finite-time error convergence, does not rely on consensus filters, and eliminates the need for a central computing unit to get the k -WTA result during the control process. We demonstrate the effectiveness of the proposed method through theoretical analysis and simulations. Compared to traditional methods, our method leads to smaller total moving distances and speed norms, which underscores the significance of our method in enhancing the efficiency and performance of mobile robots in dynamic task allocation.

Analytic Solution for Nonlinear Impact-Angle Guidance Law with Time-Varying Thrust

This paper presents an impact-angle guidance law of unmanned aerial vehicles (UAVs) with time-varying thrust in a boosting phase. Most current research on impact-angle guidance law assumes that UAV speed is constant in terms of controlled thrust. However, the UAV speed and the acceleration in a boosting phase keep changing because of time-varying thrust. Environmental factors and manufacturing process error may prohibit accurately predicting vehicle-thrust profiles. We propose a nonlinear impact-angle guidance law by analytically solving second-order error dynamics with nonlinear time-varying coefficients. The proposed analytic solution enables one to update guidance gains according to initial and current states so that desired impact angle is met while the miss-distance error is reduced. We prove the finite-time error convergence of the proposed guidance law with the Lyapunov stability theory. Various simulation studies are performed to verify the proposed guidance law.

Finite-Time Approximation-Free Attitude Control of Quadrotors: Theory and Experiments

In this article, a novel finite-time approximation-free control scheme is proposed for the attitude tracking of quadrotor unmanned aerial vehicles. Prescribed performance functions are employed to transform the original attitude tracking problem into an alternative system stabilization problem. By incorporating a finite-time error compensation mechanism into the recursive control design, the finite-time error convergence, and singularity-free property can be guaranteed simultaneously. Compared with the existing approximation-based control schemes, the presented controller has a simple cascade proportional-like structure and less computational burden, and the coupling among the roll, pitch, and yaw dynamics can be successfully handled without requiring any model information or function approximations. With the proposed control scheme, the attitude tracking error can be retained within a prescribed boundary and converge into a sufficiently small region around origin in finite time. Extensive comparative experiments on a three degree-of-freedom (3-DOF) quadrotor platform are performed to validate the effectiveness of the proposed control scheme.

Anti-saturation adaptive finite-time neural network based fault-tolerant tracking control for a quadrotor UAV with external disturbances

This brief is focused on the finite-time tracking control of the quadrotor unmanned aerial vehicle (UAV) subject to external disturbances, parametric uncertainties, actuator faults, and input saturation. According to the principle of the Euler-Lagrangian methodology, a comprehensive dynamics is first decomposed into the position and attitude subsystems to accommodate the controller design. Different from the most of previous studies with an ideal assumption that velocity information is available, a robust exact differentiator is employed to gain the precise information of unavailable velocity in finite time. Then, by utilizing the strong approximation of the radial basis function neural network (RBFNN), the NN-based fault-tolerant control scheme is proposed to compensate for parametric uncertainties, external disturbances and actuator faults. More importantly, a novel adaptive mechanism is responsible for automatically adjusting the NN's parameters, which not only can effectively avoid the selection of large adaptive gains, but can also greatly decrease the number of online-updated leaning parameters. To solve the input saturation problem, an auxiliary dynamics system is constructed. Based on the Lyapunov theoretical framework, it is proved that all the closed-loop signals are uniformly ultimately bounded and the tracking errors can converge into small neighborhoods around the origin in finite time. Finally, simulation results are verified to intuitively reveal the good tracking performance of the introduced composite controller in terms of the finite-time error convergence, strong robustness, fault tolerance, and saturation elimination.

Sensor-less Speed and Flux Control of Dual Stator Winding Induction Motors Based on Super Twisting Sliding Mode Control

This paper proposes a direct speed and flux control system for Dual Stator Winding Induction Machines (DSWIMs) based on Super Twisting Sliding Mode Control (STSMC). The proposed nonlinear controller which has finite time convergence of error to zero, is designed such that the Lyapunov stability condition is satisfied. Furthermore, a novel torque-sharing algorithm is introduced for DSWIMs. This algorithm enables them to operate in a wide speed region, including zero speed, such that the required electromagnetic torque is supplied by two winding sets based on their power ratings. In addition, a Sliding Mode Control (SMC) based full order observer is proposed for DSWIMs. This observer, which is able to estimate the winding fluxes, flux angles and rotor speed with high-accuracy, guarantees the optimal flux condition. The functionality of the proposed sensor-less DSWIM drive scheme is evaluated through some experimental tests performed on a 3.3 kW DSP-based DSWIM drive system. The experimental results confirm the effectiveness of the proposed control method, torque sharing algorithm and the full order observer in various speed regions.

Robust Intelligent Control for a Class of Power-Electronic Converters Using Neuro-Fuzzy Learning Mechanism

This article considers a robust intelligent control problem for a class of power-electronic converters via a neuro-fuzzy learning mechanism. First, a terminal sliding-mode control (TSMC) is designed to ensure finite-time error convergence and further enhance the system performance. Meanwhile, a saturation function is utilized in the proposed TSMC. Then, by using type-2 fuzzy neural network (T2FNN) to approximate the developed TSMC, the corresponding adaptive T2FNN controller with online parameter adjustment is established. To enhance the generalization ability for the uncertainties, the recurrent feature-selection algorithm is added into T2FNN. Moreover, the existence of adaptive compensator comprised by upper bound updated law can avoid the impact of the approximation error. Finally, to show the superiorities of the T2FNN controller, it is applied to active power filter, and the simulation and experimental results are compared with the existing literature.

Supertwisting Control-Based Cooperative Salvo Guidance Using Leader–Follower Approach

This article proposes a leader–follower cooperative salvo guidance strategy to intercept nonmaneuvering targets by exploiting the advantages of supertwisting sliding mode control. An improved estimate of time-to-go, that does not assume interceptor's small heading angle, is used in the guidance design. This allows the guidance strategy to remain effective even for large initial heading of the interceptor. Under the action of supertwisting control, the error in impact time settles precisely to zero in finite time. The proposed guidance strategy provides robustness against uncertainties and a smooth control signal, along with finite-time convergence of error. The guidance performance has been shown for one-to-one engagement, and in a cooperative framework, to achieve a salvo in a predetermined time. Numerical simulations are presented for various engagement scenarios to aid the analysis, and illustrate the efficacy of the proposed guidance scheme, even under noisy environment.

Robust adaptive integral terminal sliding mode control for steer-by-wire systems based on extreme learning machine

In this paper, a novel extreme-learning-machine (ELM)-based robust adaptive integral terminal sliding mode (AITSM) control strategy is developed for the precise tracking control of a steer-by-wire (SBW) system with uncertain dynamics. The proposed control not only ensures the finite-time error convergence but also effectively estimates the lumped uncertainty via a single-hidden layer feedforward network (SLFN) with ELM. Different from conventional ELM using least square optimization approach, the ELM in this work is designed to adaptively estimate the lumped uncertainty from the perspective of global stability of the closed-loop system. The stability of the closed-loop control system is proved in Lyapunov sense. Simulations are carried out to demonstrate the superior control performance of the proposed control.

Extreme-learning-machine-based FNTSM control strategy for electronic throttle

A novel extreme-learning-machine-based robust control scheme for automotive electronic throttle systems with uncertain dynamics is presented in this paper. It is shown that the well-known extreme learning machine (ELM) is used to estimate the upper bound of the lumped uncertainty while a fast nonsingular terminal sliding mode feedback controller is designed to achieve global stability and finite-time convergence for the closed-loop system. Although the ELM used in this paper has the same structure as the one in the conventional least-square-based ELM used for pattern classifications, i.e., the input weights are randomly chosen, the ELM adopted in the closed-loop control system is designed to achieve global control purpose. The output weights of the ELM will be adaptively adjusted in Lyapunov sense from the perspective of global stability of the closed-loop system, rather than local optimization in conventional ELM. The proposed control can thus not only realize the finite-time error convergence but also needs no prior knowledge of lumped uncertainty. Simulation results are demonstrated to verify the excellent tracking performance of the proposed control in comparison with other existing control methods.

Non-singular Terminal Sliding Mode Control of Robot Manipulators with $$H_\infty $$ Trajectory Tracking Performance

This paper develops a novel non-singular terminal sliding mode control scheme for trajectory tracking of robot manipulators in the presence of external disturbances and uncertainties. Firstly, with the introduction of two nonlinear terms, a newly terminal sliding surface is designed. Then utilizing this sliding surface, a novel non-singular terminal sliding mode controller is proposed to eliminate the reaching interval, singularity issue and subsequently with this controller, the finite time error convergence is also assured. In the proposed controller, radial basis function neural network is employed to approximate highly uncertain nonlinear dynamics of robot manipulators using update laws derived with Lyapunov approach. Meanwhile, the effects of approximation errors are attenuated with $$H_\infty $$ performance criterion by introducing a robust term into the controller. As a result of proposed approach, asymptotic convergence of tracking errors is achieved within finite time and the approximation errors are attenuated to desired levels. The numerical simulation result shows the effectiveness of proposed controller for the case of microbot type robot manipulator.

Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle

In this paper, a robust finite time trajectory tracking control approach is proposed for autonomous underwater vehicle (AUV), which belongs to the class of highly nonlinear, coupled dynamics with motion in 6-degrees-of-freedom (DOF). The finite-time error convergence and robust control task is accomplished by designing a non-singular fast fuzzy terminal sliding mode controller (NFFTSMC) with disturbance estimator for the 6-DOF dynamics of an AUV. The proposed NFFTSMC incorporates a non-singular fast terminal sliding mode controller (NFTSMC) which not only assures faster and finite convergence of the tracking errors to the equilibrium from anywhere in the phase portrait but also eliminates the issue of singularity dilemma appeared in conventional terminal sliding mode controller (TSMC); a fuzzy logic control (FLC) tool is employed to generate the hitting control signal in order to reduce chattering in control inputs, which commonly occur in conventional TSMC, and an estimated uncertainty term to compensate for the un-modeled dynamics, external disturbances, and time-varying parameters. Furthermore to investigate the effectiveness of the proposed method, it has been extended to task space control problem of an AUV - manipulator system (AUVMS) employed for underwater manipulation tasks. Simulation studies confirms the potency of the proposed method.

A Bio-Inspired Global Finite Time Tracking Control of Four-Rotor Test Bench System

Introduction: We present a bio-inspired global finite time control using global fast-terminal sliding mode controller and radial basis function network to address the attitude tracking control problem of the three degree-of-freedom four rotor hover system. The proposed controller provides convergence of system states in a pre-determined finite time and estimates the unmodeled dynamics of the four rotor system. Methods: The dynamic model of the four rotor system is derived from Newton’s force equations. The unknown dynamics of the four rotor systems are estimated using Radial basis function. The bio-inspired global fast terminal sliding mode controller is proposed to provide chattering free finite time error convergence and to provide optimal tracking of the attitude angles while being subjected to unknown dynamics. The global stability proof of the designed controller is provided on the basis of the Lyapunov stability theorem. Results: The proposed controller is validated by (i) conducting an experiment through implementing it on the laboratory based hover system, and (ii) through simulations. Performance of the proposed control scheme is also compared with classical and intelligent controllers. The performance comparison exhibits that the designed controller has quick transient response and improved chattering free steady state performance. Conclusion: The proposed bio-inspired global fast terminal sliding mode controller offers improved estimation and better tracking performance than the traditional controllers. In addition, the proposed controller is computationally cost effective and can be implanted on multirotor unmanned air vehicles with limited computational processing capabilities.

Design and Implementation of Adaptive Terminal Sliding-Mode Control on a Steer-by-Wire Equipped Road Vehicle

This paper proposes a novel adaptive terminal sliding-mode (ATSM) control scheme for a Steer-by-Wire (SBW) vehicle. It is shown that the developed ATSM controller can drive the closed-loop error dynamics to converge to zero in a finite time, where adaptive laws are applied to estimate the uncertain bounds of the system parameters and disturbances in Lyapunov sense. Compared with the sliding-mode-based SBW control systems, the proposed ATSM control not only assures the finite-time error convergence and strong robustness with respect to parameter uncertainties and varying driving conditions, but also requires no prior knowledge of the system parameters and road information. Experimental results from an SBW vehicle are demonstrated to verify the remarkable performance of the proposed control in terms of the robustness, error convergence, and road disturbance attenuation, in comparison with other control strategies.

Barrier Lyapunov function-based model-free constraint position control for mechanical systems

In this article, a motion constraint control scheme is presented for mechanical systems without a modeling process by introducing a barrier Lyapunov function technique and adaptive estimation laws. The transformed error and filtered error surfaces are defined to constrain the motion tracking error in the prescribed boundary layers. Unknown parameters of mechanical systems are estimated using adaptive laws derived from the Lyapunov function. Then, robust control used the conventional sliding mode control, which give rise to excessive chattering, is changed to finite time-based control to alleviate undesirable chattering in the control action and to ensure finite-time error convergence. Finally, the constraint controller from the barrier Lyapunov function is designed and applied to the constraint of the position tracking error of the mechanical system. Two experimental examples for the XY table and articulated manipulator are shown to evaluate the proposed control scheme.

Rock slope stability analyses using extreme learning neural network and terminal steepest descent algorithm

The analysis of rock slope stability is a classical problem for geotechnical engineers. However, for practicing engineers, proper software is not usually user friendly, and additional resources capable of providing information useful for decision-making are required. This study developed a convenient tool that can provide a prompt assessment of rock slope stability. A nonlinear input–output mapping of the rock slope system was constructed using a neural network trained by an extreme learning algorithm. The training data was obtained by using finite element upper and lower bound limit analysis methods. The newly developed techniques in this study can either estimate the factor of safety for a rock slope or obtain the implicit parameters through back analyses. Back analysis parameter identification was performed using a terminal steepest descent algorithm based on the finite-time stability theory. This algorithm not only guarantees finite-time error convergence but also achieves exact zero convergence, unlike the conventional steepest descent algorithm in which the training error never reaches zero.

Synchronization of Micro-Electro-Mechanical-Systems in Finite Time

Finite time synchronization of chaotic Micro-Electro-Mechanical Sys-tems (MEMS) is considered. In particular, a Lyapunov-based adaptive controller is developed such that convergence of synchronization error is guaranteed globally in the presence unknown perturbations. The system under consideration suffers from bounded parametric uncertainties, additive external disturbances as well as dead zone input nonlinearities. We establish the controller on being resistance against hard nonlinearities by a novel scheme which can be developed to general chaotic systems even. We provide rigorous stability analysis to come up with sufficient conditions that guarantee finite time error convergence of perturbed system. Several simulation scenarios are carried out to verify the effectiveness of obtained theoretical results.

Adaptive Observer-Based Parameter Estimation With Application to Road Gradient and Vehicle Mass Estimation

A novel observer-based parameter estimation scheme with sliding mode term has been developed to estimate the road gradient and the vehicle weight using only the vehicle's velocity and the driving torque. The estimation algorithm exploits all known terms in the system dynamics and a low-pass filtered representation of the dynamics to derive an explicit expression of the parameter estimation error without measuring the acceleration. The proposed parameter estimation scheme which features a sliding-mode term to ensure the fast and robust convergence of the estimation in the presence of persistent excitation is augmented to an adaptive observer and analyzed using Lyapunov Theory. The analytical results show that the algorithm is stable and ensures finite-time error convergence to a bounded error even in the presence of disturbances. In the absence of disturbances, convergence to the true values in finite time is guaranteed. A simple practical method for validating persistent excitation is provided using the new theoretical approach to estimation. This is validated by the practical implementation of the algorithm on a small-scaled vehicle, emulating a car system. The slope gradient as well as the vehicle's mass/weight are estimated online. The algorithm shows a significant improvement over previous results.

Adaptive parameter identification of linear SISO systems with unknown time-delay

An adaptive online parameter identification is proposed for linear single-input-single-output (SISO) time-delay systems to simultaneously estimate the unknown time-delay and other parameters. After representing the system as a parameterized form, a novel adaptive law is developed, which is driven by appropriate parameter estimation error information. Consequently, the identification error convergence can be proved under the conventional persistent excitation (PE) condition, which can be online tested in this paper. A finite-time (FT) identification scheme is further studied by incorporating the sliding mode scheme into the adaptation to achieve FT error convergence. The previously imposed constraint on the system relative degree is removed and the derivatives of the input and output are not required. Comparative simulation examples are provided to demonstrate the validity and efficacy of the proposed algorithms.

Discrete Time Sliding Mode Flow Controllers for Connection-Oriented Networks with Lossy Links

Abstract In this paper we propose two discrete-time sliding mode flow controllers for multisource connection-oriented networks. Each connection in the considered networks is characterized by a time delay and a packet loss ratio. The proposed controllers take advantage of appropriately designed sliding hyperplanes, which ensure the closed-loop system stability and finite-time error convergence to zero. Moreover, the proposed controllers ensure full utilization of the bottleneck link available bandwidth, guarantee bounded transmission rates, and eliminate the risk of buffer overflow in the bottleneck node. Since the primary controller may lead to excessive values of the transmission rate at the beginning of the control process, the modified controller is designed using the concept of the reaching law, which helps the removing of the undesirable effect.