Finite-time Trajectory Tracking Control Research Articles

Adaptive Disturbance Observer-Based Finite-Time Command Filtered Control of Nonlinear Systems

This article examines the finite-time trajectory tracking control problem for a category of nonlinear perturbed systems. A novel observation mechanism is constructed to mitigate the effects of complex system disturbances. Then, a new adaptive finite-time backstepping nonlinear control algorithm is designed by integrating this disturbance observer with a command filter method. The synthesized control strategy not only effectively suppresses external disturbances and avoids the differential explosion problem of traditional backstepping methods but also ensures the convergence of the trajectory tracking error and filtering error compensation signal within a finite time. Finally, the validity of the suggested approach is confirmed via comparative simulations.

Performance-optimisation-based repetitive trajectory tracking control for autonomous farming vehicle

The high precision trajectory tracking for the autonomous farming vehicle (AFV) is closely related to work quality and crop yield. Farmland operations are usually repetitive tillages, and the farmland soil is relatively soft, slippery, and uneven, which can easily lead to uncertain problems such as slippage, parameter perturbation, and external disturbance. This paper proposes a finite-time repetitive trajectory tracking control strategy integrated with particle swarm optimisation (PSO) and equivalent input disturbance (EID) for the AFV to achieve performance optimisation. The repetitive control framework with finite-time convergence technique can effectively realise the iterative convergence performance of the repetitive trajectory tracking. The PSO algorithm is integrated into determining the control gains to optimise the dynamic and steady-state performances of the trajectory tracking control system. The EID method enhances the tracking precision and robustness to internal and external disturbances. Under MATLAB/Simulink and CarSim co-simulation environment, the effectiveness and advantages of the designed control strategy are illustrated by comparing it with the traditional repetitive control, the EID-based PI control, the active-disturbance-rejection-control-based nonsingular terminal sliding mode control, as well as the sliding-mode-observer-based integral sliding mode control strategies for a farming vehicle.

Finite-time control of uncertain Euler–Lagrange systems using ELM-based velocity observer

This paper is concerned with the finite-time trajectory tracking control of a class of Euler–Lagrange (EL) systems under unknown velocity information, dynamic uncertainties and disturbances. An extreme learning machine (ELM) algorithm is employed to approximate the uncertainties, while an adaptive algorithm is proposed to tune output weights of the ELM, as well as to eliminate the negative effects of residual errors and disturbances. Then an adaptive finite-time ELM-based velocity observer is developed to estimate the unavailable velocity states. Further, based on the estimations and the approximations of model uncertainties, an adaptive finite-time observer-based nonsingular terminal sliding mode (TSM) control strategy is constructed to guarantee the finite-time bounded tracking of the uncertain EL system by using the Lyapunov stability theorem. Simulation results on a robotic manipulator platform demonstrate the efficiency of the developed finite-time observation and control methods.

Order-supplementary finite-time trajectory tracking control of quadrotor unmanned aerial vehicles

Order-supplementary finite-time trajectory tracking control of quadrotor unmanned aerial vehicles

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.

Adaptive Finite-Time Trajectory Tracking Control for Underactuated Surface Vehicles Based on Adaptive Disturbance Compensating

Adaptive Finite-Time Trajectory Tracking Control for Underactuated Surface Vehicles Based on Adaptive Disturbance Compensating

Rotation matrix-based finite-time trajectory tracking control of AUV with output constraints and input quantization

This study investigated a rotation-matrix-based finite-time trajectory tracking problem for autonomous underwater vehicles (AUVs) in the presence of output constraints, input quantization, and uncertainties. First, a rotation matrix-based attitude representation is introduced, which allow attitude dynamics to be globally and uniquely represented without unwinding. To satisfy the finite-time stability of AUV tracking control and the output constraints imposed by introducing the new attitude error vector, a novel finite-time command-filtered backstepping controller (FTCFBC) is proposed based on the asymmetrical time-varying barrier Lyapunov function (TVBLF). Subsequently, a second-order auxiliary dynamic system (ADS) is proposed to estimate the negative effects that of input quantization errors. Because the quantized control inputs can be switched at an appropriate earlier or later switching timing depending on the output of the ADS, the negative impact of quantization errors on the control accuracy is reduced. Moreover, an adaptive finite-time disturbance observer (AFTDO) is developed to estimate the lumped uncertainties without prior information on the bounds of the uncertainties. Finally, the results of the theoretical analysis verified that the tracking errors can converge within a finite time. Numerical simulations confirmed the effectiveness of the proposed control scheme.

Finite-Time Tracking Control of a Flexible Link Manipulator Based on an Extended State Observer

In this paper, the finite-time trajectory tracking control problem of a flexible link manipulator (FLM) system with unknown parameters is investigated in joint space. An adaptive nonsingular terminal sliding mode (ANTSM) controller based on an extended state observer (ESO) is proposed to ensure that the tracking error converges to a small neighborhood of zero. Firstly, an adaptive ESO is introduced, which is used to estimate unknown system parameters, including the unknown rigid-flexible coupling coefficient and the unknown control gain. Then, an ESO based on the parameters estimated above is proposed to estimate the unmodeled dynamics and external disturbances of the system in real-time. Finally, an ANTSM controller based on ESO is studied to achieve finite-time trajectory tracking control and vibration suppression without any prior knowledge of system uncertainties and external disturbances. The finite-time convergence ability of the closed-loop system is proved by Lyapunov theory. Experimental results on the Quanser Flexible Link System verify the effectiveness of the proposed controller.

Adaptive Finite-Time Trajectory Tracking Control for Coaxial HAUVs Facing Uncertainties and Unknown Environmental Disturbances

In this paper, the problems of system design, dynamic modeling, and trajectory tracking control of coaxial hybrid aerial underwater vehicles (HAUVs) with time-varying model parameters and composite marine environment disturbances are investigated. It is clear that a stable transition between different media remains a challenge in the practical implementation of amphibious tasks. For HAUVs, accurate dynamic modeling to describe complex dynamic variations during vehicle takeoff from underwater to air is a huge challenge. Meanwhile, due to the rapid changes in model parameters and the external environment, vehicles are likely to fall into the sea during the cross-domain process. An integrated continuous dynamic model considering hydrodynamic changes is established by introducing a linear switching coefficient during the process of trans-medium motion. A nonsingular fast terminal sliding-mode control (NFTSMC) algorithm combined with adaptive technology is used to design the position and attitude of the controller. With no previous knowledge of external interferences and lumped uncertainties of the HAUV, the adaptive NFTSMC (ANFTSMC) algorithm achieves the control objectives; at the same time, the inherent chattering problems of sliding mode control (SMC) are weakened. The finite-time stability of the global system is proven strictly using a series of mathematical derivations based on Lyapunov theory. The effect of the controller applied is analyzed through a series of simulations with representative working conditions. The results show that the proposed ANFTSMC can realize a “seamless” air–water trans-medium process, which proves the superiority and robustness of the proposed control algorithm.

Observer based incremental backstepping terminal sliding-mode control with learning rate for a multi-vectored propeller airship

The problem of finite-time trajectory tracking control for a multivectored propeller airship with model parameter uncertainties and unknown disturbances is addressed in the paper. In order to obtain a fast transient response and finite time convergence without singularity, an incremental backstepping nonsingular terminal sliding mode controller is designed to track desired trajectory within finite time. To overcome the limitation of backstepping terminal sliding-mode control design being dependant on prior knowledge, a nonlinear disturbance-observer is designed to estimate the external observable disturbances. Meanwhile, to reduce system chattering when the tracking error reaches the sliding mode surface, an adaptive learning rate design is proposed for the terminal sliding mode controller such that the tracking error approaches the sliding mode surface at a low speed and so the system chattering is restrained. The closed-loop trajectory tracking control system is proved to be stable and finite time convergence by using Lyapunov theory. The results are compared with traditional backstepping sliding mode control and different learning rate based control design, and they demonstrate the averaged tracking error in altitude and pitch motion is reduced more than 30% by using the disturbance-observer based incremental backstepping terminal sliding mode controller for the multivectored propeller airship to execute a realistic trajectory tracking mission, even in the presence of aerodynamic coefficient uncertainties, unknown disturbances.

Finite-time trajectory tracking control of dynamic positioning ship based on discrete-time sliding mode with decoupled sampling period

In this paper, the finite-time trajectory tracking control problem of a dynamic positioning ship with model uncertainty and time-varying environmental disturbances is investigated based on the discrete-time sliding mode with decoupled sampling period. To overcome the influence of the sampling period variation on the system’s control effect, a finite-time discrete sliding mode controller with decoupled sampling period is designed based on the new discrete-time adaptive fast power reaching law. The sampling period condition that guarantees the finite-time convergence of the system is given. A new finite-time high-order discrete disturbance observer is proposed to estimate model uncertainty and environmental disturbance, which reduces the dependence of the observer’s estimation accuracy on the sampling period. To realize the transformation from position tracking to velocity tracking in a finite time, a new finite-time discrete virtual velocity controller is designed. The proposed control strategy decouples the sampling period and enables the finite-time trajectory tracking control of the dynamic positioning ship over a wider sampling period range. The stability analysis demonstrates that all tracking errors of the closed-loop system can converge to a small domain near zero in a finite time. Two simulation examples verify the effectiveness of the proposed control method.

Event trigger based adaptive neural trajectory tracking finite time control for underactuated unmanned marine surface vessels with asymmetric input saturation

An adaptive finite time trajectory tracking control method is presented for underactuated unmanned marine surface vessels (MSVs) by employing neural networks to approximate system uncertainties. The proposed algorithm is developed by combining event-triggered control (ETC) and finite-time convergence (FTC) techniques. The dynamic event-triggered condition is adopted to avert the frequent acting of actuators using an adjustable triggered variable to regulate the minimal inter-event times. While solving the system uncertainties and asymmetric input saturation, an adaptive neural networks based backstepping controller is designed based on FTC under bounded disturbances. In addition, via Lyapunov approach it is proved that all signals in the closed-loop system are semi-global uniformly ultimately bounded. Finally, simulations results are shown to demonstrate the effectiveness of this proposed scheme.

Event-triggered adaptive finite time trajectory tracking control for Underactuated Vessel considering unknown time-varying disturbances

Abstract This paper aims to solve the finite-time trajectory tracking problem of underactuated surface ships under the influence of dynamic uncertainty, unknown external time-varying interference and limited communication resources, an event-triggered robust adaptive finite-time trajectory tracking control method for underactuated ships is designed by combing the existing trajectory tracking control methods and engineering needs in actual navigation. It can obviously improve the tracking accuracy of the ship, and complete the tracking task safely and efficiently. This scheme transforms the composite uncertain vector synthesized by uncertain parameters and external disturbances into a linear parameterized form. Next, considering the limitation of communication resources, a relative threshold event triggering mechanism is introduced to further extend the triggering time interval on the basis of the fixed threshold triggering scheme. Then, an event-triggered robust adaptive finite-time trajectory tracking control scheme is designed for underactuated ships, and a rigorous stability proof is provided for the finite-time trajectory tracking control scheme designed above through Lyapunov stability theory. Simulation experiment is carried out in MATLAB and the results show that the finite-time trajectory tracking control scheme proposed in this paper can effectively solve the problems of dynamic uncertainty, unknown time-varying interference from the outside world, and limitation of communication resources. This paper can provide theoretical support for the autonomous navigation of intelligent ships.

Finite-time trajectory tracking control for a two degrees of freedom pneumatic dexterous finger

Finite-time trajectory tracking control for a two degrees of freedom pneumatic dexterous finger

Finite-time trajectory tracking control of quadrotor UAV via adaptive RBF neural network with lumped uncertainties

The trajectory tracking control of the quadrotor with model uncertainty and time-varying interference is studied. The RBF neural network is combined with the global fast terminal sliding mode (GFTSM) control method to converge tracking errors in finite time. To ensure the stability of the system, an adaptive law is designed to adjust the weight of the neural network by the Lyapunov method. The overall novelty of this paper is threefold, 1) Owing to the use of a global fast sliding mode surface, the proposed controller has no problem with slow convergence near the equilibrium point inherently existing in the terminal sliding mode control. 2) Benefiting from the novel equivalent control computation mechanism, the external disturbances and the upper bound of the disturbance are estimated by the proposed controller, and the unexpected chattering phenomenon is significantly attenuated. 3) The stability and finite-time convergence of the overall closed-loop system are strictly proven. The simulation results indicated that the proposed method achieves faster response speed and smoother control effect than traditional GFTSM.

Finite-time self-structuring neural network trajectory tracking control of underactuated autonomous underwater vehicles

A finite-time self-structuring neural network (SSNN) trajectory tracking control scheme is proposed for an input-constrained underactuated autonomous underwater vehicle (AUV) with unknown external disturbances. First, a time-varying barrier Lyapunov function is proposed to constrain and prevent excessive consistency errors and reduce computational effort. Second, a finite-time controller is presented to achieve finite-time convergence of the closed-loop system, while dynamic surface control (DSC) is used to reduce the computational complexity of the system. Third, a finite-time SSNN method is developed to obtain the optimal number of neurons with simple computation and better approximation to estimate uncertain disturbances. Moreover, the Lyapunov stability proof indicates that all signals in the closed-loop system are ultimately bounded uniformly with respect to the initial constraints, and the trajectory tracking errors can converge to near zero in a finite time. Finally, simulations not only evaluate the performance of the proposed controller-controlled system but also verify the effectiveness of the methodology in this paper.

Command filtered-based neuro-adaptive robust finite-time trajectory tracking control of autonomous underwater vehicles under stochastic perturbations

In this paper, the problem of finite-time trajectory tracking control is studied and addressed for a 6 degree of freedom (DOF) autonomous underwater vehicle (AUV) subjected to unknown dynamic model, stochastic perturbations, external disturbances (matched and mismatched) and saturation input nonlinearities. Based on the backstepping control approach, novel finite-time control inputs are designed and proposed. Artificial neural networks (ANNs) and finite-time adaptation laws are exploited to approximate the nonlinear dynamics of AUV, the stochastic perturbations and the upper bound of external disturbances. To handle the destructive effects of saturation input nonlinearities, finite-time auxiliary system method is utilized. To overcome the explosion of complexity problem of backstepping control strategy, compensator-based finite-time command filter approach is exploited. By utilizing the Lyapunov stability theorem, it is mathematically proven and demonstrated that the suggested nonlinear control inputs are able to guarantee the semi-global finite-time stability in probability (SGFSP) of the closed-loop AUV system. Finally, numerical simulations are carried out to illustrate and depict the effectiveness and performance of the proposed neuro-adaptive robust finite-time control scheme.

Online recorded data-based finite-time composite neural trajectory tracking control for underactuated MSVs.

This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS) method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on an MSV verify the effectiveness of the proposed control scheme.

Event-triggered finite-time adaptive trajectory tracking control for a class of nonlinear non-strict-feedback systems with input saturation and application to a single-link robot

Event-triggered finite-time adaptive trajectory tracking control for a class of nonlinear non-strict-feedback systems with input saturation and application to a single-link robot

Improving trajectory tracking performance of autonomous farming vehicles using adaptive extended state observer and finite-time technique

The ability of the autonomous farming vehicle to accurately and quickly track complex reference trajectories in the field is critical to crop yields and farmer incomes. The novelty of this paper is to design a new adaptive finite-time trajectory tracking control strategy with an adaptive extended state observer to improve the autonomous farming vehicle’s trajectory tracking accuracy and convergence speed in the complex farm operating environment. The adaptive extended state observer is constructed to deal with the slip disturbance and parameter uncertainty to improve the tracking accuracy. The finite-time control strategy is adopted to improve the convergence speed of the trajectory tracking of the autonomous farming vehicle. The effectiveness and advantages of the proposed control strategy are verified by comparing it with the active disturbance rejection control and traditional PID control strategies under MATLAB/Simulink environment.