Adaptive Fixed-Time Research Articles

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization (FTS) of delayed memristor-based neural networks (MNNs) with discontinuous activations is studied in this paper. Both continuous and discontinuous activations are considered for MNNs. And the mixed delays which are closer to reality are taken into the system. Besides, two kinds of control schemes are proposed, including feedback and adaptive control strategies. Based on some lemmas, mathematical inequalities and the designed controllers, a few synchronization criteria are acquired. Moreover, the upper bound of settling time (ST) which is independent of the initial values is given. Finally, the feasibility of our theory is attested by simulation examples.

Distributed Adaptive Fixed-Time Robust Platoon Control for Fully Heterogeneous Vehicles

This article focuses on the distributed adaptive fixed-time platoon tracking problem for third-order fully heterogeneous nonlinear vehicles. The modified dynamics of each vehicle are constructed, and a practically fixed-time criterion is set up. Moreover, the singularity problem in the fixed-time and finite-time control is addressed well by designing new virtual signals and exploiting the inequality technique and power transformation scheme instead of the approximation method. The distributed nonlinear fixed-time tracking protocol is constructed by virtue of the recursive algorithm, and the design process is simplified by a tracking differentiator. In particular, the upper bound of the settling time has nothing to do with initial conditions. Further, the disturbances are tackled via robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control theory. Finally, simulation tests are contained to illustrate the performance of the proposed protocols.

Fixed-Time Prescribed Performance Adaptive Fixed-Time Sliding Mode Control for Vehicular Platoons With Actuator Saturation

This paper investigates a prescribed tracking performance vehicular platoon control problem with actuator saturation, dynamics uncertainties, and unknown disturbances. First, a novel Gaussian error function (GEF)-based saturation function is introduced to approximate nonsmooth actuator saturation of each vehicle in a smooth way. Then, a fixed-time performance function (FPF) is proposed. Subsequently, an adaptive fixed-time sliding mode control scheme is developed based on the GEF and the FPF, which guarantees all signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in fixed time. Meanwhile, string stability and traffic stability are also guaranteed. Finally, the effectiveness of the proposed algorithm is verified through numerical simulations.

Adaptive fixed-time quantized fault-tolerant attitude control for hypersonic reentry vehicle

This paper focuses on the adaptive fixed-time quantized fault-tolerant attitude tracking problem for hypersonic reentry vehicle (HRV). Due to the strong nonlinearity, tight coupling, uncertain characteristics and potential actuator faults, the attitude control of HRV poses a considerable challenge. By resorting to feedback linearization technique, the inherently nonlinear attitude model of HRV is decoupled into a linear control-oriented model, where the actuator malfunction, quantization nonlinearities and multiple disturbances are incorporated into the lumped disturbance. Then a fixed-time neural network disturbance observer is designed to estimate the lumped disturbance, with the practical fixed-time stability of the observation error ensured independent of initial conditions. Subsequently, by using a hyperbolic-tangent-like function, a novel paradigm is proposed for achieving adaptive fixed-time convergence and based on the paradigm, an adaptive fixed-time nonsingular sliding mode controller is proposed. The main features of the controller include: 1) The controller gain is adjusted adaptively following the current magnitude of the output variable to obtain high transient performance. 2) The tracking error can converge to zero within a fixed time even in the case of actuator faults and signal quantization. 3) A hysteretic quantizer is implemented in the attitude control loop such that the on-board communication load can be significantly reduced. Moreover, the proposed fault-tolerant control scheme design is non-recursive, rendering the controller structure simple. Ultimately, the effectiveness of the proposed method is demonstrated by numerical simulations.

Distributed Adaptive Fixed-Time Fault-Tolerant Control for Multiple 6-DOF UAVs With Full-State Constraints Guarantee

In contrast with most existing results concerning unmanned aerial vehicles (UAVs) wherein material points or only attitude/longitudinal dynamics are considered, this article proposes a distributed fixed-time fault-tolerant control methodology for networked fixed-wing UAVs whose dynamics are six-degree-of-freedom with twelf-state-variables subject to actuator faults and full-state constraints. More precisely, state transformations with the scaling function are devised to keep the involved velocity and attitude within their corresponding constraints. The fixed-time property is obtained in the sense of guaranteeing that the settling time is lower bounded by a positive constant, which is independent of initial states. The actuator faults as well as the network induced errors are handled via the bound estimation approach and well-defined smooth functions. By strict Lyapunov arguments, all closed-loop signals are proved to be semiglobally uniformly ultimately bounded, and the tracking errors of velocity and attitude converge to the residual sets around origin within a fixed time.

Neural Adaptive Fixed-time Consensus Tracking for Multiple Euler-Lagrange Systems with Quantized Inputs

Neural Adaptive Fixed-time Consensus Tracking for Multiple Euler-Lagrange Systems with Quantized Inputs

Event-Based Adaptive Fixed-Time Fuzzy Control for Active Vehicle Suspension Systems With Time-Varying Displacement Constraint

This article addresses the fixed-time control problem for the constrained quarter active vehicle suspension systems (AVSSs) via an event-triggered based adaptive fuzzy fixed-time control method. The benefit of the usage of the time-varying barrier Lyapunov function is to avoid the violation of the time-varying displacement constraint so that the stability and safety of AVSSs can be guaranteed. The relative threshold based event-triggered controller is devised so as to reduce the communication burden from the controller to the actuator. In the light of fixed time theory, it is proved that both the stability and tracking performance of the closed-loop system can be obtained in fixed time. The fixed-time based event-triggered control strategy is independent of initial states of AVSSs in comparison with the existing finite-time results. Some simulation results and comparisons on a quarter-car AVSS indicate better performance in terms of feasible fixed-time control and exact trajectory tracking.

Antisaturation Adaptive Fixed-Time Sliding Mode Controller Design to Achieve Faster Convergence Rate and Its Application

This brief proposes an antisaturation adaptive fixed-time sliding mode controller for a class of second-order nonlinear systems with the saturation constraint. Based on the developed fixed-time stable system, a novel nonsingular fast fixed-time sliding mode surface is designed to circumvent the singularity and acquire a faster convergence rate. To avoid choosing inappropriate control gain, an adaptive mechanism is designed. Furthermore, an auxiliary compensation system is developed to solve the saturation constraint. It is rigorously proved that the system is practical fixed-time stable and the tracking error will fast converge to bounded regions within a fixed time. Finally, the obtained results are employed to realize the quadrotor attitude stabilization, and superior control performance can be illustrated via simulations and experiments.

Adaptive Fixed-Time Attitude Tracking Control of Spacecraft With Uncertainty-Rejection Capability

For high-resolution imaging implementations, the spacecraft attitude tracking control accuracy is crucial to determining the imaging quality. This investigation addresses the attitude tracking issue of imaging spacecraft subject to system uncertainties (unavailable inertia tensor, unexpected disturbances, and actuator faults). An adaptive sliding mode control (SMC) strategy is proposed to guarantee practical fixed-time closed-loop stability even in the presence of system uncertainties. Unlike existing methodologies, the sliding mode surface is developed to satisfy a novel sufficient condition of fixed-time stability. The sliding manifold design also circumvents the unwinding phenomenon arising in quaternion representations. Particularly, this controller is developed to generate a smooth control profile by using a new parameter update law. Rigorous Lyapunov analyses are further employed to ensure the fixed-time closed-loop stability irrespective of the system initial states. Finally, numerical examples are performed to demonstrate the feasibility and highlight the inherent features of the derived control law.

Event-Triggered Fuzzy Adaptive Fixed-Time Tracking Control for Nonlinear Systems.

In this article, the problem of event-based adaptive fuzzy fixed-time tracking control for a class of uncertain nonlinear systems with unknown virtual control coefficients (UVCCs) is considered. The unknown nonlinear functions of the considered systems are approximated by fuzzy-logic systems (FLSs). Moreover, a novel Lyapunov function is designed to remove the requirement of lower bounds of the UVCC in control laws. In addition, an event-triggered control method is developed by using the backstepping technique to save the network resources. Through theoretical analysis, the event-based fixed-time controller was proposed, which can guarantee that all signals of the controlled system are bounded and the tracking error can converge to a small neighborhood of the origin in a fixed time. Meanwhile, the convergence time is independent of the initial states. Two numerical examples are presented to demonstrate the effectiveness of the proposed approach.

Adaptive neural network fixed-time fault-tolerant control of an uncertain nonlinear system with full-state constraints

In this paper, a fixed-time fault-tolerant controller is designed for the tracking control problem of an uncertain nonlinear system under full-state constraints, uncertainties and actuator faults. Since the controller is designed in the framework of backstepping method, to handle the “explosion of complexity” problem, an adaptive fixed-time filter is constructed. It ensures that the filter error converges to an arbitrarily small vicinity of zero in fixed time. A state transformation function is applied to solve full-state constraints. Radial basis function neural network (RBFNN) and adaptive technique are respectively used for dealing with uncertainties and actuator faults. Based on Lyapunov theory, the closed-loop system is proved to be bounded in fixed time and all states are kept in their constraints. At the end, the effectiveness of the designed control strategy is verified by numerical simulation and an application of a permanent magnet synchronous motor (PMSM) system.

Adaptive Fixed-Time Neural Networks Control for Pure-Feedback Non-Affine Nonlinear Systems with State Constraints.

A new fixed-time adaptive neural network control strategy is designed for pure-feedback non-affine nonlinear systems with state constraints according to the feedback signal of the error system. Based on the adaptive backstepping technology, the Lyapunov function is designed for each subsystem. The neural network is used to identify the unknown parameters of the system in a fixed-time, and the designed control strategy makes the output signal of the system track the expected signal in a fixed-time. Through the stability analysis, it is proved that the tracking error converges in a fixed-time, and the design of the upper bound of the setting time of the error system only needs to modify the parameters and adaptive law of the controlled system controller, which does not depend on the initial conditions.

Neural Adaptive Fixed-Time Attitude Stabilization and Vibration Suppression of Flexible Spacecraft

This paper proposes a novel neural adaptive fixed-time control approach for the attitude stabilization and vibration suppression of flexible spacecraft. First, the neural network (NN) was introduced to identify the lumped unknown term involving uncertain inertia, external disturbance, torque saturation, and elastic vibrations. Then, the proposed controller was synthesized by embedding the NN compensation into the fixed-time backstepping control framework. Lyapunov analysis showed that the proposed controller guaranteed the stabilization of attitude and angular velocity to the adjustable small neighborhoods of zero in fixed time. The proposed controller is not only robust against uncertain inertia and external disturbance, but also insensitive to elastic vibrations of the flexible appendages. At last, the excellent stabilization performance and good vibration suppression capability of the proposed control approach were verified through simulations and detailed comparisons.

Event-Triggered Fuzzy Adaptive Fixed-Time Output-Feedback Control for Nonlinear Systems With Multiple Objective Constraints

Event-Triggered Fuzzy Adaptive Fixed-Time Output-Feedback Control for Nonlinear Systems With Multiple Objective Constraints

Adaptive Fixed-Time Control for Attitude Consensus of Disturbed Multi-Spacecraft Systems With Directed Topologies

In this paper, the problem of leaderless fixed-time attitude consensus is studied for rigid spacecraft systems, where each spacecraft is subject to disturbance and the communication graph is directed. Based on the backstepping technique, a distributed control protocol is proposed to solve fixed-time attitude consensus problem. Then, to remove the dependence of control gains on the global information, an adaptive fixed-time control for attitude consensus is presented. Unlike the most existing consensus protocols, the parameters in the controllers for the spacecraft are chosen independently and can be different from each other. Finally, the performances of the proposed control protocol is illustrated through a numerical simulation.

Tracking Design of an Uncertain Autonomous Underwater Vehicle with Input Saturations by Adaptive Regression Matrix-Based Fixed-Time Control.

In this study, a simplified model of an autonomous underwater vehicle (AUV) with input saturation based on kinematic and dynamic equations was built. Subsequently, a simplified model of the AUV was used to represent its main dynamic features. In terms of trajectory tracking, only the system’s structure (i.e., the regression matrix, which is flexible and non-unique) from the nominal model of the transformed system was required to design the proposed adaptive regression matrix-based fixed-time controller (ARM-FTC). A nonlinear auxiliary sliding surface was contained in the control design to shape the system’s frequency response. When the operating point was in the neighborhood of the zero auxiliary sliding surface, nonlinear filtering gains were increased to accelerate its tracking ability. Furthermore, the skew-symmetric property condition of the time-derivative of the inertia matrix and the Coriolis and centrifugal force matrices was not necessitated for the controller design. Under an appropriate condition for lumped uncertainties, the fixed-time convergence of the auxiliary sliding surface and the corresponding tracking error is guaranteed to go to zero by the Lyapunov stability theory. Finally, a comparative study was conducted through simulations for the AUV with external disturbance and input saturation among the known parameters, learning parameters reflecting a regression matrix, and another asymptotical robust tracking control scheme. The results validate the fast tracking ability of a desired time-varying trajectory of the proposed control scheme.

Adaptive Fixed-Time Fault-Tolerant Tracking Control and Its Application for Robot Manipulators

This article studies an adaptive fault-tolerant approach with a fixed-time sliding mode for trajectory tracking of uncertain robot manipulators with actuator effectiveness faults. An equivalent system with an adaptive technique is developed to remove the effects of uncertainties on tracking performance, whereas an appropriate system transformation is accomplished to eliminate the effects of the actuator effectiveness faults. A significant feature of this study is that the fixed-time stability is guaranteed theoretically and practically in the presence of uncertainties and actuator effectiveness faults. Moreover, the appearing advantages are that the proposed approach yields an improved tracking performance without utilizing the overestimated control gain and prior knowledge of a robot and, then, overcomes the singularity and algebraic loop problems completely. The effectiveness of the proposed approach for tracking systems is accomplished on simulation and experimental results from a qualitative and quantitative analysis.

Adaptive Fixed-Time Neural Network Tracking Control of Nonlinear Interconnected Systems.

In this article, a novel adaptive fixed-time neural network tracking control scheme for nonlinear interconnected systems is proposed. An adaptive backstepping technique is used to address unknown system uncertainties in the fixed-time settings. Neural networks are used to identify the unknown uncertainties. The study shows that, under the proposed control scheme, each state in the system can converge into small regions near zero with fixed-time convergence time via Lyapunov stability analysis. Finally, the simulation example is presented to demonstrate the effectiveness of the proposed approach. A step-by-step procedure for engineers in industry process applications is proposed.

Adaptive Fixed-Time Tracking Consensus Control for Multiagent Nonlinear Pure-Feedback Systems with Performance Constraints

This paper investigates adaptive fixed-time tracking consensus control problems for multiagent nonlinear pure-feedback systems with performance constraints. Compared with existing results of first/second/high-order multiple agent systems, the studied systems have more complex nonlinear dynamics with each agent being modeled as a high-order pure-feedback form. The mean value theorem is introduced to address the problem of nonaffine structure in nonlinear pure-feedback systems. Meanwhile, radial basis function neural networks (RBFNNs) are employed to approximate unknown functions. Furthermore, a constraint variable is used to guarantee that all local tracking errors are within the prescribed boundaries. It is shown that, by utilizing the proposed consensus control protocol, each tracking consensus error can converge into a neighborhood around zero within designed fixed time, the tracking consensus performance can be ensured during the whole process, and all signals in the investigated systems are bounded. Finally, two simulations are performed and the results demonstrate the effectiveness of the proposed control strategy.

Adaptive Fixed-Time Trajectory Tracking Control for Underactuated Hovercraft with Prescribed Performance in the Presence of Model Uncertainties

This paper develops an adaptive fixed-time trajectory tracking controller of an underactuated hovercraft with a prescribed performance in the presence of model uncertainties and unknown time-varying environment disturbances. It is the first time that the proposed method is applied to the motion control of the hovercraft. To begin with, based on the hovercraft's four degrees of freedom (DOF) model, the virtual control laws are designed using an error transforming function and the fixed-time stability theory to guarantee that the position tracking errors are constrained within the prescribed convergence rates and minimum overshoot. In addition, by combining the Lyapunov direct method and the adaptive radial basis function neural network (ARBFNN), the actual control laws are designed to ensure that the velocity tracking errors converge to a small region containing zero while handling model uncertainties and external disturbances effectively. Finally, all tracking errors of the closed-loop system are uniformly ultimately bounded and fixed-time convergent. Results from a comparative simulation study verify the effectiveness and advantage of the proposed method.