Prescribed Performance Function Research Articles

Improved FPTPPF-based predefined-time tracking control of a UVMS with actuator faults

In this paper, a new predefined-time control scheme is proposed for the trajectory tracking problem of an underwater vehicle-mechanic system (UVMS) with external disturbances, model uncertainties and actuator faults. First, a predefined-time controller is proposed to achieve convergence in a predefined time so that the convergence time does not depend on the initial value of the system. Second, considering the possible grasping and transportation tasks for the UVMS, an improved flexible predefined-time prescribed performance function (FPTPPF) with self-adjustment capability is proposed to avoid the vulnerabilities of the existing prescribed performance functions. A control framework is constructed for the integral barrier Lyapunov function and FPTPPF, which can achieve good tracking performance. Third, a predefined-time extended state observer (ESO) is constructed to address the problems caused by external disturbances, model uncertainties and actuator faults. For strong sudden disturbances, the H∞ control strategy is designed via the backstepping method, which effectively improves the robustness. Finally, the predefined-time stability of the system is proven via Lyapunov stability theory, where the tracking errors can converge to a small region of the null domain in a predefined time. The performance and superiority of the proposed predefined-time control method are verified via simulation comparisons.

Adaptive performance optimal control for flexible-joint robots with random noises: Design and experiment

This study developes a flexible performance optimal control scheme via reinforcement learning strategy and event-triggered mechanism for flexible-joint robots with random noise and non-affine input. It is notable that an event-triggered optimization mechanism is developed, which meets the optimality principle and saves communication resources. Nevertheless, the existing event-triggered strategy is unable to handle non-affine input, which limits the applicability of this method. To overcome the above problems, a modified event-triggered mechanism is proposed. At the same time, the optimal solution of the system is given by an optimized control algorithm based on the improved performance index function. In the controller design, neural network is used to deal with random disturbances and uncertainties, and an adaptive law is designed to replace the identifier structure. Besides, a flexible prescribed performance function is constructed to yield multiple prescribed performance behaviors by adjusting the key parameters, while the tracking error is stayed within a prescribed boundary. Finally, the effectiveness of the proposed control scheme is further demonstrated by simulation and the experiment of the 2-link flexible-joint robot on the Quanser platform.

Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.

Comparative study of adaptive trajectory tracking controller for four-wheel mobile robot with prescribed-prediction performance

The nonlinear external disturbances and unmodeled dynamics characteristics have crucial impacts on trajectory tracking control accuracy of a four-wheel mobile robot (FWMR) under complicated working conditions. In this work, an adaptive trajectory tracking controller is designed for the FWMR to achieve the prescribed-prediction performance. On the basis of establishing the FWMR’s dynamics equations, an enhanced prescribed performance function (EPPF) is constructed to restrain the tracking errors of the FWMR within a certain range without requiring the exact initial conditions, thus guaranteeing the transient performance of the control system. Then, an optimal-predictive control (OPC) approach is presented to fulfill the asymptotic stability of the tracking errors of the FWMR. Specifically, the radial basis function neural network (RBFNN) incorporating a minimum parameter learning approach that are implanted into the expected controller is designed to attenuate the nonlinear external disturbances and the unmodeled dynamics of the FWMR. Lastly, comparative simulation investigations are carried out to illustrate the superiority of the proposed EPPF-OPC controller, and moreover, the comparative experiments are further performed to validate the practical effectiveness of the EPPF-OPC controller based on a self-established robot operating system (ROS) test platform of the FWMR.

SDO-Based Command Filtered Adaptive Neural Tracking Control for MIMO Nonlinear Systems With Time-Varying Constraints.

In this article, an adaptive neural tracking control based on saturation disturbance observer (SDO) and command filter is studied for multiple-input-multiple-output nonlinear systems with time-varying constraints and system uncertainties. By employing neural networks (NNs), the system uncertainties are approximated. The SDO is proposed to estimate the composited disturbances which consist of NN approximation errors and the external bounded disturbances. Compared with the traditional disturbance observer, the SDO can reduce the estimation error to some extent. The control requirements are achieved based on the multiconstraints which contain three layers: 1) prescribed performance functions (PPFs); 2) actual constraints; and 3) virtual constraints. The errors remain within the prescribed small neighborhood of zero by using the PPFs, the error constraints ensure that the time-varying constraints are never violated even if the PPFs are not available, and the virtual constraints are applied in a new time-varying barrier Lyapunov function (TVBLF) to design virtual controllers and controller to solve the singularity problem of the traditional TVBLF. In addition, the command filter is introduced to solve the problem of "explosion of complexity." Finally, a numerical simulation verifies the effectiveness of the proposed scheme for a flight control of unmanned aerial vehicle.

Adaptive Fuzzy Tracking Control With Global Prescribed-Time Prescribed Performance for Uncertain Strict-Feedback Nonlinear Systems.

For strict-feedback systems with mismatched uncertainties, adaptive fuzzy control techniques are developed to provide global prescribed performance with prescribed-time convergence. First, a class of prescribed-time prescribed performance functions are designed to quantify the performance constraints of the tracking error. Additionally, a novel error transformation function is provided to eliminate the initial value limitations and resolve the singularity issue in previous research. To ensure the convergence of the tracking error into a prescribed bounded region within a prescribed time and satisfactory transient performance, controllers with or without approximating structures are established. Notably, the settling time and initial condition of the prescribed performance function are completely independent of the initial tracking error and system parameters, thereby improving upon existing results. Furthermore, the disadvantage of the semi-global boundedness of tracking error induced by dynamic surface control can be eliminated through the use of a novel Lyapunov-like energy function. Finally, the effectiveness of the proposed strategies is validated through numerical simulations performed on practical examples.

Preassigned Time Adaptive Neural Tracking Control for Stochastic Nonlinear Multiagent Systems With Deferred Constraints.

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

Event‐triggered optimal control based on prescribed performance for a two‐link robotic manipulator

SummaryIn this article, an event‐triggered optimal control method based on prescribed performance is investigated for a constrained two‐link robotic manipulator system. To satisfy the performance constraints of the system, an equated error model of the dynamics model is established by means of two auxiliary functions and the prescribed performance technique. A predictive controller based on an adaptive event triggering mechanism is obtained by solving a constraint optimization problem for this transformed error model, and the triggering threshold can be adjusted based on real‐time changes of the system. This controller realizes the tracking of the joint angle with the desired angle and meets the prescribed performance conditions. Finally, the control algorithm is shown to be an effective method for improving control performance through numerical simulations and comparison with other prescribed performance functions.

An Adaptive Characteristic Model-Based Event-Triggered Sigmoid Prescribed Performance Control Approach for Tracking the Trajectory of Autonomous Underwater Vehicles

This paper introduces an event-triggered sigmoid prescribed performance control method, enhanced by an adaptive characteristic model, for tracking the trajectory of autonomous underwater vehicles (AUVs). The AUV model is simplified into a function reliant solely on second-order parameter information through the use of characteristic modeling and a compression algorithm, which is then approximated by a neural network. We propose integrating prescribed performance control into event-triggered sliding mode control to accelerate convergence in AUV trajectory tracking. A novel prescribed performance function is employed in this integration, creating an event-triggered, non-singular terminal sliding mode control strategy. The stability of this controller is rigorously proven. This control strategy is not only robust against model uncertainties but also mitigates the jitter commonly associated with sliding mode control and the singularities from preset performance control due to sudden random disturbances. Comparative simulation experiments demonstrate that the proposed control method achieves superior control accuracy and a quicker response.

Fixed-time disturbance observers-based fault-tolerant control for a class of nonlinear systems with prescribed performance

This paper explores the issue of fault-tolerant control for a class of nonlinear systems that encounter the actuator fault and external disturbances. The uncertainties arising from the actuator fault and external disturbances are treated as lumped uncertainties, and fixed-time observers are designed to observe them. The fault-tolerant controller with full-state constraints is then developed using the fixed-time backstepping method, integrating the Improved Prescribed Performance Function (IPPF) method and the Barrier Lyapunov Function (BLF) method. Additionally, command filters with error compensations are devised to resolve the ‘explosion of complexity’ problem during the controller derivation process. The parameters of the designed controller are optimised using the Northern Goshawk Optimization (NGO) algorithm to enhance nonlinear systems’ dynamic performance. Lastly, the validity and practicality of the proposed approach are verified through the comparative study of simulations and experiments, with the permanent magnet synchronous motor (PMSM) position system employed as a case study.

Prescribed-Time Trajectory Tracking Control for Unmanned Surface Vessels with Prescribed Performance Considering Marine Environmental Interferences and Unmodeled Dynamics

This article investigates a prescribed-time trajectory tracking control strategy for USVs considering marine environmental interferences and unmodeled dynamics. Firstly, a fixed-time extended state observer is introduced to quickly and accurately observe the compound perturbations including ocean disturbances and unmodeled dynamics. Subsequently, a prescribed-time prescribed performance function is utilized to obtain guaranteed transient performance within a predefined time. Finally, combining the fixed-time extended state observer, dynamic surface control technique, and prescribed-time prescribed performance control, a prescribed-time prescribed performance control strategy is developed to guarantee that the tracking errors converge to a predefined performance constraint boundary within a prescribed time. The effectiveness and superiority of the presented control strategy is verified by the simulation results.

Application of improved appointed time control in helicopter mode of a tilt-rotor eVTOL aircraft

In this paper, an appointed time sliding mode control scheme is proposed for trajectory tracking control of a tilt-rotor electric vertical takeoff and landing (eVTOL) aircraft. First, the error dynamic model of helicopter mode of the tilt-rotor eVTOL aircraft is presented. Second, an appointed time prescribed performance function (ATPPF) is designed as the expected value of the error, which guides the error to converge to zero at the appointed time. Then, a predefined time controller ensures that the actual error tracks the expected error before the settling time set by the ATPPF. By setting the time parameters of the ATPPF and the predefined time controller to the same value, the actual error will converge to zero vicinity at the appointed time. Finally, the predefined time convergence of the closed-loop system is proved via Lyapunov analysis. The effectiveness of the appointed time control strategy is demonstrated in the simulation results in the presence of external disturbances, dynamic uncertainties and control input constraints.

Fixed-time anti-disturbance control for nonlinear turbofan engine with impulsive prescribed performance

To analyze the robust control problem of turbofan engine within a large flight envelope, a fixed-time prescribed performance control scheme is proposed for the nonlinear turbofan engine in presence of unknown disturbances and possibly discontinuous reference signals. Firstly, the equilibrium manifold expansion (EME) modeling method is adopted for the turbofan engine to construct an affine nonlinear model. Then, considering the possibly discontinuous reference signals, a novel fixed-time prescribed performance function (FxTPPF) with impulsive characteristic is presented to successfully deal with the singularity problem caused by its discontinuity situation. In what follows, a fixed-time nonlinear disturbance observer (FxTNDO) is developed to realize fast estimation of disturbances within fixed time. According to the transformed error system and disturbance estimations, a fixed-time anti-disturbance composite controller is further developed. By borrowing Lyapunov stability theory, the boundedness of all error signals in the impulsive closed-loop system is proved. Finally, simulation results indicate that this control scheme can ensure rotor speeds effectively to track the desired commands within a predefined time after the appearance of a discontinuity and the tracking errors are limited to the performance bound all along.

Adaptive event-triggered finite-time prescribed performance control of PMSM stochastic system considering time-varying delays

This paper investigates the finite-time prescribed performance tracking control problem of permanent magnet synchronous motor (PMSM) considering stochastic disturbances and time-varying delays under event-triggered mechanism. A quintuple polynomial finite-time prescribed performance function (FPPF) is introduced to ensure the transient and steady-state performance of the system output, and a nonlinear transformation function is employed to convert the constrained error into an unconstrained one. The Lyapunov-Krasovskii function is constructed to address time delays. And the system uncertainties are approximated by the radial basis function neural networks (RBFNN). For the “explosion of complexity” caused by backstepping method, a tracking differentiator (TD) is employed. By combining finite time control, command filtering backstepping control, and event-triggered mechanism, the effect of the filter errors is decreased, and the update frequency of the control signals are reduced. It is shown that the proposed controller can guarantee finite time convergence bounded of all signals in the closed-loop system, and the tracking error can converge in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

Dynamical analysis and event-triggered adaptive finite-time prescribed performance control of the FO coupled MEMS resonators

This paper explores the dynamic behaviors and control method of weakly coupled micro-electro-mechanical system (MEMS) resonators with fractional-order (FO) dynamics. In the dynamics analysis session, Lyapunov exponents, bifurcation theory, and phase diagrams are used to analyze the effects of system parameters, coupling stiffness, and FO on the complex dynamical behaviors such as periodicity, pseudo-periodicity, and chaos oscillations. To suppress chaotic oscillations, a dynamic event-triggered finite-time prescribed performance controller is proposed. The unknown nonlinear functions are approximated through the interval type-3 fuzzy system (IT3FS) with an adaptive law. A novel finite-time prescribed performance function (finite-time PPF) is constructed to establish constrained boundaries for tracking errors. Compared with the existing PPFs, the proposed approach allows for more flexible setting of the convergence boundary before reaching steady-state. Subsequently, the constrained tracking errors are mapped to an unconstrained form using a nonlinear transformation function, whether the error constraint is symmetric or asymmetric. To circumvent the “explosion of complexity” arising from backstepping design process, a tracking differentiator (TD) is utilized. Additionally, to alleviate strain on communication resources, an event-triggered mechanism is devised to update control signals. The trigger threshold of the control signals can be adaptively adjusted based on the values of the Lyapunov function and the dynamic auxiliary variables. This control method guarantees finite-time convergence for all signals of the system. Finally, extensive simulations are performed to verify the effectiveness of the proposed algorithm.

Neuroadaptive‐based fixed‐time control for robotic manipulators with uniform prescribed performance under unknown disturbance

AbstractAchieving faster convergence, smaller transient overshoots, and higher steady‐state tracking accuracy is essential to improve the efficiency, robustness, and applicability of robotic manipulators. This article introduces an innovative adaptive fixed‐time uniform prescribed performance controller for the manipulator facing model uncertainties and unknown disturbances. Initially, by designing a modified prescribed performance function inspired by variable superposition, this study redefines the unified prescribed performance control problem into a simplified parameter selection problem. This approach allows for the incorporation of varied performance metrics within a singular control scheme, addressing both transient and steady‐state performances concurrently without shifting control frameworks. Then, to alleviate computational demands, an adaptive neural network employing a single‐parameter weight update technique compensates for uncertainties of the manipulator dynamic model. Additionally, a disturbance observer is designed to mitigate the impact of non‐parametric disturbances. Moreover, integrating fixed‐time theory with the Lyapunov stability analysis method guarantees the convergence of all error signals to a near‐zero compact neighborhood at a fixed time. Finally, the advantages and comprehensive performance of the proposed method are confirmed by numerical simulations and real‐world experiments.

Adaptive neural network fault-tolerant control of hypersonic vehicle with immeasurable state and multiple actuator faults

This paper proposes a fault-tolerant control scheme for tracking and controlling hypersonic vehicles with unknown dynamics, actuator failures, and unmeasurable states. The approach involves using a radial-based neural network to approximate the unknown dynamics and reconstruct the entire system model. Additionally, a neural network state observer is proposed to estimate the unmeasurable state of the system. To address the impact of actuator faults, a nonlinear observer is designed to estimate and compensate for the approximation error of the neural network system and fault values. Furthermore, a prescribed performance function is introduced to ensure both transient and steady-state performance of the system. The bounded stability of the closed-loop system is demonstrated through Lyapunov stability analysis.

Predefined-time prescribed performance second-order sliding mode path following control for underactuated marine surface vehicles using self-structuring NN

This paper proposes a predefined time-prescribed performance second-order sliding mode path following controller for underactuated marine surface vehicles (MSVs) with unknown external environmental disturbances based on predefined time predictor line-of-sight (PTPLOS) guidance. First, a predefined time predictor is designed to address the problem of time-varying sideslip angles, and then a guidance law is designed. Second, a prescribed performance function with predefined times is proposed, which can not only set the rate of convergence and the final convergence range but also set an upper bound on the convergence time. Third, the predefined-time controller is designed in combination with second-order sliding mode control. Then, a self-structuring neural network (SSNN) is developed to approximate external disturbances and uncertainties, and this approach can adaptively adjust the number of neurons, reducing the computational burden while maintaining high approximation accuracy. After that, the closed-loop system is proven to be predefined-time stable by using of the Lyapunov stability theory. Finally, the control method proposed in this paper is validated through numerical simulations, demonstrating its effectiveness.

Switching periodic event‐triggered global prescribed performance control of uncertain strict‐feedback systems with sensor faults

AbstractThis study investigates the global adaptive prescribed performance control (PPC) of a class of uncertain strict‐feedback nonlinear systems with sensor faults based on the switching periodic event‐triggering mechanism (SPETM). Due to the existence of sensor faults, the controlled system is first remodeled by utilizing the available variables. To reduce the communication frequency, a novel SPETM is proposed by combining the advantages of the static and the dynamic event‐triggering mechanisms. This mechanism can not only avoid continuously monitoring the event‐triggering condition and avoid the Zeno phenomenon in mechanism, but also reduce the trigger frequency while ensuring the system performance by adjusting the event‐triggering threshold dynamically. Meanwhile, a time‐varying scaling function, whose reciprocal is considered as a prescribed performance function, is designed to achieve the global PPC by combining the nonlinear transformation technique. The adaptive control algorithm design is completed by employing the backstepping methodology, which can guarantee that all closed‐loop signals are bounded and the actual system output signal evolves within the prescribed performance boundary for arbitrary initial values. The effectiveness and the advantages of the proposed control algorithm are illustrated through an application example of the network‐based robotic manipulator system.

Prescribed performance based adaptive model-free control for highly flexible spacecraft detumbling rotating satellites

The method, using a servicing spacecraft (SS) mounted with very flexible operation devices (FOD), has shown promising application in detumbling rotating satellites due to its unique advantage of compliant contact processes. The SS is highly flexible, and successful implementation of detumbling rotating satellites is dependent on the advanced controller with high performance. However, the controller design suffers from two problems: (i) since the uncertain dynamics arising from the FOD lead to difficulty in acquiring an accurate dynamic model of the SS, the conventional model-based controllers are unable to achieve high performance; (ii) the large deformation of the FOD caused by contact processes generates impactive disturbance that severely deteriorates the transient and steady-state performances. To address these problems, this paper proposes a prescribed performance based adaptive model-free control for the first time. In the controller design process, a finite-time prescribed performance function is designed to incorporate into the model-free controller, which ensures the user-specified error constraints concerning the convergence rate, overshoot, and tracking accuracy. Meanwhile, an adaptive estimation algorithm is developed to significantly enhance the robustness against the disturbance. Moreover, an anti-windup compensator is constructed to effectively handle the adverse effect of thruster saturation. Simulation results validate the effectiveness of the proposed controller, and further show that the SS can successfully detumble the rotating satellite while achieving prescribed performance.