Fixed-time Disturbance Observer Research Articles

Fixed-time trajectory tracking control of a quadrotor UAV under time-varying wind disturbances: Theory and experimental validation

Abstract This paper adopts a fixed-time method to study the trajectory tracking issue of a quadrotor unmanned aerial vehicle (UAV) under time-varying wind disturbances. Firstly, in order to address the impact of time-varying wind disturbances on UAV, a fixed-time disturbance observer (FxTDO) is constructed to accurately estimate wind disturbances. Secondly, to improve control accuracy and convergence rate, the robust fixed-time controller is designed for the position and attitude system by combining the sliding mode control theory with fixed-time technique. Furthermore, it is rigorously analyzed that the tracking error of the observer and controller can converge to zero via Lyapunov criterion, and the convergence time is independent of the initial state.Finally, the effectiveness and robustness of the designed control strategy are verified by numerical simulations and actual flight experiments, providing an effective connection between control theory and practical applications.

Distributed Event-Triggered Control for Manipulator with Fixed-Time Disturbance Observer

This article studies an event-triggered fixed-time trajectory tracking control problem of an n-joint manipulator system. Firstly, a fixed-time disturbance observer is proposed to reconstruct the total disturbance composed of external disturbances and model uncertainties, using the estimation as feedforward compensation to enhance the system robustness. Subsequently, based on the backstepping framework, a fixed-time controller with an event-triggering mechanism is designed for the manipulator to ensure the convergence of tracking errors to zero within a fixed time. Additionally, two event-triggering conditions are devised to reduce the transmission time of control input and the computation time of control output. Simultaneously, Zeno behavior is excluded through theoretical proof, validating the fixed-time stability of the closed-loop system. Finally, simulation verification is conducted on a two-joint manipulator, with results confirming the effectiveness of the control strategy.

Robust fixed-time flight controller for a dual-system convertible UAV in the cruise mode

This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle (UAV) in the presence of parameter uncertainties, unmodeled uncertainties and wind disturbances. First, a fixed-time disturbance observer (FXDO) based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model. Then, a fixed-time integral sliding mode control (FXISMC) is combined with the FXDO to achieve strong robustness and chattering reduction. Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability. Finally, numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances. In addition, the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.

Disturbance observer based fixed-time control of stochastic systems

In this paper, the novel fixed-time anti-disturbance control scheme is proposed for a class of stochastic systems subjected to multiple disturbances and faults, and the disturbances consist of derivative-bounded disturbanes and multiply noise. Based on the pole placement method, the fixed-time disturbance observer (Fixed-time DO) is devised to estimate derivative-bounded disturbances and an adaptive law is employed to approach the time-varying fault. Then a composite fixed-time controller is constructed to make the system converge to equilibrium position within a pre-specified time. At the same time, simulation examples illustrate that the proposed controller is effective and the convergence time is not related to the initial states of the system.

Fixed-Time Trajectory Tracking Control of Fully Actuated Unmanned Surface Vessels with Error Constraints

This paper proposes a fixed-time prescribed performance control technique to address the challenge of precise trajectory tracking control for unmanned surface vessels (USVs) in the presence of external time-varying disturbances and input saturation. To begin with, a fixed-time disturbance observer is created to handle the time-varying external interference. The observer can accurately estimate and compensate for the disturbance in a fixed time, which effectively improves the robustness of the system. Furthermore, to guarantee both the transient and steady-state response of the system, we employed a specific control technology that ensures the trajectory tracking error remains within a preset bounded range. Then, combined with the fixed-time disturbance observer, the command filter, the prescribed performance control technology, and the fixed-time stability theory, a fixed-time trajectory tracking control law is designed to make the trajectory tracking error of the system converge in a fixed time. Finally, an experiment was designed to validate the suggested control scheme. The results show that under the same conditions, compared with the nonlinear controller and the finite-time controller, the absolute error tracking index of this paper is the lowest, which means that the presented control scheme has higher accuracy.

Trajectory Tracking Control of Remotely Operated Vehicles via a Fast-Sliding Mode Controller with a Fixed-Time Disturbance Observer

Time-varying nonlinear external disturbances, as well as uncertainties in model and hydrodynamic parameters, make remotely operated vehicles (ROVs) trajectory tracking control complex and difficult. To solve this problem, this paper proposes a fast sliding mode controller with a fixed-time disturbance observer (FSMC-FDO), which consists of a sliding mode controller based on a fast reaching law and a novel fixed-time disturbance observer. The FSMC can solve the contradiction between system response time and chatter amplitude in sliding mode control. The FDO can compensate for time-varying external disturbances. The Lyapunov theory is used to prove the stability of the entire control scheme. Simulation results show that FSMC-FDO exhibits a good trajectory tracking performance with a better robustness than the conventional sliding mode control (CSMC) on the basis of exponential reaching law (ERL), while significantly reducing chatter.

Fixed-time anti-saturation control with concise system structure for the 6-DOF motion of spacecraft

Abstract This paper proposes a fixed-time anti-saturation (FT-AS) control scheme with a simple control loop for the 6-Degree-of-Freedom tracking (6-DOF) control problem of spacecraft with parameter uncertainties, external disturbances and input saturation. Considering the external disturbance and parameter uncertainties, the dynamical model of the tracking error is established. The traditional methods of handling input saturation usually add anti-saturation subsystems in the control system to suppress the impact of input overshoot. However, this paper directly inputs the input overshoot into the tracking error model, thus constructing a modified lumped disturbance term that includes the influence of input overshoot. Then, a novel fixed-time disturbance observer (FT-DO) is designed to estimate and compensate for this modified lumped disturbance. Therefore, there is no need to add the anti-saturation structures in the control loop, significantly reducing the complexity of the system. Finally, an observer-based fixed-time non-singular terminal sliding mode (FT-NTSM) controller is designed to guarantee the fixed-time stability of the whole system. In this way, the convergence time of the proposed scheme does not depend on the system’s initial conditions. Simulation results illustrate that the proposed method keeps the control input within the limit while achieving high-precision tracking control of attitude and position.

Fixed time containment control of multi-agent system under multi-source mismatched disturbance

Aiming at the cooperative control problem of multi-agent system, the fixed-time containment control of general second-order multi-agent system under mismatched disturbances is studied. Firstly, the problem of multi-agent system fixed-time containment control in ideal state is analyzed, and a distributed control protocol based on variable structure control is proposed. Then, a nonlinear fixed-time disturbance observer is designed, aiming at the mismatched disturbance, and a fixed-time control protocol based on the nonlinear disturbance observer is proposed. Finally, the effectiveness of the proposed control protocol under switching topology and multi-source disturbance is verified by numerical simulation.

Disturbance observer-based fixed-time control for hypersonic morphing vehicles with uncertainties

Abstract The attitude-tracking problem of hypersonic morphing vehicles (HMVs) is investigated in this research. After introducing variable-span wings, the optimal aerodynamic shape is available throughout the entire flight mission. However, the morphing wings cause significant changes in aerodynamic coefficients and mass distribution, challenging the attitude control. Therefore, a complete design procedure for the flight control system is proposed to address the issue. Firstly, the original model and the control-oriented model of HMVs are built. Secondly, in order to eliminate the influence caused by the multisource uncertainties, an adaptive fixed-time disturbance observer combined with fuzzy control theory is established. Thirdly, the fixed-time control method is developed to stabilise hypersonic morphing vehicles based on a multivariable sliding mode manifold. The control input can be obtained directly. Finally, the effectiveness of the proposed method is proved with the help of the Lyapunov theory and simulation results.

Event-triggered fault-tolerant attitude tracking control for spacecraft with fixed-time controller and disturbance observer under input constraints

This paper studies the attitude tracking problem for rigid spacecraft under restricted communication resources. This work proposes a novel composite control scheme for spacecraft subjected to system uncertainty, exogenous disturbance, periodic vibrations and uncertain modeled disturbance of actuator, actuator faults, and input saturation, which consists of a fixed-time controller (FiTC) based on an integral non-singular fast terminal sliding mode technique and a fixed-time disturbance observer (FiTDO). The FiTDO estimates the total disturbance (combination of the abovementioned effects) within a fixed time. Further, it improves the attenuation disturbance property of the composite controller by feedforward compensation. The proposed controller relaxes the prior upper-bound knowledge of the total disturbance and has anti-unwinding characteristics. Moreover, the designed event-triggered mechanism reduces control workload reduction and guarantees the Zeno-free behavior in the proposed composite scheme. The stability analysis of the closed-loop system under the proposed scheme using Lyapunov theory ensures the system states converge to a small invariant set within a fixed time. Simulation analysis and comparative studies demonstrate that the proposed scheme is effective in terms of convergence time, steady-state performance, and anti-interference ability, rate of controller update.

Fixed time control of free-flying space robotic manipulator with full state constraints: a barrier-Lyapunov-function term free approach

Space robotic manipulator (SRM) should be always performed in the given workspace for safety concern. This requires the system states such as rotation of each joint, attitude of base, and their velocities to be always constrained in the given regions. In this article, a new sliding mode control scheme based on a fixed time disturbance observer is proposed to realize the fixed time coordinate motion control of SRM with full-state constraints. Firstly, the tracking error and error velocity at the novel sliding manifold can converge to the equilibrium within a fixed time without violating their state constraints. Then, the control law based on the fixed time disturbance observer is designed to achieve the sliding manifold within a fixed time, which simultaneously satisfies the state constraints during the approaching stage. Unlike the most existing state constraint control schemes, the proposed controller does not include any Barrier Lyapunov Function (BLF) terms of system states, and therefore the risk of controller outputting inappropriately high control commands is eliminated. Moreover, the proposed control scheme is compatible to the initial system states violating their constraints, which thereby removes the assumption of feasible initial states. Furthermore, the proposed sliding manifold solves the singularity issue by a continuously varying power of tracking error, which thereby does not need an additional switch mechanism of manifold compared to the conventional fixed time controllers. The stability of the proposed control scheme is proven by using the Lyapunov theory, and the effectiveness is verified by numerical simulations.

Fixed-time event-triggered sliding mode cooperative path-following control with prescribed performance for USVs based on lumped disturbance observer

In order to solve the problem of Unmanned Surface Vehicles being unable to accurately cooperative path-following under the parameter uncertainties, actuator faults, and external disturbances, this paper mainly combines the fixed-time and sliding mode theory to design the control strategy. Firstly, a fixed-time disturbance observer is adopted to estimate composite disturbances. Then, a fixed-time heading-surge guidance law that satisfies the fixed-time stability of the position error system is designed, and the synchronization of the formation on the full paths is realized by the fixed-time path parameter consensus. On this basis, a fixed-time dynamic event-triggered sliding mode controller with prescribed performance is proposed to ensure that the velocity error system is stable in fixed time and the tracking error is strictly within the specified range. Due to the application of fixed-time theory in cooperative path-following, the whole closed-loop system is proved to be fixed-time stable. Moreover, the dynamic event-triggered mechanism is introduced to reduce the energy consumption. Finally, the effectiveness and superiority of the proposed control method are verified by simulations.

Observer-based fixed-time dynamic surface tracking control for autonomous surface vehicles under actuator constraints and denial-of-service attacks

This paper proposes a novel trajectory tracking control strategy for autonomous surface vehicles (ASVs), subject to actuator constraints and under denial-of-service (DoS) attacks. Firstly, a fixed-time disturbance observer (FTDO) is used to estimate and compensate unknown external disturbances, which enhances the robustness of the motion system. Secondly, a novel fixed-time filter is designed by combining dynamic surface technology with fixed-time control, which avoids the problem of differential explosion, and reduces the filtering error. Lastly, in order to address the effects of actuator constraints and DoS attacks, an auxiliary system (AS) and a compensation system (CS) are included in the fixed-time dynamic surface controller based on FTDO. The proposed method improves the robustness, stability and accuracy of the closed-loop system. Additionally, the reference tracking error converges to the neighborhood of the origin within a fixed-time. The superiority of the proposed control method over traditional control strategies from the existing literature is demonstrated in simulations.

Disturbance observer–based fixed-time sliding mode trajectory tracking control for marine surface vehicles with uncertain dynamics

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

Non-singular fixed-time robust containment control for autonomous surface vehicles

For the containment control problem of autonomous surface vehicles with external disturbances, a novel non-singular fixed-time control scheme is developed, where the multi-ship system consists of real leaders and followers. In contrast with traditional containment cases studied in most of the existing literature, real leaders are required to track the desired trajectories, and the followers need to get into the convex hull spanned by the real leaders in a fixed time. The method for solving the fixed-time containment control problem is divided into the following steps: Firstly, a fixed-time disturbance observer is designed to estimate the external disturbance for the leaders and the followers, and the estimation result is used to compensate for the input of the control system; Second, combined with fixed-time stability theory and a switch function, a non-singular fixed-time trajectory tracking controller for leaders is designed, such that the position tracking error could be bounded within a fixed time; Third, to achieve formation efficiently, a non-singular fixed-time containment controller strategy incorporating with graph theory is proposed for coordinating followers, such that the fixed-time stability can be ensured. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.

Fuzzy disturbance observer-based dynamic sliding mode control for hypersonic morphing vehicles

This research discusses the attitude-tracking problem of hypersonic morphing vehicles (HMVs) in the presence of multi-source uncertainties. The hypersonic flight vehicle with variable-span wings is introduced. Considering the dramatic aerodynamic characteristic changes caused by morphing-span wings, strong robustness and great adaption are demanded. The sliding mode control technique is adopted to build the flight control system since the robustness is what the aircraft orders. In order to obtain fast attitude-tracking performance, the terminal function and adaptive laws are developed to achieve finite-time control with high adaptation to varying aerodynamic characteristics. For a hypersonic flight with guts, robustness enhancement is required. Therefore, a novel fixed-time disturbance observer is proposed to enhance the robustness against multi-source uncertainties. Unlike the existing finite-time observers, the settling time is independent of the initial conditions. Based on the disturbance observer and the adaptive technique, finite-time flight control is developed to provide strong robustness and adaptation, achieving uncertainty compensation. The effectiveness of the designed controller is revealed with the help of Lyapunov synthesis. Several flight scenarios are introduced to analyze the performance.

Reconfigurable tolerant control of nonlinear Euler–Lagrange systems under actuator fault: A reinforcement learning-based fixed-time approach

This paper presents a novel fixed-time adaptive Fault Tolerant Control (FTC) framework for MIMO nonlinear Euler-Lagrange systems using sliding mode-based strategy, reinforcement learning (RL) and fixed-time disturbance observer. The primary objective is to enhance system reliability in the presence of actuator faults, uncertainties and disturbances. The proposed RL algorithm incorporates an actor-critic neural network (NN), where the actor NN estimates the uncertainty and the critic NN evaluates the performance cost function. Additionally, a fixed-time adaptive observer is designed to estimate the lumped term of faults and disturbances. To achieve high precision trajectory tracking within a fixed-time interval, a nonsingular fast terminal sliding mode scheme is designed. This scheme ensures fixed-time convergence of the tracking error and facilitates disturbance attenuation and fault mitigation, which are key features of the proposed fixed-time secure control strategy. Furthermore, the closed-loop system's fixed-time stability is analyzed using Lyapunov theory. Experimental results demonstrate the effectiveness of the proposed FTC framework in mitigating the adverse effects of faults, uncertainties and disturbances, thereby enhancing system performance and reliability.

Fixed time prescribed performance dynamic positioning control design for surface vessels

This paper addresses the problem of fixed time dynamic positioning (DP) control for surface vessels under the influence of external disturbances, while considering input and output constraints. Using the hyperbolic tangent function, a saturation handling method with an auxiliary control system is constructed, which can handle the saturation constraints of both the control input and its rate of change within a same control framework. By incorporating an auxiliary sliding mode variable, a fixed time disturbance observer (FTDO) is developed to estimate external disturbances. This FTDO ensures that the estimation error converges within a fixed time and provides users with the flexibility to determine the desired convergence time. Moreover, a nonlinear function is introduced in the FTDO to reduce the possibility of singular problems in the control system. Combining the developed FTDO, prescribed performance control strategy and backstepping control technique, a novel DP control strategy is proposed, which not only ensures that the positioning error satisfies the output constraint requirements within a fixed time but also guarantees the fixed time stability of the closed-loop system. Finally, to validate the effectiveness of the proposed DP control law, numerical simulation analysis is carried out on a supply vessel.

Vision-based adaptive fixed-time uncooperative target tracking for QUAV with unknown disturbances

This article investigates the problem of the vision-based uncooperative target tracking control for a quadrotor unmanned aerial vehicle (QUAV) with unknown external disturbances. Note that the uncooperative target information cannot be obtained directly and need to be measured by a monocular sensor installed on the QUAV. In the light of the monocular sensor, a vision-based adaptive fixed-time control scheme is constructed to deal with the uncooperative target tracking problem. To efficiently observe unknown external disturbances, a fixed-time disturbance observer (FTDO) is designed by using the super-twisting (ST) algorithm. Finally, with the help of the Lyapunov stability theory, which guarantees the boundedness of all closed-loop signals, the QUAV is capable of tracking the uncooperative target in fixed time. The results of the simulation demonstrate the effectiveness of the proposed control strategy.

Distributed Event-Triggered Fixed-Time Leader–Follower Formation Tracking Control of Multiple Underwater Vehicles Based on an Adaptive Fixed-Time Observer

This paper focuses on the fixed-time leader–follower formation control of multiple underwater vehicles (MUVs) in the presence of external disturbances. First, an adaptive fixed-time disturbance observer (AFxDO) is developed to deal with unknown time-varying environmental disturbances. The developed AFxDO guarantees the fixed-time convergence property of the disturbance observation error and no prior information on the external disturbances or their derivatives is required. Then, with the aid of the developed AFxDO, a distributed event-triggered fixed-time backstepping controller was developed to achieve the leader–follower formation tracking control of MUVs. To solve the “explosion of complexity” problem inherent in the conventional backstepping, a nonlinear filter is introduced to obtain the derivative of the virtual control law. Furthermore, to reduce the communication burden, the event-triggered mechanism is integrated into the formation tracking controller. The stability analysis shows that the closed-loop MUV system is practical fixed-time stable. Finally, simulation results demonstrate the effectiveness of the proposed scheme.