Fixed-time Disturbance Observer Research Articles

Error-constrained fixed-time trajectory tracking control for a stratospheric airship with disturbances

In this paper, a novel fixed-time trajectory tracking control method is presented for a six degrees of freedom (6-DOF) stratospheric airship with time-varying error constraints and disturbances. The tan-type barrier Lyapunov function (BLF) method is extended by the adding a power integrator technique to deal with the time-varying error constraints with the fixed-time stability guaranteed, which ensures that the convergence of a stratospheric airship to the reference trajectory can be achieved in a finite time regardless of its initial condition. Also the complex differential calculation is avoided in the backstepping design. A new fixed-time disturbance observer (DO), which counts on less prior knowledge of disturbances, is constructed to estimate the unknown disturbances. The proposed control method is developed based on the transformed error model, thus can be readily extended to a wide range of second-order mechanical systems. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme.

Fixed-Time Disturbance Observer-Based Adaptive Finite-Time Guidance Law Design considering Impact Angle Constraint and Autopilot Dynamics

This paper aims to establish an effective guidance law to accomplish the interception guidance mission for a missile intercepting a target with impact angle constraint and autopilot dynamics. To achieve this purpose, a fixed-time disturbance observer-based adaptive finite-time guidance law is presented. First, a fixed-time disturbance observer (FTDO) is designed to guarantee the fast estimation of the lumped disturbance caused by the target maneuver. Then, the FTDO-based adaptive integral sliding mode backstepping (AISMB) guidance law is constructed for the interception guidance problem. Besides, several adaptive laws are established to estimate the derivative of virtual control inputs, making the “differential explosion problem” of conventional backstepping get avoided. The finite-time convergence characteristic of the closed-loop system is analyzed by utilizing the Lyapunov stability theory. Finally, the simulation examples are conducted to demonstrate the effectiveness of the proposed composite guidance law.

Fixed-time output tracking control for a class of uncertain nonlinear MIMO systems

This article proposed a new fixed-time output tracking control scheme for a class of high-order MIMO nonlinear systems with unknown nonlinearities, parameter uncertainties and external disturbances. Firstly, a novel nonsingular recursive integral terminal sliding mode (ITSM) surface is designed by employing appropriate integral function and integer orders. Then the lumped system matched and mismatched uncertainties are estimated by developing a new adaptive fixed-time disturbance observer (AFTDO) based on super-twisting technique. The chattering problem existed in traditional disturbance observer (DO) can be reduced with the proposed AFTDO allowing the gains to adapt the changed derivative of lumped disturbances, effectively. Furthermore, semi-global fixed-time stability analysis is presented by means of Lyapunov stability theorem and it is proved that the system convergence time is independent of the system initial states and allowed to be arbitrarily adjusted based on practical demands. Finally, theoretical results are supported by numerical simulation and experimental results.

Predefined-time control for a horizontal takeoff and horizontal landing reusable launch vehicle

PurposeThis paper aims to investigate the problem of attitude control for a horizontal takeoff and horizontal landing reusable launch vehicle.Design/methodology/approachIn this paper, a predefined-time attitude tracking controller is presented for a horizontal takeoff and horizontal landing reusable launch vehicle (HTHLRLV). Firstly, the attitude tracking error dynamics model of the HTHLRLV is developed. Subsequently, a novel sliding mode surface is designed with predefined-time stability. Furthermore, by using the proposed sliding mode surface, a predefined-time controller is derived. To compensate the external disturbances or model uncertainties, a fixed-time disturbance observer is developed, and its convergence time can be defined as a prior control parameter. Finally, the stability of the proposed sliding mode surface and the controller can be proved by the Lyapunov theory.FindingsIn contrast to other fixed-time methods, this controller only requires three control parameters, and the convergence time can be predefined instead of being estimated. The simulation results also demonstrate the effectiveness of the proposed controller.Originality/valueA novel predefined-time attitude tracking controller is developed based on the predefined-time sliding mode surface (SMS) and fixed-time disturbance observer (FxTDO). The convergence time of the system can be selected as a prior control parameter for SMS and FxTDO.

Fixed-Time Tracking Control of Wireless Power Transfer Systems with Disturbances and Current Constraints

This article investigates the tracking control of the wireless power transfer (WPT) system with disturbances and constraints. Using the generalized state-space averaging method, a small signal perturbation model of the system is obtained. To estimate the perturbation faster and more accurately, the fixed-time disturbance observer is introduced. Then a fixed-time disturbance observer-based controller (DOBC) is designed. In addition, to ensure the WPT current constraint not be violated, tan type Barrier Lyapunov Functions (BLFs) are added. To illustrate the robustness of the WPT system, a 100-watt WPT system is built and the closed system is proved to be effective. Experimental results show that the startup response time of the current is 4 ms without overshoot. Under loads and resonance capacitors changes, the WPT current can also converge to the reference value within 4 ms.

Cooperative Guidance Law with Predefined-Time Convergence for Multimissile Systems

To intercept the maneuvering target through multimissile cooperation, predefined-time cooperative guidance (PTCG) law is presented with constraints including the impact time and the line-of-sight (LOS) angle. In order to achieve simultaneous interception, we propose a PTCG law in the LOS direction based on a predefined-time consensus protocol, which guarantees the achievement of consensus on each missile’s impact time within the predefined time. Furthermore, to ensure the predefined-time convergence of the LOS angle and the predefined-time convergence of the LOS angular rate, a PTCG law with a fixed-time disturbance observer (FxTDO) is presented in the normal direction of the LOS. Compared with the traditional finite-time or fixed-time cooperative guidance laws, the proposed PTCG law predefines the upper bound of the settling time as an explicit parameter. Finally, the simulation results of the PTCG law verify the efficiency of the proposed method.

Fixed-time disturbance observer-based nearly optimal control for reusable launch vehicle with input constraints

In this paper, a fixed-time disturbance observer-based nearly optimal control (FTDO-NOC) scheme is proposed for reusable launch vehicle (RLV) subject to model uncertainties, input constraints, and unknown mismatched/matched disturbances. The dynamics of RLV attitude motion are divided into outer-loop subsystem and inner-loop subsystem. For the outer-loop subsystem, to address the problems of unknown mismatched disturbances and model uncertainties, a novel adaptive-gain multivariable generalized super-twisting (AMGST) controller is proposed. Two modified gain-adaptation laws are derived for tuning the control gains of AMGST controller, which attenuates chattering efficiently. For the inner-loop subsystem, considering the effect of unknown matched disturbances, a fixed-time disturbance observer (FTDO) is utilized to estimate the matched disturbances and the time derivative of virtual control input. Incorporated with the designed FTDO, a nearly optimal controller (NOC), which is based on the critic–actor neural networks (NNs), is utilized to generate the approximate optimal control moments satisfying the input constraints. The tracking errors of inner-loop subsystem and the weight estimation errors of the critic–actor NNs are proved to be uniformly ultimately bounded (UUB) via Lyapunov technique. Finally, we provide simulation results to validate the effectiveness and superiority of the proposed control scheme.

Fixed-time disturbance observer-based chattering-free sliding mode attitude tracking control of aircraft with sensor noises

The challenging attitude tracking control problem of aircraft with external disturbance and sensor noises is investigated. A disturbance observer-based control approach is presented. In this approach, a fixed-time disturbance observer is preliminarily developed. The external disturbance is estimated with the estimation error governed to zero after a fixed-time regardless of any initial state. Moreover, with measurement noises explicitly considered, a discrete tracking differentiator extracting the real signals from the polluted measurement is introduced into that fixed-time observer to improve its application potential. Invoking the estimation information, a sliding mode attitude controller is then synthesized. The main feature of the proposed approach is that the closed-loop attitude tracking system is guaranteed to be exponentially stable. External disturbance rejection is achieved, while its upper bound is not required to implement that approach. In contrast to the conventional sliding mode control schemes, the proposed controller is chattering-free. Numerical simulation and experimental tests are finally carried out to verify the effectiveness of the proposed approach.

A Novel Fixed-Time Control Algorithm for Trajectory Tracking Control of Uncertain Magnetic Levitation Systems

In this research, a new robust control method is developed, which achieves a fixed-time convergence, robust stabilization, and high accuracy for trajectory tracking control of uncertain magnetic levitation systems. A hybrid controller is a combination of an adaptive fixed-time disturbance observer and a fixed-time control algorithm. First, to estimate precisely the total uncertain component in fixed-time, an adaptive disturbance observer is constructed. Then, a new robust control method is designed from a proposed fixed-time sliding manifold, disturbance observer's information, and a continuous fixed-time reaching law. A global fixed-time stability and convergence time boundary of the control system is obtained by Lyapunov criteria in which the settling time can be arbitrarily set using design parameters regardless of the system's initial state. Finally, the designed control strategy is implemented for a magnetic levitation system and its control performance is compared with other existing finite-time control methods to evaluate outstanding features of the proposed system. Trajectory tracking experiments in MATLAB/SIMULINK environment have been performed to exhibit the effectiveness and practicability of the designed approach.

Fixed-Time Trajectory Tracking Control of Autonomous Surface Vehicle with Model Uncertainties and Disturbances

The issue of fixed-time trajectory tracking control for the autonomous surface vehicles (ASVs) system with model uncertainties and external disturbances is investigated in this paper. Particularly, convergence time does not depend on initial conditions. The major contributions include the following: (1) An integral sliding mode controller (ISMC) via integral sliding mode surface is first proposed, which can ensure that the system states can follow the desired trajectory within a fixed time. (2) Unknown external disturbances are absolutely estimated by means of designing a fixed-time disturbance observer (FTDO). By combining the FTDO and ISMC techniques, a new control scheme (FTDO-ISMC) is developed, which can achieve both disturbance compensation and chattering-free condition. (3) Aiming at reconstructing the unknown nonlinear dynamics and external disturbances, a fixed-time unknown observer (FTUO) is proposed, thus providing the FTUO-ISMC scheme that finally achieves trajectory tracking of ASVs with unknown parameters. Finally, simulation tests and detailed comparisons indicate the effectiveness of the proposed control scheme.

Nonsingular fixed-time terminal sliding mode trajectory tracking control for marine surface vessels with anti-disturbances

In this paper, we investigate an accurate trajectory tracking control of marine surface vessels (MSVs) under external disturbances. First, introducing an auxiliary velocity vector, a complicated MSV models can be further simplified. Then, a fixed-time disturbance observer (FDO) is employed to identify external disturbances to enhance the tracking performance of the system. The estimation errors can achieve the origin within a finite time independent of the initial conditions. On the basis of the FDO, in the context of fixed-time sliding mode manifold, a novel nonsingular fixed-time terminal sliding mode (NFTSM) scheme is formulated, by which MSVs can track the reference trajectory with all states globally stabilized in a fixed time. The effectiveness of the developed scheme is validated by numerical simulation results.

Disturbance observer based fixed time sliding mode control for spacecraft proximity operations with coupled dynamics

This paper proposes a fixed time disturbance observer (FTDO) based fixed time sliding mode control scheme for spacecraft proximity operations in the presence of parameter uncertainties and disturbances. The FTDO is designed to estimate the lumped disturbance which includes kinematic couplings, parameter uncertainties, and disturbances. Based on the observation of lumped disturbance, the fixed time sliding mode control is developed to achieve fixed time convergence, where the FTDO is employed to counteract the lumped disturbances and eliminate the chattering phenomenon. What’s more, the proposed control method can speed up the convergence and improve the control accuracy. Finally, the stability of the closed-loop system is proved via the Lyapunov analysis. Numerical simulations demonstrate the effectiveness of the proposed control method.

Observer-based event-triggered fixed-time control for nonlinear system with full-state constraints and input saturation

This paper investigates the continuous composite control scheme for the tracking of nonlinear system with mismatched disturbances, input saturation and full-state constraints. Based on the fixed-time stability theory, a novel fixed-time disturbance observer is proposed, which switches from a uniform second-order sliding mode observer with high-degree term to the classical continuous super-twisting observer. Then, a command filtered backstepping control scheme is designed to enforce the tracking error into a small neighbourhood of the origin in fixed time while the full-state constraint and input saturation constraint are satisfied. To further reduce the communication burden, an event-triggered communication strategy between the controller and the actuator input is also developed. Furthermore, all the signals in the closed-loop system are proven to be bounded. Finally, the effectiveness of the proposed control strategy is illustrated by numerical simulations.

Distributed fixed-time attitude coordinated tracking for multiple rigid spacecraft via a novel integral sliding mode approach

In this paper, the distributed fixed-time attitude coordinated tracking control problem is investigated for multiple rigid spacecraft in the presence of external disturbances. A novel integral sliding mode control scheme is proposed for second order systems with external disturbances, which provides bounded convergence time independent of initial conditions. By constructing a sliding-mode estimator for each spacecraft, the requirement of the neighbours’ control input information is removed, which reduces the communication flow. A fixed-time disturbance observer is introduced to compensate external disturbances. Then, the composite attitude tracking control laws are developed to guarantee tracking errors converge to zero in fixed time. The fixed-time stability of the closed-loop system is proven by employing the Lyapunov method. Finally, the performance of the proposed control approach is illustrated by numerical simulations.

Distributed Nash equilibrium seeking for networked games of multiple high-order systems with disturbance rejection and communication delay

This paper investigates distributed Nash equilibrium seeking problems for networked games played by multiple high-order systems with disturbance rejection and communication delay, where each player’ payoff function is determined by all players’ actions. To be specific, a fixed-time disturbance observer is used to enhance the capacity of disturbance rejection. In virtue of the observed values, the backstepping technique is performed to design a seeking strategy on the basis of a synthesis of a leader–follower consensus protocol and the gradient play technique, where a fixed-time differentiator is used to overcome the problem of ‘explosion of terms.’ Detailed stability analysis is conducted via the Lyapunov–Krasovskii method to show the convergence of the players’ actions to the Nash equilibrium under both constant and time-varying delays. Moreover, the relationship between the allowed upper bound of the communication delay and the controller parameters is also obtained analytically. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed seeking algorithms.

Observer-based multivariable fixed-time formation control of mobile robots

This paper proposes a multivariable fixed-time leader-follower formation control method for a group of nonholonomic mobile robots, which has the ability to estimate multiple uncertainties. Firstly, based on the state space model of the leader-follower formation, a multivariable fixed-time formation kinematics controller is designed. Secondly, to overcome uncertainties existing in the nonholonomic mobile robot system, such as load change, friction, external disturbance, a multivariable fixed-time torque controller based on the fixed-time disturbance observer at the dynamic level is designed. The designed torque controller is cascaded with the formation controller and finally realizes accurate estimation of the uncertain part of the system, the follower tracking of reference velocity and the desired formation of the leader and the follower in a fixed-time. The fixed-time upper bound is completely determined by the controller parameters, which is independent of the initial state of the system. The multivariable fixed-time control theory and the Lyapunov method are adopted to ensure the system stability. Finally, the effectiveness of the proposed algorithm is verified by the experimental simulation.

Fixed-Time Cooperative Guidance Law With Angle Constraint for Multiple Missiles Against Maneuvering Target

This paper addresses the problem of the fixed-time cooperative guidance (FxTCG) law for multi-missiles against a single maneuvering target with constraints of both the interception time and the line-of-sight (LOS) angle. Firstly, by utilizing the consensus protocol and the fixed-time consensus theory, a new FxTCG in the LOS direction is presented to guarantee that the multiple missiles intercept the incoming target synchronously. Moreover, the acceleration of the target causes disturbance, so a simple fixed-time disturbance observer (FxTDO) is introduced to compensate FxTCG with the disturbance estimation. Subsequently, the FxTCG in the normal direction of the LOS is designed based on an adaptive fixed-time convergence reaching law and the proposed FxTDO, which ensures the fixed-time convergence of the LOS angular velocity and LOS angle between each missile and the maneuvering target. Finally, numerical simulations and adequate analyses are carried out to illustrate the accuracy, effectiveness, and robustness of the proposed FxTCG scheme.

Stabilization of USVs Under Mismatched Condition Based on Fixed-Time Observer

This study investigates the problem of asymptotic stabilization of underactuated surface vehicles (USVs) in the presence of simultaneous matched and mismatched disturbances. Within the framework of back-stepping control and by introducing a periodic term in the control laws of virtual yaw angle and surge velocity, a control design method is developed to stabilize the USVs into the bounded region. By the induction method, a novel fixed-time disturbance observer based on higher-order sliding mode differentiators are introduced. Then a control law based on the proposed observers is proposed, by which the errors between the virtual and actual yaw angle and surge velocity can converge to zero, and the state of the USVs converge to a bounded region. Numerical simulations are carried out to verify the proposed control schemes.

Asymptotic Stabilization of USVs With Actuator Dead-Zones and Yaw Constraints Based on Fixed-Time Disturbance Observer

This paper investigates the problem of asymptotic stabilization of underactuated surface vehicles (USVs) with actuator dead-zones and yaw constraints. By transforming the system model into two subsystems, a backstepping control method based on a Barrier Lyapunov Function (BLF) is introduced to stabilize the transformed system and prevent the USV from reaching the boundaries of yaw angle and velocity constraints. A fixed-time disturbance observer is involved in the USV controller to deal with actuator dead-zones and disturbances. The method is extended to cover the case in which the yaw constraints are time-varying and the initial states exceed the constraint regions. Numerical simulations have shown the effectiveness of the presented method.

Formation Control for Multiple Quadrotor Aircraft via Fixed-time Consensus Algorithm

This paper mainly studies the formation control problem of multiple quadrotor aircraft via fixed-time control theory. First, based on the bilimit homogeneous theory and the framework of multiagent theory, for multiaircraft, a fixed-time formation control strategy is proposed. Considering the external disturbance existing on the attitude loop of the aircraft, the corresponding fixed-time disturbance observer is designed with the observer technology. Then, a fixed-time attitude controller is designed based on the accurate observation and fast compensation from the disturbance observer. Finally, some simulations are performed to verify the effectiveness of the proposed theoretical method.