Fixed-time Tracking Control Research Articles

Command Filter-Based Adaptive Fuzzy Fixed-Time Tracking Control for Stochastic Nonlinear Systems with Input Saturation and Dead Zone

Command Filter-Based Adaptive Fuzzy Fixed-Time Tracking Control for Stochastic Nonlinear Systems with Input Saturation and Dead Zone

Prescribed Fixed-Time Control for Constrained Uncertain Nonlinear Cyber-Physical Systems Against Deception Attacks.

In this note, a novel prescribed fixed-time adaptive tracking control scheme is developed to cope with the fixed-time tracking control issue for a category of constrained MIMO nonlinear cyber-physical systems (CPSs) with exogenous perturbations, which suffer from deception attacks started in controller-actuator (C-A) channel. Distinguished from the conservative dynamic surface control (DSC) schemes with a linear filter, a novel nonlinear filter is designed in our strategy, which can tackle the intrinsic issue of explosion of computational complexity and promote the system performance. Besides, a new barrier Lyapunov function (BLF) is designed to ulteriorly enhance the tracking performance on the basis of the prescribed performance function (PPF) approach. Prominently, the proposed control strategy could accommodate the exogenous interferences and deception attacks simultaneously. Furthermore, we have substantiated that the developed approach can not only make certain that all the tracking errors of the resulting closed-loop system, including output tracking errors and virtual tracking errors, enter a prespecified small region near equilibrium point with fixed-time convergence rate, but also guarantee them obey the corresponding constraints throughout the entire control operation, where the regulation time and the tracking accuracy level keep prior known and could be prespecified arbitrarily. Finally, the validity and effectiveness of the proposed control scheme are illustrated through a representative application instance.

Quaternion-based fixed-time tracking control for an autonomous underwater vehicle with consideration of measurement bias

This article investigates trajectory and attitude tracking control problem of a 6-degree of freedom (DOF) autonomous underwater vehicle (AUV) subject to measurement bias and external disturbance. First, the model dynamics of rotational channels are established by unit-quaternion, which possesses simplicity and broader applicability compared to the Euler angle such that the maneuver signal could be uniquely determined. Meanwhile, by introducing constraint of the logarithm function and initial value, the unwinding phenomenon existing in rotation motion can be avoided tactfully. Considering the high requirement for sensor accuracy, the resulting measurement bias in position and velocity channels, making AUV into a mismatched system and bring the uncertain term in the process of controller design. Therefore, the echo state network (ESN) with online updates performance is applicable to approximate uncertain term simultaneously generated by measurement bias and unknown external disturbance. Then, by incorporating composite hyperbolic tangent function, the quasi-fast terminal sliding mode (QTSM) surface is constructed to realize the fixed-time convergence peculiarity of the AUV tracking system. Compared with the existing methods, the proposed algorithm can regulate artificially the stable schedule of the AUV tracking system and possess the capacity of bias tolerance and anti-disturbance. Finally, simulation results verify the validity and feasibility of the developed control algorithm.

Distributed Fixed-Time Optimal Flocking for Second-Order Multi-Agent Systems

In this paper, we investigate the problem of distributed optimization for second-order multi-agent systems with fixed-time flocking. The objective is to concurrently steer the agents towards a common velocity while optimizing the global objective function. To solve the problem, we first design a fixed-time estimator to predict the global gradient of the objective functions, then based on which, each agent is endowed with fixed-time tracking controller to track the optimal solution. Motivated by the fact that the relative velocity information is difficult to obtain accurately, the proposed algorithm is designed without using neighbors’ velocity. The upper bounds of the settling time are provided without relying on the initial states of the agents, only requiring the adjustment of parameters. The effectiveness of the proposed control protocol is also demonstrated through numerical simulations.

Fuzzy Adaptive Fixed-Time Tracking Control for State-Constrained Nonlinear Systems with Application to Induction Motors

Fuzzy Adaptive Fixed-Time Tracking Control for State-Constrained Nonlinear Systems with Application to Induction Motors

Adaptive fuzzy fixed-time control for uncertain switched nonlinear systems with non-symmetrical dead-zone

This paper addresses fuzzy adaptive fixed-time tracking control problem for uncertain switched nonlinear systems with non-symmetrical dead-zone, even if the tracking control problem for subsystems is not solvable. A fixed-time stability criterion for switched nonlinear systems using MLF(multiple Lyapunov functions) method is presented. Then, it is applied to fixed-time tracking control of uncertain strict-feedback switched nonlinear systems. The design methods of fuzzy adaptive feedback controllers and a state-dependent switching law are given to achieve the boundedness of all the signals of the resulting closed-loop system and the fixed-time output tracking control. Nonsymmetrical dead-zone model is used to estimate an adaptive factor through less parameters, which related to fixed-time tracking control for the uncertain switched nonlinear systems. Two examples are given to verify the effectiveness of the proposed design method.

Adaptive fixed-time tracking control of nonlinear systems with unmodeled dynamics

Adaptive fixed-time tracking control of nonlinear systems with unmodeled dynamics

Disturbance observer based fixed-time tracking control for unmanned aerial helicopters

In this paper, a fixed-time tracking control scheme based on the fixed-time disturbance observer is proposed for a 6-DOF unmanned aerial helicopter (UAH) with flight path constraints and composite disturbances. The composite disturbances are composed of external disturbances and system uncertainties. By using the hyperbolic tangent function, an improved disturbance observer is developed to estimate composite disturbances. Furthermore, a fixed-time back-stepping control method is employed for the position and attitude loops, which enables the UAH to track the expected path within the flight path constraints. Simulation results are given to demonstrate the effectiveness and advantages of the proposed scheme.

Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

Dynamic Event-Based Adaptive Fixed-Time Control for Uncertain Strict-Feedback Nonlinear Systems With State Constraints.

In this article, the event-triggered fixed-time tracking control is investigated for uncertain strict-feedback nonlinear systems involving state constraints. By employing the universal transformed function (UTF) and coordinate transformation techniques into backstepping design procedure, the proposed control scheme ensures that all states are constrained within the time-varying asymmetric boundaries, and meanwhile, the undesired feasibility condition existing in other constrained controllers can be removed elegantly. Different from the existing static event-triggered mechanism, a dynamic event-triggered mechanism (DETM) is devised via constructing a novel dynamic function, so that the communication burden from the controller to actuator is further alleviated. Furthermore, with the aid of adaptive neural network (NN) technique and generalized first-order filter, together with Lyapunov theory, it is proved that the states of closed-loop system converge to small regions around zero with fixed-time convergence rate. The simulation results confirm the benefits of developed scheme.

Fixed-time tracking control for state-constrained nonstrict-feedback systems without feasibility conditions

Fixed-time tracking control for state-constrained nonstrict-feedback systems without feasibility conditions

Adaptive fixed-time tracking control for nonlinear systems subject to asymmetric input saturation

For nonlinear systems with asymmetric input saturation, an adaptive fixed-time control strategy via multi-dimensional Taylor network (MTN) is proposed to effectively solve the tracking control problem. Firstly, the Gaussian error function and the differential mean value theorem are used to simulate the asymmetric input saturation model, that is, the nonlinear model is transformed into a linear model with a bounded perturbation. Secondly, MTNs are applied to control the design process, which approximate the nonlinear structures with linear combination of polynomials. Thirdly, in addition to the tracking error converging to an arbitrarily small neighborhood around the origin within a fixed time, the proposed control scheme not only guarantees that any signal in the controlled system remains bounded, but also avoids the problem of finite-time control relying on the initial state. Finally, three examples are used to validate the feasibility and superiority of the scheme.

Event-Based Nonsingular Fixed-Time Tracking Control of an Uncertain Manipulator System Subject to Full-State Static Constraints.

This article centers around investigating the event-triggered nonsingular fixed-time tracking issue for an n -link rigid robot manipulator with full-state constraints, external disturbances, and model uncertainties. We propose the definition of the constrainedly practically fixed-time stability (CPFTS) and provide a sufficient condition for CPFTS. A novel auxiliary function is developed to address the singularity issue caused by repeated differentiation in achieving the fixed-time tracking control. The uncertain parameters are approximated using the radial basis function neural network (RBFNN). This study proposes the model-based and the neutral network-based tracking control approaches, designed using the scaling function technique and the barrier Lyapunov function, respectively, to ensure that the tracking error systems are CPFTS and the full-state constraints comply. Moreover, the communication transmission load is reduced using the relative threshold event-triggered control strategy. Simulation results demonstrate the effectiveness of the proposed tracking control algorithms.

Adaptive fixed-time fuzzy fault-tolerant control for robotic manipulator with unknown friction and composite actuator faults

This paper exploits the issue of fixed-time (FT) tracking control (TC) for uncertain robotic manipulator systems (RMS) with composite actuator faults (CAFs), unknown disturbances and joint friction. The fuzzy logic system (FLS) algorithm is introduced to fit the unknown uncertainties including unmodeled parameters, CAFs and joint friction of the RMS, after which a relevant updating algorithm is employed to generate the unidentified boundary of the plant disturbance and FLS approximation error. Then a novel adaptive fuzzy sliding mode (SM) fault-tolerant controller is synthesized, which not only guarantees the boundedness of estimation errors of the involved adaptive parameters, but also actualizes the reachability of the predevised sliding surface. Furthermore, the proof that the system trajectories can achieve the FT convergence to the expected position signals, is then provided on account of the FT stability theory. Ultimately, simulation experiments exhibit the rationality based upon the current control algorithm.

Adaptive Fuzzy Fixed-Time Control for Nonlinear Systems with Unmodeled Dynamics

This article concentrates on the problem of fixed-time tracking control for a certain class of nonlinear systems with unmodeled dynamics. Unmodeled dynamics are prevalent in practical engineering systems, such as axially symmetric systems like robotic arms, spacecraft, and missiles. In this paper, the fuzzy-logic systems (FLSs) are implemented to address the challenge of accurately approximating the unknown nonlinear terms that arise during the derived control algorithm process. By employing fixed-time command filters (FTCF), the “explosion of complexity” issues encountered in traditional backstepping methods will be effectively resolved. Moreover, error compensation mechanisms are derived to effectively mitigate the filtering errors that may arise from the FTCFs. The computational burden associated with FLSs is reduced through the utilization of the weight vector estimation method based on the maximal norm and an adaptive approach. A fixed-time adaptive fuzzy tracking controller is developed within the backstepping control framework to ensure the boundedness of all signals and achieve fixed-time convergence of the tracking error for the controlled system. Illustrative examples are conducted to illustrate the viability of the derived controller.

Neural network-based practical fixed-time nonsingular sliding mode tracking control of autonomous surface vehicles under actuator saturation

The article considers the fixed-time tracking control of autonomous surface vehicles (ASVs) subject to actuator saturation. A novel sliding variable with state-dependent exponents is first constructed to alleviate chattering and overcome the singularity. By using the proposed fixed-time sliding variable and the neural network (NN), an NN-based fixed-time sliding mode control (SMC) scheme is developed. Besides, an auxiliary system is utilized to solve the input saturation constraint. Unlike some existing results for ASVs with input saturation, the designed fixed-time SMC law does not require assumptions on a priori upper bound of the lumped disturbances. Through Lyapunov analysis, it is proven that the tracking error can converge to a bounded region in a fixed time. Simulation examples are given to show the validity of the proposed control scheme.

Adaptive RBF Neural Network Tracking Control of Stochastic Nonlinear Systems with Actuators and State Constraints

This paper investigates the adaptive neural network (NN) tracking control problem for stochastic nonlinear systems with multiple actuator constraints and full-state constraints. The issue of system full-state constraints is tackled by a generalized barrier Lyapunov function (GBLF), and the output constraints of the system are considered to be in the form of time-varying functions, which are more in line with the needs of real physical systems. The NN approximation technique is utilized to overcome the influence of the uncertainty term on controller design due to randomness. Based on the backstepping technique, a neural adaptive fixed-time tracking control strategy is designed. Under the designed control strategy, the tracking accuracy of the controlled system can reach the expectation in a fixed time. The multi-actuator constraints are converted into a generalized mathematical model to simplify the controller design process. Using the characteristics of the hyperbolic tangent function, a new function called practical virtual control signal is designed using the virtual control signal as the input. Due to the saturation constraint property of the hyperbolic tangent function, it is theoretically ensured that no state of the system exceeds the constraints through to the new form of the virtual controller. Using the adaptive controller constructed in this paper, the controlled system is semi-global fixed-time stabilized in probability (SGFSP). Finally, the effectiveness of the proposed control strategy is further verified by simulation examples.

Velocity-free fixed-time attitude tracking fault-tolerant control for rigid spacecraft based on the homogeneity method

This paper examines the problem of fixed-time attitude tracking fault-tolerant for rigid spacecraft without angular velocity measurement, in the presence of uncertainties, external disturbances, and actuator faults. First, a fixed-time observer is established to obtain accurate estimates of the unmeasurable angular velocities, by applying a fixed-time observer, a fixed-time tracking control method is addressed to enable the tracking spacecraft to track the target spacecraft with time-varying attitude in a fixed time. A fixed-time output feedback attitude tracking controller is designed and the fixed time stability of the system is proved. In addition, the simulation results verify the effectiveness of the proposed control strategy.

Disturbance Observer-Based Fixed-Time Tracking Control for a Tilt Trirotor Unmanned Aerial Vehicle

This paper proposed a new fixed-time trajectory tracking control strategy based on the disturbance observer (DOB) for a tilt trirotor unmanned aerial vehicle (TTUAV) which is subject to unknown external disturbances. To facilitate the TTUAV's trajectory tracking controller design, the dynamic model of the TTUAV is divided into two subsystems, the position subsystem (outer-loop) and the attitude subsystem (inner-loop). For the dynamics of the TTUAV's outer-loop, the unknown external disturbances consist of the unknown wind disturbances, the unknown aerodynamic frictions forces, the lateral force generated by the rear servo and the states coupling between the outer-loop and the inner-loop. Then, a nonlinear DOB is designed to estimate the unknown external disturbances, and a nonsingular terminal sliding-mode controller (NTSMC) is further developed to drive the TTUAV's position tracking errors to zero in a fixed time. For the dynamics of the TTUAV's inner-loop, the unknown external disturbances are mainly introduced by the aerodynamic frictions torques. Then, a modified sliding mode controller is designed to reject the unknown external disturbances, and to ensure that the attitude tracking errors converge to zero exponentially. In addition, a composite stability analysis based on Lyapunov stability theory is provided to guarantee the fixed-time convergence of the closed-loop dynamics of the TTUAV. Finally, the results of the real-time experiments are presented to verify the effectiveness of the proposed control strategy.

Observer-based fault-tolerant fixed-time attitude tracking control for rigid spacecraft without angular velocity measurement

This paper investigates the problem of adaptive nonsingular fast terminal sliding mode fixed-time tracking control method for rigid spacecraft without angular velocity measurement. First, a novel fixed-time extended state observer is proposed to obtain accurate estimates of both unmeasurable angular velocities and integrated disturbance. Then, based on this sufficient qualification, an adaptive fast nonsingular terminal sliding mode controller is designed to make the state of the following spacecraft track a target spacecraft even when the tracking system has an actuator fault. Adaptive technology is introduced to compensate for the effect of observation error on the controller. Using the Lyapunov function and fixed-time property, it is proved that the control scheme can ensure that the attitude tracking error converges to the neighborhood of the origin in a fixed time and is independent of the initial conditions. Finally, numerical simulation examples are carried out to evaluate the effectiveness of the proposed fixed-time method.