Fixed-time Control Method Research Articles

Adaptive Fuzzy Fixed-Time Control for Uncertain Nonlinear Systems with Mismatched Disturbances

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases.

A Novel Faster Fixed-Time Adaptive Control for Robotic Systems With Input Saturation

In this paper, an adaptive anti-saturation fixed-time control method with a faster convergence rate is studied for uncertain robotic systems. Firstly, a new segmental sliding variable is constructed to solve the singularity problem brought by the terminal sliding mode control (TSMC) and achieve a faster convergence rate. Secondly, to approximate and compensate for the model uncertainty and the viscous friction parameter, an adaptive neural network (ANN) is employed. Then, a novel auxiliary system is constructed to mitigate the effects of input saturation. Based on this, a novel non-singular TSMC algorithm integrated with the ANN and the auxiliary system is designed, so that the trajectory tracking errors of the robotic system can converge within a faster fixed time with actuator saturation. Finally, the superiority and practicability of the present method are verified by comparative experiments.

Practical fixed-time neural control for MIMO non-strict feedback nonlinear systems: an adaptive neural network approach

ABSTRACT This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method.

Unified Fuzzy Control of High-Order Nonlinear Systems With Multitype State Constraints.

This article presents a unified adaptive fuzzy control approach for high-order nonlinear systems (HONSs) with multitype state constraints. Existing methods always require the upper and lower constraint boundaries are strictly positive and negative functions (or constants), respectively, which is often inconsistent with the actual constraints. In this article, "multitype state constraint" means that the upper and lower constraint boundaries include multiple types, such as both being strictly positive (or negative), sometime be positive or negative, and so on (cases ①-⑥). By designing a unified mapping function (UMF), the multitype state constraints are processed under removal the feasibility conditions (FCs). Furthermore, a technical design makes the proposed method also applicable to unconstrained HONSs without changing the control structure. By means of a fuzzy-logic system (FLS) and fixed-time stability theory (FTST), the proposed algorithm can ensure that the tracking error converges to a zero-centered neighborhood within a fixed time, and the singularity which often appears in the existing fixed-time control (FTC) methods of HONSs is effectively avoided. Simulation results demonstrate the scheme developed.

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 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.

Neural-Network-Based Adaptive Fixed-Time Control for a 2-DOF Helicopter System With Input Quantization and Output Constraints.

This study proposes a neural-network (NN)-based adaptive fixed-time control method for a two-degree-of-freedom (2-DOF) nonlinear helicopter system with input quantization and output constraints. First, a hysteresis quantizer is employed to mitigate chattering during signal quantization, and adaptive variables are utilized to eliminate errors in the quantization process. Subsequently, the system uncertainties are approximated using a radial basis function NN. Simultaneously, a logarithmic barrier Lyapunov function (BLF) is constructed to prevent the system outputs from violating the constraint boundaries. Based on a rigorous Lyapunov stability analysis and the fixed-time stability criterion, the signals of the closed-loop system are proven to be bounded within a fixed time. Finally, numerical simulations and experiments verified the feasibility of the proposed method.

Ground Experiment of Safe Proximity Control for Complex-Shaped Spacecraft

The safe proximity to spacecraft is a prerequisite for most on-orbit service missions. However, performing proximity operations on orbit is dangerous and high-cost. Therefore, pre-verification of the proximity control algorithm through ground experiments can determine the reliability and promote the success of actual on-orbit missions. This paper constructs an air floating experiment system and a guidance algorithm for the safe proximity to a complex-shaped tumbling spacecraft. The proposed control algorithm consists of two parts: one part is an improved Gaussian mixture model, with which a novel artificial potential function is designed to accurately describe the complex shape of the target and provide 3D collision avoidance constraints; the other part is to use the fixed time control method to ensure that the service spacecraft can reach the desired position within a fixed time. The numerical simulation and experiments are implemented to verify the effectiveness of the proposed algorithm.

Fully Distributed Fixed-Time Control of Cross-Domain Swarm Robots for Non-Cooperative Target Tracking

This brief focuses on solving the tracking problem of swarm robots with a non-cooperative target, where two core issues namely non-cooperative target and cross-domain collaboration are both taken into account. In order to solve the former issue, the trajectory of the non-cooperative target is constructed by a network model. This is more superior than the target system matrix observer-based method that adopted extensively in literature, as the latter one will cause the self-loop problem. Besides, the target information is no longer required in solving the regulation equation. Furthermore, a fixed-time cross-domain control method merely relying on outputs of a robot and its neighbours is proposed. Namely, the network-based fixed-time control method proposed in this brief is fully distributed without self-loop and requirement of the non-cooperative target’s system matrix. With the proposed controller, the cross-domain robots are able to successfully track a non-cooperative target within a fixed time, which is also verified by some numerical simulations.

Prescribed-time containment control of high-order nonlinear multi-agent systems based on distributed observer

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method.

IBLF-Based Fixed-Time Fault-Tolerant Control for Fixed-Wing UAV With Guaranteed Time-Varying State Constraints

This paper proposes a novel adaptive fixed-time fault-tolerant control method for the fixed-wing unmanned aerial vehicle (UAV) subject to asymmetric time-varying full state constraints. The UAV nonlinear dynamics of six-degree-of-freedom (6-DOF) with twelve-state-variables is considered in this article, rather than only longitudinal/lateral or attitude dynamics in most existing results. A novel Integral Barrier Lyapunov Function (IBLF) is applied for the first time to solve the control problem of the UAV with the asymmetric time-varying full state constraints, which reduces the conservativeness of the conventional IBLF-based method. Furthermore, a continuous switching function is introduced to solve the singularity problem which typically appears in the fixed-time control methods when tracking errors approach to zero. It is rigorously proved that all the states are forced in the asymmetric time-varying bounds and the tracking errors of velocity and attitude converge to a residual set around origin within fixed time. Finally, the simulation results are given to validate the effectiveness of the proposed scheme.

Adaptive Fuzzy Fixed-Time Tracking Control for Nonlinear Systems With Time-Varying Full-State Constraints and Actuator Hysteresis

This paper investigates the problem of adaptive fuzzy fixed-time control for a class of nonlinear systems subject to time-varying full-state constraints and actuator hysteresis. The fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear dynamics. A tan-type nonlinear mapping (NM) approach is used to solve the control problem of nonlinear systems with full-state constraints. The actuator hysteresis nonlinearities are expressed by differential equations with unknown parameters. And combining the adaptive backstepping control technique with the fixed-time stability theory, an adaptive fuzzy fixed-time control method is presented. The proposed control scheme can guarantee the boundedness of all signals in the closed-loop system without violating the state constraints, and the output can accurately track the desired signals in a fixed time. Finally, the feasibility of the presented algorithm is verified by simulation results.

Fixed-Time Anti-Synchronization of Unified Chaotic Systems via Adaptive Backstepping Approach

In this brief, the fixed-time anti-synchronization control problem is considered for two unified chaotic systems with uncertain parameters. In the process of controller design, adaptive technique is applied to approximate the uncertain constants occurred in the original systems and the piecewise functional approach is introduced to overcome the singularity problem appeared in the virtual control signals. Based on the Lyapunov theory and fixed-time control method, an adaptive fixed-time control scheme is designed. The designed controller achieves the anti-synchronization of two unified chaotic systems in a fixed-time. Theoretical analysis and simulation results demonstrate that the effectiveness of the control method.

Robust fixed-time tracking control for underactuated AUVs based on fixed-time disturbance observer

This paper investigates the fixed-time trajectory tracking control problem of underactuated autonomous underwater vehicles (AUVs) subject to external disturbances. The backstepping control technique and fixed-time control method are integrated to guarantee that the trajectory of the AUV converges to the reference trajectory within a fixed-time. A continuous fixed-time disturbance observer is developed to estimate the unknown external disturbances. A nonlinear first-order filter is applied to avoid the adverse effect of “explosion of complexity” inherent in the conventional backstepping. Theoretical analyses demonstrate that under the fixed-time backstepping controller, the tracking errors of the AUV will converge towards a residual set in fixed time. Simulation results illustrate the effectiveness and superiority of the proposed control method.

Fixed-time neural network control of a robotic manipulator with input deadzone

In this paper, a fixed-time control method is proposed for an uncertain robotic system with actuator saturation and constraints that occur a period of time after the system operation. A model-based control and a neural network-based learning approach are proposed under the framework of fixed-time convergence, respectively. We use neural networks to handle the uncertainty, and design an adaptive law driven by approximation errors to compensate the input deadzone. In addition, a new structure of stabilizing function combining with an error shifting function is introduced to demonstrate the robotic system stability and the boundedness of all error signals. It is proved that all the tracking errors converge into the compact sets near zero in fixed-time according to the Lyapunov stability theory. Simulations on a two-joint robot manipulator and experiments on a six-joint robot manipulator verified the effectiveness of the proposed fixed-time control algorithm.

New results on adaptive fixed-time control for convex-delayed neural networks

This paper studies the adaptive fixed-time synchronization issue for convex-delayed neural networks. First, the convex delay is introduced to address the state delay of neural networks in order to reflect the impacts of multiple delay components such as input transition time and switching communication. Then, a new fixed-time control method is presented to adaptively determine multi-control gains with a unified update law. Afterward, some sufficient criteria are figured out by using Lyapunov stability theorem to ensure that the delayed neural networks are fixed-timely stable. Finally, simulated examples are adopted to validate our theoretical results.

Dynamic capacity estimation of mixed traffic flows with application in adaptive traffic signal control

Intersection control plays a vital role in influencing transportation efficiency inside urban areas. Connected and Automated Vehicle (CAV) technology enables frequent traffic information sharing through vehicular networks, which emerges as a promising way to reduce vehicle traveling time and improve intersection capacity. Meanwhile, with the gradual deployment of CAVs, the traditional traffic flow consisting of human driven vehicles will evolve into a mixed traffic flow composed of traffic participants with differing intelligence capabilities. Considering the evolution towards the mixed traffic environment, we propose a dynamic capacity-aware traffic signal control method: max-pressure for mixed traffic flow (MPMF) traffic signal controller. Firstly, the lane capacity is modeled and approximated based on the saturation flow rate in mixed traffic flow considering the penetration rate of CAVs. Then the dynamic capacity is involved in calculating pressure in the max-pressure method to indicate the importance of a path in mixed traffic flow. A modification strategy for the max-pressure input value is also proposed. An isolated intersection scenario was simulated first to assess the proposed method locally. A multi-intersection network experiment was also conducted to verify the network-level performance of the proposed MPMF method. Comparative results between the proposed MPMF method, the classic max-pressure control, and the existing fixed time control method demonstrate that the MPMF can effectively improve the performance of intersections and be suitable for the multi-intersection road network.

Novel fast fixed-time sliding mode trajectory tracking control for manipulator

This paper studies the issue of high-precision trajectory tracking control for manipulator systems with uncertainty disturbances and develops a fast fixed-time control scheme. First, a new type of (FTSM) surface is constructed by combining inverse trigonometric functions, regardless of the size of the system state, which can obtain a faster convergence velocity and high accuracy. The stabilization time of this sliding mode (SM) surface is independent of the initial state. Subsequently, on this basis, an adaptive fixed-time control method is constructed by combining adaptive techniques through the new fixed-time stability lemma proposed in this paper, under which the system's SM variables and tracking errors are guaranteed to reach the region near the equilibrium point at a fixed time while the adaptive law estimates the upper bound of the disturbance and effectively weakens the chattering phenomenon. Finally, the simulation comparison is carried out under different conditions, and the simulation results show the superiority of the control scheme with high precision, fast velocity, and good robustness.

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.

Research on Three-Dimensional Integrated Guidance and Control Design with Multiple Constraints

In this paper, a fixed-time convergence-integrated guidance and control (IGC) method is proposed, which considers terminal line-of-sight (LOS) angle constraint, full-state constraints, and input saturation. Firstly, an IGC design model considering the full coupling of three channels is constructed, and a fixed-time convergence disturbance observer is used to estimate and compensate the unknown disturbances in the model. Secondly, based on the fixed-time stability theory, sliding mode control, and backstepping control, a novel IGC scheme is carried out, and the second-order instruction filter is used to restrict the system states and control instructions. Furthermore, the fixed-time stability of the close-loop system is proved and the expression of convergence time upper bound is given. Finally, comparison simulation and Monte Carlo simulation verify the effectiveness and superiority of the proposed IGC algorithm.