Finite-time Trajectory Research Articles

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

Fault-tolerant trajectory tracking control of an unmanned marine vehicle via an adaptive non-singular fast terminal sliding mode control

In this paper, a novel finite-time fault-tolerant trajectory tracking controller is created to render a marine vehicle to enhance tracking performance in the presence of complex unknown variables, including model uncertainties, environmental disturbances, and actuator faults. An adaptive fault-tolerant finite-time sliding mode controller is designed by introducing adaptive control techniques, the non-singular fast terminal sliding mode (NSFTSM) function, and a radial base function (RBF) neural network. The radial base function neural network (RBFNN) is developed to eliminate the influences of model uncertainties and environmental disturbances. A fault compensation by integrating the adaption technique is designed to reduce the effects of actuator faults and approximation errors. Suffering from uncertainties and actuator faults, the proposed finite-time tracking controller can track the desired trajectory with high precision. Simulation results and compared simulations indicate the efficiency and superiority of the proposed controller.

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.

Finite-time velocity-free trajectory tracking control for a stratospheric airship with preassigned accuracy

AbstractThis paper concentrates on the trajectory tracking problem for a stratospheric airship subject to underactuated dynamics, unmeasured velocities, modeling inaccuracies and environmental disturbances. First, a coordinate transformation is performed to solve the underactuated issue, which simultaneously permits a priori assignment of the tracking accuracy. Second, a finite-time observer is integrated into the control structure to offer the exact information of unmeasured velocities and uncertainties in an integral manner. Then, by combining the backstepping technique with the method of adding a power integrator, a new output-feedback control strategy is derived with several salient contributions: (1) the airship’s position errors fall into a predetermined residual region near zero within a finite settling time and stay there, while all the closed-loop signals maintain bounded during operation; and (2) no artificial neural networks and filters are adopted, resulting in a low-complexity control property. Furthermore, the presented method can be extended readily to a broad range of second-order mechanical systems as its design builds upon a transformed system model. Rigorous mathematical analysis and simulations demonstrate the above theoretical findings.

Finite time trajectory tracking control of autonomous agricultural tractor integrated nonsingular fast terminal sliding mode and disturbance observer

A novel control strategy is proposed in this paper to improve the trajectory tracking performance of the autonomous agricultural tractor on both straight-line parallel tracks and headland turning curve tracks in the face of slippage, which combines the nonsingular fast terminal sliding mode (NFTSM) control with a kind of finite time disturbance observer (FDO). The designed FDO ensures robustness outside the sliding mode surface, while the constructed NFTSM ensures the fast convergence of tracking errors and chattering suppression. The effectiveness and advantages of the designed control strategy are verified by simulation comparison with the existing results under MATLAB/Simulink and CarSim co-simulation environment.

Quaternion-based finite-time fault-tolerant trajectory tracking control for autonomous underwater vehicle without unwinding

This brief disposes the finite-time anti-unwinding trajectory tracking control problem of the autonomous underwater vehicle (AUV) encountering model uncertainties, ocean disturbances and actuator failures. Primarily, the kinematic model of translational and rotational motions is depicted by unit quaternion in lieu of classical Euler angle such that the AUV’s dynamics could be globally and uniquely formulated. Subsequently, two finite-time control strategies are presented here to leave the state variables of AUV can converge to an adjustable region. Additionally, the adaptive laws could be applicable to the existence of actuator faults by utilizing a passive fault-tolerant technology. By integrating the initial value of the scalar quaternion into the sliding mode surface, the proposed controllers are characterized with anti-unwinding property. Then, with the application of hyperbolic tangent function, finite-time stability will be achieved for tracking errors without singularity. Stability of the closed-loop system is verified via the Lyapunov theorem. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

Event-triggered finite-time tracking control of underactuated MSVs based on neural network disturbance observer

In this work, a trajectory tracking control issue is discussed for the underactuated marine surface vessels (MSVs) with uncertain dynamic and unknown external disturbances. In the control design, the neural network approximation technology is applied to reconstruct the unknown dynamic, and a finite-time disturbance estimator is established to reconstruct the lumped uncertainties including the unknown external disturbance and approximation error online. Under the design framework of line-of-sight, a new finite-time trajectory tracking control scheme for underactuated MSVs is developed combining the finite-time control theory with the backstepping design method. The developed control scheme has the following remarkable characteristics: (1) it realizes the fast and accurate online reconstruction of lumped uncertainties; (2) it can release the requirement of online disturbance estimation technology on an accurate MSV motion model and expand the application range of online disturbance estimation technology; (3) the unnecessary wear and tear of actuators is suppressed by introducing the event-triggered control (ETC) approach. Based on the Lyapunov theory, it is proved that all signals in the closed-loop tracking control system are bounded. Finally, the effectiveness of the proposed control scheme is verified by the simulation and comparison.

Trajectory Tracking Robust Control Method Based on Finite-Time Convergence of Manipulator with Nonsingular Fast Terminal Sliding Mode Surface

In order to make the manipulator track the desired trajectory in a finite time, a new control method based on fast nonsingular terminal sliding mode has been designed. This method combines the traditional fast terminal sliding mode with the nonsingular terminal sliding mode, has rapidity, nonsingularity, finite-time convergence, and strong robustness, and can effectively suppress the inherent chattering phenomenon of the sliding mode controller. The nonsingular fast terminal sliding mode surface is used to accelerate the convergence speed of manipulator trajectory tracking error, and the singularity problem in terminal sliding mode is solved. The finite-time convergence of the algorithm is proved by the Lyapunov function. The simulation results demonstrate that the proposed method can achieve accurate finite-time trajectory tracking characteristics and has robustness against external disturbances.

SLIDING MODE CONTROL OF UNMANNED AERIAL VEHICLE BASED FINITE-TIME DISTURBANCE OBSERVER

Because of the advantages of high maneuverability, vertical takeoff and landing, free hovering, and easy portability, quadrotor UAVs have become one of the research hotspots in recent years. Aiming at the finite-time trajectory tracking control problem for quadrotor under unknown environmental disturbance and modeling uncertainty, a fast terminal sliding mode control method using a finite-time disturbance observer is proposed. First, the modeling uncertainty and unknown external disturbance of the quadrotor were combined into lumped disturbance, and a finite-time disturbance observer was designed to estimate the lumped disturbance online. Secondly, a fast terminal sliding mode controller was constructed for the realization of a finite-time tracking control of the quadrotor, and the estimated value of the limited-time disturbance observer was compensated to the controller. Thereby, the influence of compound disturbance was eliminated, the quadrotor can achieve a finite-time trajectory, and the disturbance suppression capability of tracking control was improved. Finally, we conducted simulation experiments and confirmed that the control strategy proposed in this paper is effective.

Adaptive Finite-Time Trajectory Tracking Control of Autonomous Vehicles That Experience Disturbances and Actuator Saturation

Adaptive Finite-Time Trajectory Tracking Control of Autonomous Vehicles That Experience Disturbances and Actuator Saturation

Finite-time trajectory tracking control for under-actuated unmanned surface vessels with saturation constraint

This article investigates the robust finite-time trajectory tracking control problem of under-actuated unmanned surface vessels (USVs) subject to model uncertainties, saturation constraints, and external disturbances. Firstly, the kinematic and dynamic models of under-actuated USVs are transformed into an equivalent tracking error dynamic by resorting to a novel output redefinition-based dynamic transformation (ORDT). Secondly, a smooth dead-zone operator-based model (DOBM) is introduced to deal with the control input saturation constraints problem. On basis of these, a sliding mode-based controller (SMC) is developed, which possesses the properties of chattering-free and finite-time convergence. Later, Lyapunov stability proved that the proposed control strategy is capable of guaranteeing the boundedness of all closed-loop signals, in spite of the parametric uncertainties, external disturbance, and input saturation constraints. Finally, numerical simulations illustrate the effectiveness of the proposed control approach.

Formal synthesis of closed-form sampled-data controllers for nonlinear continuous-time systems under STL specifications

We propose a counterexample-guided inductive synthesis framework for the formal synthesis of closed-form sampled-data controllers for nonlinear systems to meet STL specifications over finite-time trajectories. Rather than stating the STL specification for a single initial condition, we consider an (infinite and bounded) set of initial conditions. Candidate solutions are proposed using genetic programming, which evolves controllers based on a finite number of simulations. Subsequently, the best candidate is verified using reachability analysis; if the candidate solution does not satisfy the specification, an initial condition violating the specification is extracted as a counterexample. Based on this counterexample, candidate solutions are refined until eventually a solution is found (or a user-specified number of iterations is met). The resulting sampled-data controller is expressed as a closed-form expression, enabling both interpretability and the implementation in embedded hardware with limited memory and computation power. The effectiveness of our approach is demonstrated for multiple systems.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

Finite-time adaptive event-triggered command filtered backstepping control for a QUAV

In this paper, the problem of event-triggered finite-time trajectory tracking control for a quadrotor unmanned aerial vehicle (QUAV) is studied. For the translation and rotation subsystems of QUAV, the finite-time command filter can make the derivative of virtual control signals be quickly approximated, and the effect of filtered error is eliminated by constructing the fractional power error compensated mechanism. By synthesizing command filter technique and event-triggered mechanism into the framework of backstepping design procedure, the finite-time adaptive control strategy for a QUAV is proposed, which reduces the resource occupation and maintains the stability and performance. It is proved that the position and attitude tracking errors can converge to a small neighborhood near the origin in a finite time. Finally, the availability and superiority of the proposed finite-time algorithm are verified by a comparative simulation.

Adaptive on-Line Approximator-Based Finite-Time Trajectory Tracking Control for the Surface Vessel

An adaptive finite-time trajectory tracking scheme is proposed to solve the problem of trajectory tracking of underactuated surface ship affected by dynamic uncertainties and external disturbances. In this scheme, underactuated transformation is performed by using kinematic virtual control law transformation and bounded constraint. By designing adaptive control to approach the upper bound of uncertainty and unknown disturbance, the problem of parameter uncertainty and external disturbance are solved. It is proven by Lyapunov theory that the error signals in the system can converge quickly to the stable region in finite time. Finally, by comparing the simulation results, it is verified that the proposed control scheme can make the underactuated ship track the desired trajectory in finite time. Compared to the traditional control method, the convergence rate of the system error is faster, and it exhibits strong robustness in the face of unknown external disturbances. This has a certain reference value for practical engineering applications.

Event-Triggered Composite Learning Finite-Time Trajectory Tracking Control for Underactuated MSVs Subject to Uncertainties

In this paper, a novel event-triggered composite learning finite-time control scheme is presented for underactuated marine surface vehicles (MSVs) trajectory tracking under unknown dynamics and unknown time-varying disturbances. Line-of-sight (LOS) tracking control method is employed to address the underactuation problem of MSVs. The neural networks (NNs) are untilized to approximate unknown dynamics. The serial-parallel estimation model is employed to construct the prediction error, and the prediction errors and tracking errors are fused with construct the NN weights updating. Combining the result of approximation information, the disturbances observers can be created to achieve disturbance estimation. Fractional power technology is artistically introduced to realize the finite-time trajectory tracking control of MSVs based on composite learning. The proposed control scheme ensures the simultaneous realization of high precision tracking performance and unknown information approximation. Moreover, an event-triggered mechanism is introduced to reduce the transmission load and the execution rate of actuators. It is proved that the proposed control scheme ensures all error signals of the MSVs trajectory tracking control system can converge to the neighborhood of zero within a finite time. Finally, the simulation results on an MSV verify the effectiveness and superiority of the proposed control scheme.

State recovery and disturbance estimation-based fast trajectory tracking of autonomous surface vehicles: A finite-time approach

This paper investigates the problem of finite-time trajectory tracking for fully actuated autonomous surface vehicles without the velocity measurements, in the presence of uncertain parameters and complex environmental disturbances. Firstly, a generalized nonlinear finite-time extended state observer is proposed to recover the velocities and synthetic disturbances simultaneously. The generalized structure can further enhance the estimation accuracy and the observation errors are proved to be finite-time uniformly ultimately bounded stable. Then, a two-loop control law is developed by using virtual velocity command and fast non-singular integral terminal sliding controller. The observer is integrated with the controller to overcome the problem of unavailable surge, sway, yaw velocities and to rapidly reject disturbances, thereby contributing to fast and accurate trajectory tracking of the vehicle. Theoretical analysis for finite-time stability of the closed-loop system is rigorously derived through the Lyapunov’s stability theory. Finally, comparative simulation results are given to illustrate the effectiveness and superiority of the proposed control approach.

Geometric finite-time inner-outer loop trajectory tracking control strategy for quadrotor slung-load transportation

Geometric finite-time inner-outer loop trajectory tracking control strategy for quadrotor slung-load transportation

Dual-disturbance-observer-based robust finite-time trajectory tracking control for robotic surface vehicle under measurement uncertainties

In this paper, the finite-time trajectory tracking control of a fully actuated robotic surface vehicle (RSV) with multiple uncertainties is investigated. Particularly, besides model uncertainties, environmental disturbances, and actuator saturation, the measurement uncertainties are also taken into account. When considering the measurement uncertainties, the RSV becomes a mismatching system, which brings a great difficulty to the control design. To resolve this problem, a novel robust finite-time control approach is proposed based on a dual-disturbance-observer-based architecture. First, two finite-time disturbance observers are developed to estimate the mismatched and matched lumped disturbances in the kinematics and dynamics of the RSV, respectively. Then, the robust finite-time controller is synthesized by incorporating the two finite-time disturbance observers into the adding a power integrator technique. It is strictly proved that the robust finite-time controller can ensure the actual position and velocity tracking errors stabilize to the small neighborhoods around the origin in finite time. Benefiting from the feedforward disturbance compensation, the proposed controller is not only robust against model uncertainties and environmental disturbances, but also insensitive to measurement uncertainties. At last, the effectiveness and advantages of the proposed control approach are verified through numerical simulations on a benchmark RSV model called CyberShip Ⅱ.

Reinforcement learning-based finite-time tracking control of an unknown unmanned surface vehicle with input constraints

In this paper, subject to completely unknown system dynamics and input constraints, a reinforcement learning-based finite-time trajectory tracking control (RLFTC) scheme is innovatively created for an unmanned surface vehicle (USV) by combining actor-critic reinforcement learning (RL) mechanism with finite-time control technique. Unlike previous RL-based tracking which requires infinite-time convergence thereby rather sensitive to complex unknowns, an actor-critic finite-time control structure is created by employing adaptive neural network identifiers to recursively update actor and critic, such that learning-based robustness can be sufficiently enhanced. Moreover, deduced from the Bellman error formulation, the proposed RLFTC is directly optimized in a finite-time manner. Theoretical analysis eventually shows that the proposed RLFTC scheme can ensure semi-global practical finite-time stability (SGPFS) for a closed-loop USV system and tracking errors converge to an arbitrarily small neighborhood of the origin in a finite time, subject to optimal cost. Both mathematical simulation and virtual-reality experiments demonstrate remarkable effectiveness and superiority of the proposed RLFTC scheme.