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The purpose of this paper, is to solve the problem of finite-time fault-tolerant attitude synchronization and tracking control of multiple rigid bodies in presence of model uncertainty, external disturbances, actuator faults and saturation. It is assumed that the rigid bodies in the formation may encounter loss of effectiveness and/or bias actuator faults.

For the purpose, adaptive terminal sliding mode control and neural network structure are used, and a new sliding surface is proposed to guarantee known finite-time convergence not only at the reaching phase but also on the sliding surface. The sliding surface is then modified using a proposed auxiliary system to maintain stability under actuator saturation.

Assuming that the communication topology between the rigid bodies is governed by an undirected connected graph and the upper bounds on the actuators’ faults, estimation error of model uncertainty and external disturbance are unknown, not only the attitudes of the rigid bodies in the formation are synchronized but also they track the time-varying attitude of a virtual leader. Using Lyapunov stability approach, finite-time stability of the proposed control algorithms demonstrated on the sliding phase as well as the reaching phase. The effectiveness of the proposed algorithm is also validated by simulation.

The proposed controller has the advantage that the need for any fault detection and diagnosis mechanism and the upper bounds information on estimation error and external disturbance is eliminated.

The purpose of this paper is to investigate the time-varying finite-time formation tracking control problem for multiple unmanned aerial vehicle systems under switching topologies, where the states of the unmanned aerial vehicles need to form desired time-varying formations while tracking the trajectory of the virtual leader in finite time under jointly connected topologies.

A consensus-based formation control protocol is constructed to achieve the desired formation. In this paper, the time-varying formation is specified by a piecewise continuously differentiable vector, while the finite-time convergence is guaranteed by utilizing a non-linear function. Based on the graph theory, the finite-time stability of the close-loop system with the proposed control protocol under jointly connected topologies is proven by applying LaSalle’s invariance principle and the theory of homogeneity with dilation.

The effectiveness of the proposed protocol is verified by numerical simulations. Consequently, the proposed protocol can successfully achieve the predefined time-varying formation in finite time under jointly connected topologies while tracking the trajectory generated by the leader.

This paper proposes a solution to simultaneously solve the control problems of time-varying formation tracking, finite-time convergence, and switching topologies.

The purpose of this paper is to develop some interesting results in the field of chaotic synchronization with a new finite-time controller to reduce the time of convergence.

This article proposes a finite-time controller for the synchronization of hyper(chaotic) systems in a given time. The chaotic systems are perturbed by the model uncertainties and external disturbances. The designed controller achieves finite-time synchronization convergence to the steady-state error without oscillation and elimination of the nonlinear terms from the closed-loop system. The finite-time synchronization convergence reduces the hacking duration and recovers the embedded message in chaotic signals within a given preassigned limited time. The free oscillation convergence keeps the energy consumption low and alleviates failure chances of the actuator. The proposed finite-time controller is a combination of linear and nonlinear parts. The linear part keeps the stability of the closed-loop, the nonlinear part increases the rate of convergence to the origin. A generalized form of analytical stability proof is derived for the synchronization of chaotic and hyper-chaotic systems. The simulation results provide the validation of the accomplish synchronization for the Lu chaotic and hyper-chaotic systems.

The designed controller not only reduces the time of convergence without oscillation of the trajectories which can run the system for a given time domain.

This work is originally written by the author.

The finite-time visual servoing control problem is considered for dynamic wheeled mobile robots (WMRs) with unknown control direction and external disturbance.

By using finite-time control method and switching design technique.

First, the visual servoing kinematic WMR model is developed, which can be converted to the dynamic chained-form systems by using a state and input feedback transformation. Then, for two decoupled subsystems of the chained-form systems, according to the finite-time stability control theory, a discontinuous three-step switching control strategy is proposed in the presence of uncertain control coefficients and external disturbance.

A class of discontinuous anti-interference control method has been presented for the dynamic nonholonomic systems.

This paper aims to investigate the problem of finite-time consensus tracking control without unwinding for formation flying spacecraft in the presence of external disturbances.

Two distributed finite-time controllers are developed using the backstepping sliding mode. The first robust controller can compensate for external disturbances with known bounds, and the second one can compensate for external disturbances with unknown bounds.

Because the controllers are designed on the basis of rotation matrix, which represents the set of attitudes both globally and uniquely, the system can overcome the drawback of unwinding, which results in extra fuel consumption. Through introducing a novel virtual angular velocity, exchange of control signals between neighboring spacecraft becomes unnecessary, and it is able to reduce the communication burden.

The two robust controllers can deal with unwinding that may result in fuel consumption by traveling a long distance before returning to a desired attitude when the closed-loop system is close to the desired attitude equilibrium.

Two finite-time controllers without unwinding are proposed for formation flying spacecraft by using backstepping sliding mode. Furthermore, exchange of control signals between neighboring spacecraft is unnecessary.

The purpose of this paper is to construct an event-triggered finite-time fault-tolerant formation tracking controller, which can achieve a time-varying formation control for multiple unmanned aerial vehicles (UAVs) during actuator failures and external perturbations.

First, this study developed the formation tracking protocol for each follower using UAV formation members, defining the tracking inaccuracy of the UAV followers’ location. Subsequently, this study designed the multilayer event-triggered controller based on the backstepping method framework within finite time. Then, considering the actuator failures, and added self-adaptive thought for fault-tolerant control within finite time, the event-triggered closed-loop system is subsequently shown to be a finite-time stable system. Furthermore, the Zeno behavior is analyzed to prevent infinite triggering instances within a finite time. Finally, simulations are conducted with external disturbances and actuator failure conditions to demonstrate formation tracking controller performance.

It achieves improved performance in the presence of external disturbances and system failures. Combining limited-time adaptive control and event triggering improves system stability, increase robustness to disturbances and calculation efficiency. In addition, the designed formation tracking controller can effectively control the time-varying formation of the leader and followers to complete the task, and by adding a fixed-time observer, it can effectively compensate for external disturbances and improve formation control accuracy.

A formation-following controller is designed, which can handle both external disturbances and internal actuator failures during formation flight, and the proposed method can be applied to a variety of formation control scenarios and does not rely on a specific type of UAV or communication network.

The purpose of this paper is to present a novel guidance law that is able to control the impact time while the seeker’s field of view (FOV) is constrained.

The new guidance law is derived from the framework of Lyapunov stability theory to ensure interception at the desired impact time. A time-varying guidance gain scheme is proposed based on the analysis of the convergence time of impact time error, where finite-time stability theory is used. The circular trajectory assumption is adopted for the derivation of accurate analytical estimation of time-to-go. The seeker’s FOV constraint, along with missile acceleration constraint, is considered during guidance law design, and a switching strategy to satisfy it is designed.

The proposed guidance law can drive missile to intercept stationary target at the desired impact time, as well as satisfies seeker’s FOV and missile acceleration constraints during engagement. Simulation results show that the proposed guidance law could provide robustness against different engagement scenarios and autopilot lag.

The presented guidance law lays a foundation for using cooperative strategies, such as simultaneous attack.

This paper presents further study on the impact time control problem considering the seeker’s FOV constraint, which conforms better to reality.

The purpose of this paper is to resolve complex nonlinear dynamical problems of the pitching axis of solar sail in body coordinate system compared with inertial coordinate system. And saturation condition of controlled torque of vane in the orbit with big eccentricity ration, uncertainty and external disturbance under complex space background are considered.

The pitch dynamics of the sailcraft in the prescribed elliptic earth orbits is established considering the torques by the control vanes, gravity gradient and offset between the center-of-mass (cm) and center-of-pressure (cp). The maximal torques afforded by the control vanes are numerically determined for the sailcraft at any position with any pitch angle, which will be used as the restriction of the attitude control torques. The finite/infinite time adaptive sliding mode saturation controller and Bang–Bang–Radial Basis Function (RBF) controller are designed for the sailcraft with restricted attitude control torques. The model uncertainty and the input error (the error between real input and ideal control law input) are solved using the RBF network.

The finite true anomaly adaptive sliding mode saturation controller performed better than the other two controllers by comparing the numerical results in the paper. The control torque saturation, the model uncertainty and the external disturbance were also effectively solved using the infinite and finite time adaptive sliding mode saturation controllers by analyzing the numerical simulations. The stabilization of the pitch motion was accomplished within half orbit period.

The complex accurate dynamics can be approximated using the RBF network. The controllers can be applied to stabilization of spacecraft attitude dynamics with uncertainties in complex space environment.

Advanced control method is used in this paper; saturation of controlled torque of vane is resolved when the orbit with big eccentricity ration is considered and uncertainty and external disturbance under complex space background are settled. Moreover, complex and accurate nonlinear dynamical model of pitching axis of solar sail in body coordinate system compared with inertial coordinate system is provided.

Quadrotors have been applied in various fields. However, because the quadrotor is subject to multiple disturbances, consisting of external disturbances, actuator faults and parameter uncertainties, it is difficult to control the unmanned aerial vehicle (UAV) to achieve high-precision tracking performance. This paper aims to design a safety controller that uses observer and neural network method to improve the tracking performance of UAV under multiple disturbances. The experiments prove that this method is effective.

First, to actively estimate and compensate the synthetic uncertainties of the system, a finite-time extended state observer is investigated, and the disturbances are transformed into the extended state of the system for estimation. Second, an adaptive neural network controller that does not accurately require the dynamic model knowledge is designed based on the estimated value, where the weights of the neural network can be dynamically adjusted by the adaptive law. Furthermore, the finite-time bounded convergence of the proposed observer and the stability of the system are proved through homogeneous theory and Lyapunov method.

The figure-“8” climbing flight simulation and real flight experiments illustrate that the proposed safety control strategy has good tracking performance.

This paper proposes the safety control structure of the UAV, which combines the extended state observer with the neural network method. Numerical simulation results and actual flight experiments demonstrate the effectiveness of the proposed control strategy.

The purpose of this paper is to design a disturbance observer-based finite-time global sliding mode control scheme for the attitude tracking control problem of the reentry vehicle with parameter uncertainties and disturbances.

Feedback linearization is first introduced to transform vehicle model into three independent second order uncertain subsystems. Then a finite-time controller (FTC) is proposed for the nominal system on the basis of the homogeneity theory. Thereafter the integral sliding mode method is introduced for the vehicle with disturbances. The finite time convergence is achieved and global robustness is also assured by the combination of finite time control method and integral sliding mode strategy. Furthermore, to improve the attitude angle tracking accuracy a novel finite time disturbance observer (DO) is constructed.

Simulation is made for the reentry vehicle with disturbances involved. And the results show the finite-time convergence, tracking accuracy and robustness of the proposed strategy.

The proposed control strategy has three advantages. First of all it can achieve finite time convergence and avoid singularity. Moreover, it can also realize global robustness. Finally, a new kind of DO is introduced to improve the tracking accuracy.