Fixed-time Control Research Articles

Adaptive Neural Fixed-Time Control for Uncertain Nonlinear Systems

The article addresses the adaptive fixed-time system control problem subject to unknown nonlinear functions. By employing backstepping technique, fixed-time control, and neural networks (NNs), an adaptive fixed-time control approach is developed. NNs are utilized to package the unknown nonlinearities in the controlled system. The hyperbolic tangent functions are firstly utilized to solve the singular problem, which may exist in the derivation of virtual controller. Meanwhile, the jitter phenomenon is avoided. The developed controller design scheme not only assures the signals’ boundedness within fixed-time interval, but also makes the tracking error converge. Finally, on the aid of the simulation results, the effective of the designed control technique is shown.

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case

Adaptive Fixed-Time Control for Full State-Constrained Nonlinear Systems: Switched-Self-Triggered Case

Fixed-Time Pinning Common Synchronization and Adaptive Synchronization for Delayed Quaternion-Valued Neural Networks.

This article focuses on the fixed-time pinning common synchronization and adaptive synchronization for quaternion-valued neural networks with time-varying delays. First, to reduce transmission burdens and limit convergence time, a pinning controller which only controls partial nodes directly rather than the entire nodes is proposed based on fixed-time control theory. Then, by Lyapunov function approach and some inequalities techniques, fixed-time common synchronization criterion is established. Second, further to realize the self-regulation function of pinning controller, an adaptive pinning controller which can adjust automatically the control gains is developed, the desired fixed-time adaptive synchronization is achieved for the considered system, and the corresponding criterion is also derived. Finally, the availability of these results is tested by simulation example.

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.

Distributed Fixed-Time Leader-Following Consensus for Multi-Agent Systems: An Event-Triggered Mechanism

In this work, a fixed-time leader-following event-triggered (ET) consensus problem for multi-agent systems (MASs) with external disturbances is investigated. A distributed observer is developed to achieve the estimated state of the leader. By means of the observation information, the consensus error system for multi-agents is reformulated into a tracking error system, wherein individual follower agent aims to track the leader agent. Building upon Lyapunov technology and fixed-time stability theory, a new ET protocol is introduced to mitigate communication wastes. Notably, the proposed controller incorporates a strong robust fixed-time control form with lower complexity, and a reliable dynamic triggering condition also ensures the excellent performance of the system. Rigorous demonstrations underscore the stability and robustness of the ET method, while guaranteeing the avoidance of Zeno behavior. Finally, several numerical simulations are provided to underscore the efficacy of the proposed protocols.

Fixed-time tracking control of manipulators based on non-singular fast terminal sliding surface

As for the problem of trajectory tracking of a multi-joint serial manipulator, a novel fixed-time control scheme is proposed based on non-singular fast terminal sliding mode control. By employing a fast terminal sliding mode surface, we solve the singularity problem existed in traditional terminal sliding mode surface. In the meantime, in order to improve the rapidity of the system, the fixed-time control is incorporated with the fast terminal sliding mode surface control. Theoretical analysis proves that the proposed control scheme guarantees that better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states. In addition, a reaching law with the exponential approach characteristic is added to the control law, which effectively reduces the chattering phenomenon in the controller design. Finally, the effectiveness and feasibility of the designed controller are verified through a 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.

A generalized super-twisting algorithm-based adaptive fixed-time controller for spacecraft pose tracking

Abstract A generalized super-twisting second-order sliding mode adaptive fixed-time control law, which is used for spacecraft pose tracking in the presence of internal and external uncertainties, is proposed. Lie group SE(3) (for special Euclidean group), which is the configuration space for rigid body motion, is used for modeling the six-degrees-of-freedom dynamics of spacecraft. A fixed-time sliding mode surface is proposed and applied to design an generalized super-twisting sliding mode control law. A novel dual-layer adaption law for the controller is proposed to the ensure the gains varying rapidly with the disturbance. The adaptive second-order sliding mode controller guarantees a uniform exact convergence for the closed-loop tracking control system with less energy consumption. Numerical simulations are performed to demonstrate the excellent performances of the control law.

A new fixed-time terminal sliding mode control for second-order nonlinear systems

In this paper, the fixed-time control for a class of second-order nonlinear systems with matched disturbance is addressed by using terminal sliding mode control technique. To improve the control performance of traditional fixed-time control method, a new fixed-time stability theorem is constructed by introducing a simple linear term, and theoretical analysis shows that the proposed control method provides faster convergence speed and more accurate estimate of the upper bound of settling time. Moreover, the practical fixed-time stability is also discussed in details. Based on the proposed fixed-time stability theorem, a fixed-time terminal sliding mode controller for a class of second-order nonlinear system is designed to obtain a bounded settling time independently of the initial conditions of the system. Simulations are carried out to verify the feasibility of the proposed control method.

Output-constrained fixed-time coordinated control for multi-agent systems with event-triggered and delayed communication

In this study, we propose a fixed-time coordinated controller for high-order multi-agent systems dealing with output constraints and switching digraphs while considering event-triggered and delayed communication. To tackle the scenario where only a subset of agents have direct access to the leader, a novel event-triggered fixed-time observer is first devised. This observer effectively estimates the state of the leader, considering the influence of communication delays. Subsequently, a neural network-based fixed-time controller is formulated under output constraints, utilizing the estimated leader commands to achieve the desired control objectives. Finally, practical experiments are conducted using omni-mecanum-wheeled robots to demonstrate the practical feasibility and superior performance of the theoretical findings. This study contributes significantly by tackling the challenging problem of output-constrained fixed-time coordinated control in event-triggered and delayed communication within switching digraphs. This area has yet to be previously explored.

Fixed-time [formula omitted] tracking control of unmanned underwater vehicles with disturbance rejection via Port-Hamiltonian framework

The fixed-time tracking control schemes of unmanned underwater vehicles (UUVs) are investigated in body-fixed coordinates frame based on Port-Hamiltonian (PH) model with external disturbances. The novel locally and globally fixed-time control laws via the interconnection and damping assignment passivity-based control (IDA-PBC) are designed for trajectory tracking in UUVs. The virtual desired equilibria consisted of the tracking error and the desired trajectory are established by the matching conditions. Moreover, the fixed-time stabilization of the UUV induced of variable parameter matrixes is analyzed. Compared with the traditional IDA-PBC controller, the UUV is guaranteed to achieve the reference trajectory within a fixed time regardless of initial conditions. In the presence of external disturbances, the H∞ laws are incorporated in the fixed-time control for the UUV, which can ensure faster trajectory tracking and strong anti-disturbance. Finally, the simulation results demonstrate the effectiveness of the main schemes.

Fixed-Time Control and Estimation of Discontinuous Fuzzy Neural Networks: Novel Lyapunov Method of Fixed-Time Stability.

This article considers the fixed-time stability (FXTS) issue for discontinuous system described by differential equation (DE) with time-varying parameters. Using the tool of differential inclusion (DI), several improved FXTS criteria and estimation formulas of settling time (SET) are derived by employing a relaxed Lyapunov method. The special novelty of the developed Lyapunov method is that the derivative of Lyapunov function possesses indefiniteness. As an important application, the established FXTS theorems are utilized to deal with fixed-time (FXT) synchronization issue for fuzzy neural networks (FNNs) possessing state discontinuity, where the fuzzy operation is used in the synaptic law computing, and one typical time-varying switching control protocol is designed. Moreover, a series of estimations of SET for FXT synchronization are given out. Finally, the simulation examples are present to substantiate the validity of the obtained results.

Fixed-time Sliding Mode-based Adaptive Path Tracking Control of Maize Plant Protection Robot via Extreme Learning Machine

During the maize middle and late periods, the soil between rows is soft and also involved with weeds and straw. When the plant protection robot (PPR) moves on the soil, there exists uncertain shear perturbation because of the shear action and pressure subsidence, leading to the difficulty of the controller design. In this work, we propose an adaptive path tracking control (PTC) considering disturbances for the PPR. The disturbance of PRR in contact with soil is first revealed according to Bekker pressure subsidence and Janosi shear models, through which the plant model of PPR system is established. Then, we propose an adaptive fixed-time sliding mode (AFTSM)-based PTC to achieve excellent path tracking performance, where an extreme learning machine (ELM) estimator is developed, releasing the requirement for bound derivations in the control design. Using the fixed-time control and the ELM techniques in the proposed control, a remarkable control performance is well ensured, i.e., high-accuracy tracking, fast convergence, and excellent robustness. Experimental studies on a PPR are executed for demonstrating the validity and good performance of the designed controller.

A New Event-Triggered Adaptive Fixed-Time Control Design for Uncertain Nonlinear Systems.

This article investigates the problem of dynamic memory event-triggered (DMET) fixed-time tracking control within time-varying asymmetric constraints for nonaffine nonstrict-feedback uncertain nonlinear systems with unmodeled dynamics and unknown disturbances. The existing dynamic event-triggered control methods cannot handle the nonlinear systems with unmodeled dynamics and nonaffine inputs, which greatly limits the applicability of the strategy. To this end, a novel DMET adaptive fuzzy fixed-time control protocol is constructed based on the idea of command filtered backstepping, in which a new dynamic signal function is established to deal with the unmodeled dynamics and an improved DMET mechanism (DMETM) is designed to solve the problem of nonaffine inputs. It is proved that the newly DMET control strategy ensures the tracking error converges to an arbitrarily small compact set in a fixed time and all the signals of the closed-loop systems are bounded. The effectiveness of the proposed approach is demonstrated by two simulation examples.

Coaxial Tilt-Rotor UAV: Fixed-time Control, Mixer, and Flight Test

Coaxial Tilt-Rotor UAV: Fixed-time Control, Mixer, and Flight Test

Distributed fixed-time control strategy for islanded microgrids considering perturbations and switching topologies

Distributed fixed-time control strategy for islanded microgrids considering perturbations and switching topologies

Nonlinear system controlled using novel adaptive fixed-time SMC

<abstract><p>This work introduces a novel adaptive fixed-time control strategy for nonlinear systems subject to external disturbances. The focus pertains to the introduction of the fixed-time terminal sliding mode control (FxSMC) technique. The proposed scheme exhibits rapid convergence, chatter-free and smooth control inputs, and stability within a fixed time. The utilization of an adaptive methodology in combination with the FxSMC yields the proposed strategy. This approach is employed to address the dynamic system in the presence of external disturbances. The results obtained from the Lyapunov analysis will provide insights into the stability of the closed-loop system in a fixed time. In the end, the simulation results are presented in order to assess and demonstrate the effectiveness of the methodology.</p></abstract>

Fixed-Time Control of a Novel Thrust-Vectoring Aerial Manipulator via High-Order Fully Actuated System Approach

Fixed-Time Control of a Novel Thrust-Vectoring Aerial Manipulator via High-Order Fully Actuated System Approach

Model-free scheme using time delay estimation with fixed-time FSMC for the nonlinear robot dynamics

<abstract><p>This paper presents a scheme of time-delay estimation (TDE) for unknown nonlinear robotic systems with uncertainty and external disturbances that utilizes fractional-order fixed-time sliding mode control (TDEFxFSMC). First, a detailed explanation and design concept of fractional-order fixed-time sliding mode control (FxFSMC) are provided. High performance tracking positions, non-chatter control inputs, and nonsingular fixed-time control are all realized with the FxSMC method. The proposed approach performs better and obtains superior performance when FxSMC is paired with fractional-order control. Furthermore, a TDE scheme is included in the suggested strategy to estimate the unknown nonlinear dynamics. Afterward, the suggested system's capacity to reach stability in fixed time is determined by using Lyapunov analyses. By showing the outcomes of the proposed technique applied to nonlinear robot dynamics, the efficacy of the recommended method is assessed, illustrated, and compared with the existing control scheme.</p></abstract>

Distributed fixed-time control strategy for islanded microgrids considering perturbations and switching topologies

Distributed fixed-time control strategy for islanded microgrids considering perturbations and switching topologies