Fixed-time Control Scheme Research Articles

Event-triggered-based fixed-time adaptive prescribed tracking control for stochastic nonlinear systems with actuator faults

In this paper, the event-triggered fixed-time control scheme is developed for a class of stochastic nonlinear systems with prescribed boundary constraints and actuator faults. For the controlled systems with unknown nonlinear functions, the neural networks are employed to reestablish the system model. Based on the event-triggered control technology, an original adaptive fixed-time control strategy with prescribed performance and the fault state is proposed by using the backstepping technique. Under the developed adaptive controller, the tracking error satisfies the predefined boundary functions and all the closed-loop system signals are bounded in probability in a fixed time, and the convergence time is irrelevant to the initial states of the system. The practicability of the designed controller is illustrated by a simulation example.

Neural network-based fixed-time sliding mode control for a class of nonlinear Euler-Lagrange systems

In this paper, the problem of robust fixed-time trajectory tracking control for a class of nonlinear Euler-Lagrange (EL) systems with exogenous disturbances and uncertain dynamics is addressed. A neural network (NN)-based adaptive estimation algorithm is employed to approximate the continuous uncertain dynamics, so that the dynamics of the EL system can be rebuild based on the estimations. In order to guarantee the EL system following the desired trajectory within a fixed-time, an adaptive fixed-time sliding mode control law is proposed to remedy the negative influence of uncertain dynamics and exogenous disturbances. Lyapunov stability theory is utilized to prove the stability and fixed-time convergence of the EL system. The efficiency of the developed NN-based adaptive fixed-time control strategy is substantiated with simulation results.

A multi-agent based cellular automata model for intersection traffic control simulation

The transportation system is a complex system with multiple transportation elements. Therefore, how to simulate a complex transportation system is a difficult point in transportation research. The complex element in transportation can be regarded as a multi-agent system, based on this, this paper proposes a multi-agent based cellular automata model. Applying multi-agent theory to simulate complex elements in traffic, and due to the simplified rules and high simulation efficiency of cellular automata, the model can efficiently simulate complex traffic scenes. In the model, car-following and lane-changing rules applied to different traffic scenarios are proposed, and the model is used to simulate the fixed time strategy and induction control strategy of road intersections. The simulation results show that the traffic control effect under the induction control strategy is better than the traditional fixed time control strategy. In the induction control strategy, the average speed of the vehicle is faster, the travel time and the queue length are shorter, and the road congestion problem caused by saturated traffic volume can be effectively avoided.

A Novel Fast Fixed-Time Control Strategy and Its Application to Fixed-Time Synchronization Control of Delayed Neural Networks

A Novel Fast Fixed-Time Control Strategy and Its Application to Fixed-Time Synchronization Control of Delayed Neural Networks

Adaptive fixed-time sensorless maximum power point tracking control scheme for DFIG wind energy conversion system

This work investigates the adaptive fixed-time control scheme to the maximum power point tracking (MPPT) control of double-fed induction generator (DFIG) based wind energy conversion system (WECS). Firstly, a fixed-time observer is designed to estimate the aerodynamic torque without the wind speed sensors. Optimal torque control is employed to obtain the real-time value of the optimal rotation speed by the torque observer. Then, an adaptive fixed-time nonsingular terminal sliding mode controller is proposed to implement optimal rotation speed tracking for MPPT of DFIG based WECS without the upper bound information of disturbances and system uncertainties in advance. The complete proof process of the stability of system and fixed-time convergence characteristics of the observer and the controller based on the Lyapunov theorem is constructed. Finally, simulation studies verify the effectiveness and strong robustness of the proposed method by Matlab/Simulink.

Singularity-Free Fixed-Time Fuzzy Control for Robotic Systems With User-Defined Performance

In this article, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as a multiple-input-multiple-output system.To implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this article are to establish a new error conversion mechanism and design corresponding BLF that can be integrated into fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstepping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems.

This paper examines the adaptive control of high-order nonlinear systems with strict-feedback form. An adaptive fixed-time control scheme is designed for nonlinear systems with unknown uncertainties. In the design process of a backstepping controller, the Lyapunov function, an effective controller, and adaptive law are constructed. Combined with the fixed-time Lyapunov stability criterion, it is proved that the proposed control scheme can ensure the stability of the error system in finite time, and the convergence time is independent of the initial condition. Finally, simulation results verify the effectiveness of the proposed control strategy.

Distributed fixed-time attitude coordinated control for multiple spacecraft with actuator saturation

This paper investigates the distributed fixed-time attitude coordinated control problem for multiple spacecraft subject to actuator saturation under the directed topology. First, a distributed fixed-time observer is presented for each follower spacecraft to estimate the leader spacecraft’s states. Compared with the commonly used fixed-time observer, the settling time of the proposed fixed-time observer can be easily adjusted by some free design parameters. Next, a distributed fixed-time control scheme is derived by using the estimates of the leader spacecraft's states and the adding a power integrator technique. When considering actuator saturation, an auxiliary system is utilized to compensate the saturation. Further, a rigorous theoretical proof is provided to show that the practical fixed-time stability of the closed-loop system is ensured. Finally, simulation results illustrate the benefits and effectiveness of the developed control scheme.

Adaptive Fast Nonsingular Fixed-Time Tracking Control for Robot Manipulators

This paper studies the fixed-time trajectory tracking control problem of robot manipulators in the presence of uncertain dynamics and external disturbances. First, a novel nonsingular fixed-time sliding mode surface is presented, which can ensure that the convergence time of the suggested surface is bounded regardless of the initial states. Subsequently, a novel fast nonsingular fixed-time sliding mode control (NFNFSMC) is developed so that the closed-loop system is fixed-time convergent to the equilibrium. By applying the proposed NFNFSMC method and the adaptive technique, a novel adaptive nonsingular fixed-time control scheme is proposed, which can guarantee fast fixed-time convergence of the tracking errors to small regions around the origin. With the proposed control method, the lumped disturbance is compensated by the adaptive technique, whose prior information about the upper bound is not needed. The fixed-time stability of the trajectory tracking control under the proposed controller is proved by the Lyapunov stability theory. Finally, corresponding simulations are given to illustrate the validity and superiority of the proposed control approach.

Event-triggered integral sliding mode fixed time control for trajectory tracking of autonomous underwater vehicle

In this paper, an event-triggered integral sliding mode fixed-time control method for trajectory tracking problem of autonomous underwater vehicle (AUV) with disturbance is investigated. Initially, the global fixed time stability is ensured with conventional periodic sampling method for reference trajectory tracking. By introducing fixed time integral sliding mode manifold, fixed time control strategy is expressed for the AUV, which can effectively eliminate the singularity. Correspondingly, in order to reduce the damage caused by chattering phenomenon, an adaptive fixed-time method is proposed based on the designed continuous integral terminal sliding mode (ITSM) to ensure that the trajectory tracking for AUV is achieved in fixed-time with external disturbance. In order to reduce resource consumption in the process of transmission network, the event-triggered sliding mode control strategy is designed which condition is triggered by an event. Also, Zeno behavior is avoided by proof of theoretical. It is shown that the upper bounds of settling time are only dependent on the parameters of controller. Theoretical analysis and simulation experiment results show that the presented methods can realize the control object.

Adaptive Neural Network Fixed-Time Control Design for Bilateral Teleoperation With Time Delay.

In this article, subject to time-varying delay and uncertainties in dynamics, we propose a novel adaptive fixed-time control strategy for a class of nonlinear bilateral teleoperation systems. First, an adaptive control scheme is applied to estimate the upper bound of delay, which can resolve the predicament that delay has significant impacts on the stability of bilateral teleoperation systems. Then, radial basis function neural networks (RBFNNs) are utilized for estimating uncertainties in bilateral teleoperation systems, including dynamics, operator, and environmental models. Novel adaptation laws are introduced to address systems' uncertainties in the fixed-time convergence settings. Next, a novel adaptive fixed-time neural network control scheme is proposed. Based on the Lyapunov stability theory, the bilateral teleoperation systems are proved to be stable in fixed time. Finally, simulations and experiments are presented to verify the validity of the control algorithm.

Adaptive Fuzzy Practical Fixed-Time Tracking Control of Nonlinear Systems

This article investigates an adaptive practical fixed-time control strategy for the output tracking control of a class of strict feedback nonlinear systems. By utilizing a backstepping algorithm, finite-time Lyapunov stable theory, and fuzzy logic control, a novel adaptive practical fixed-time controller is constructed. Fuzzy logic systems are introduced to approximate the unknown items of the system. Theoretical analysis proves that under the presented control strategy, the closed-loop system is practically fixed-time stable, and the tracking error converges to a small neighborhood of the origin within a fixed-time interval, in which the convergence time has no connection with the initial states of the system. In the meantime, all the signals of the closed-loop system are bounded. Finally, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.

Fixed-Time Output Consensus Tracking for High-Order Multi-Agent Systems With Directed Network Topology and Packet Dropout

This paper studies the problem of fixed-time output consensus tracking for high-order multi-agent systems (MASs) with directed network topology with consideration of data packet dropout. First, a predictive compensation based distributed observer is presented to compensate for packet dropout and estimate the leader's states. Next, stability analysis is conducted to prove fixed time convergence of the developed distributed observer. Then, adaptive fixed-time dynamic surface control is designed to counteract mismatched disturbances introduced by observation error, and stabilize the tracking error system within a fixed time, which overcomes explosion of complexity problem and singularity problem. Finally, simulation results are provided to verify the effectiveness and superiority of the consensus tracking strategy proposed. The contribution of this paper is to provide a fixed-time distributed observer design method for high-order MAS under directed graph subject to packet dropout, and a novel fixed-time control strategy which can handle mismatched disturbances and overcome explosion of complexity and singularity problem.

Coordinated Arterial Dilemma Zone Protection Through Dynamic Signal Timing Optimization

Vehicles trapped in dilemma zones on arterial streets are at high risk of rear-end collision or right-angle collision. Most of extant studies focus on dilemma zone protection at isolated signalized intersections. A coordinated arterial dilemma zone protection model at the lane group level, aiming to minimize the weighted combination of safety and efficiency performance indicators, is proposed to improve the safety of arterial traffic by dynamically optimizing the timing parameters of arterial signals. The problem is solved with the rolling optimization technique which enumerates and evaluates feasible green phase durations for all lane groups over each time horizon by embedding the cell transmission model for traffic prediction and the genetic algorithm for signal timing optimization. The effectiveness of the dynamic optimization method is verified by comparing it with actuated control and isolated and coordinated fixed-time control strategies. The results show that the proposed method is able to obtain better safety performance by tending to choose longer cycle lengths and that the proposed method is more suitable for situations where traffic demand changes drastically. With the aid of a traffic surveillance system, the proposed model can be used to provide coordinated dynamic dilemma zone protection for arterial traffic.

Fixed-time control for automatic carrier landing with disturbance

This paper addresses the fixed-time control problem for automatic carrier landing. By transforming a six-degrees-of-freedom fixed-wing aircraft model into the affine form with angle of attack controlled by thrust independently, backstepping technique is able to be adopted as the main control frame. Subsequently, for the purpose of improving convergent performance and success rate for carrier landing, fixed-time control method for a high-order multivariable system is proposed, and it is applied to the automatic carrier landing control system. In order to realize complete fixed-time convergence performance for the closed-loop system, fixed-time disturbance observers are employed in the control structure to efficiently estimate the external disturbances. Moreover, nonlinear fixed-time filters are incorporated to avoid tedious derivative calculation without affecting the fixed-time convergence performance of the system. Finally, the comparative simulation results with other methods demonstrate the effectiveness and superiority of proposed fixed-time control scheme.

Neural-Network-Based Adaptive Singularity-Free Fixed-Time Attitude Tracking Control for Spacecrafts.

In this article, a neural-network-based adaptive fixed-time control scheme is proposed for the attitude tracking of uncertain rigid spacecrafts. A novel singularity-free fixed-time switching function is presented with the directly nonsingular property, and by introducing an auxiliary function to complete the switching function in the controller design process, the potential singularity problem caused by the inverse of the error-related matrix could be avoided. Then, an adaptive neural controller is developed to guarantee that the attitude tracking error and angular velocity error can both converge into the neighborhood of the equilibrium within a fixed time. With the proposed control scheme, no piecewise continuous functions are required any more in the controller design to avoid the singularity, and the fixed-time stability of the entire closed-loop system in the reaching phase and sliding phase is analyzed with a rigorous theoretical proof. Comparative simulations are given to show the effectiveness and superiority of the proposed scheme.

Event-triggered adaptive fixed-time NN control for constrained nonstrict-feedback nonlinear systems with prescribed performance

In this paper, an observer-based adaptive fixed-time control strategy is put forward for uncertain nonstrict-feedback nonlinear systems subject to prescribed performance, full-state constraints and event-triggered mechanism. The difficulty of control design is to use the state observer to estimate unmeasurable states for nonstrict-feedback form in the fixed-time convergence setting. Neural networks are implemented to model the unknown nonlinearities of system. Via introducing fixed-time theory and asymmetric barrier Lyapunov function (ABLF), the fixed-time control problem of the full-state contrained nonlinear system with prescribed performance is solved. Meanwhile, the problem of “explosion of complexity” caused by backstepping technique is averted by utilizing the dynamic surface control technique. Furthermore, an event-triggered controller is devised, which can significantly save communication resources. Moreover, it is concluded that all signals involved are bounded, full-state constraints are not transgressed, tracking error remains within a prescribed domain and Zeno phenomenon is completely circumvented. Finally, the effectiveness of the proposed algorithm is verified by some simulation results.

Model-free prescribed performance fixed-time control for wearable exoskeletons

In this paper, a model-free fixed-time control strategy with prescribed performance is proposed for the wearable exoskeleton angle tracking control. Firstly, an ultra-local model is employed to formulate the plant dynamic relation between control input and output. Then, an intelligent-proportional-derivative controller is designed based on the time delay estimation technique. To improve the tracking precision, a prescribed performance sliding mode controller is designed and a uniform robust exact disturbance observer is employed to compensate the controller. Besides, based on the universal barrier Lyapunov function, the stability is analyzed for the closed-loop system and the prescribed performance is proved. Finally, a 5 degree-of-freedom wearable exoskeleton virtual prototype is developed in SOLIDWORKS and transferred to MATLAB/SimMechanics as the controlled object of visualization simulation, simulation results show the effectiveness of the proposed control strategy.

Fixed-Time Fuzzy Control for a Class of Nonlinear Systems.

Fixed-time tracking control is considered for a class of nonlinear systems in this article. Different from the conventional literature on fixed-time control studies, in this article, the nonlinearities of systems are all completely unknown. Fuzzy-logic systems are utilized to model these unknown nonlinearities. To deal with the fixed-time control under the approximation errors, three steps are taken. First, a new criterion of fixed-time stability is developed; second, a new fixed-time control scheme is proposed, which is different from the existing adaptive design method; and third, to analyze the fixed-time stability of the system, two novel inequalities are established. It shows that the proposed fuzzy control scheme can guarantee system performance in a fixed time, and the upper bound of the settling time only depends on the design parameters.

Distributed Adaptive Fixed-Time Tracking Consensus Control for Multiple Uncertain Nonlinear Strict-Feedback Systems under a Directed Graph

In this brief, we study the distributed adaptive fixed-time tracking consensus control problem for multiple strict-feedback systems with uncertain nonlinearities under a directed graph topology. It is assumed that the leader’s output is time varying and has been accessed by only a small fraction of followers in a group. The distributed fixed-time tracking consensus control is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader and ensure the error convergence time is independent of the systems’ initial state. The function approximation technique using radial basis function neural networks (RBFNNs) is employed to compensate for unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem and graph theory, it is shown that, by using the proposed fixed-time control strategy, all signals in the closed-loop system and the consensus tracking errors are cooperatively semiglobally uniformly bounded and the errors converge to a neighborhood of the origin within a fixed time. Finally, the effectiveness of the proposed control strategy has been proved by rigorous stability analysis and two simulation examples.