Prescribed Performance Function Research Articles

Neural network-based prescribed performance tracking control for a class of nonlinear systems with mismatched disturbances

This paper addresses the prescribed performance tracking control problem for a class of nonlinear systems subject to mismatched uncertainties. A novel disturbance observer-based control (DOBC) scheme is proposed through combining radial basis function neural network (RBFNN) and prescribed performance function (PPF). In contrast to traditional DOBC, the proposed approach employs RBFNN technology to approximate unknown nonlinear functions in the system, instead of treating them as part of lumped disturbances. A novel disturbance observer is developed to estimate disturbances characterised by a nonlinear exogenous system. To enhance control performance, a PPF that characterises both transient and steady-state behaviour is used for the transformation of tracking errors. It can be proved that all the states of the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB), and that the tracking error evolves within the prespecified boundaries. Theoretical results are validated and supported by two simulation examples.

Fixed-Time Adaptive Event-Triggered Guaranteed Performance Tracking Control of Nonholonomic Mobile Robots under Asymmetric State Constraints

A fixed-time adaptive guaranteed performance tracking control is investigated for a category of nonholonomic mobile robots (NMRs) under asymmetric state constraints. For the sake of favorable transient and steady-state properties of the system, a prescribed performance function (PPF) is introduced and a transform function is further constructed. Based on the backstepping technique, an asymmetric barrier Lyapunov function is formulated to ensure the tracking errors converge within a human-specified time. On the foundation of this, the occupation of communication channel is effectively reduced by assigning an event-triggered mechanism (ETM) with relative threshold to the process of controller design. By utilizing the proposed control strategy, the NMR is capable of implementing the enemy dislodging mission while the enemy can always be caught by the NMR and the collision would never be presented. Finally, two simulation experiments are given to verify the effectiveness of the proposed scheme.

Fixed-time event-triggered sliding mode time-varying formation control for multiple surface vessels with fast convergence

ABSTRACT This paper proposes a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve control performance and ensure navigation safety. First, a fixed-time extended state observer (FxESO) is designed to provide estimations of velocities and lumped disturbances. Then, the event-triggered fixed-time distributed time-varying formation control law is designed based on prescribed performance function (PPF) and fixed-time nonsingular terminal sliding mode (FxNTSM) manifold. Finally, system stability is analyzed based on Lyapunov theory. The salient features of the proposed scheme are as follows. First, a novel hyperbolic cosecant PPF is incorporated into the control scheme to enhance control performance. Then, the proposed scheme is combined with relative threshold event-triggered strategy to reduce unnecessary updates of actuators. Finally, a uniform exact differentiator is introduced to avoid the formation control law including the acceleration of adjacent vessel. Comparative results are given to demonstrate the superiority of the proposed scheme.

Dynamic event-triggered fixed-time consensus control for coupled multi-permanent magnet synchronous motors stochastic system with prescribed performance

With the ubiquity of permanent magnet synchronous motors (PMSM), multi-PMSMs are increasingly being elastically coupled to achieve greater output power. The authors establish a general mathematical model of coupled multi-PMSMs system. The dynamic analysis of the coupled multi-PMSMs system is analyzed using coupled three-PMSMs system as an example, and a dynamic event-triggered fixed-time consensus controller with prescribed performance is constructed for coupled PMSMs stochastic system. In addition, Interval Type-3 Fuzzy System (IT3FS) is employed to estimate unknown functions, the computing cost is reduced by updating the weights based on only one adaptive law per PMSM. To enhance the efficiency of communication resource utilization, a dynamic event-triggered mechanism is introduced, where the triggering condition depends on a dynamic auxiliary variable. Moreover, fixed-time control technical is applied to guarantee the setting time and a novel fixed-time prescribed performance function (PPF) is constructed to constrain consensus errors. To cope with the “complexity explosion”, a fixed-time tracking differentiator (TD) is introduced and the corresponding filtered error compensation signals is designed. Finally, the authors demonstrate the system is fixed-time stabilized in probability by applying fixed-time stabilization Lyapunov stability criterion, and the simulation results of a coupled three-PMSMs stochastic system show that the presented algorithm is feasible.

Event-Based Adaptive NN Fixed-Time Cooperative Formation for Multiagent Systems.

This article focuses on the fixed-time formation control problem for nonlinear multiagent systems (MASs) with dynamic uncertainties and limited communication resources. Under the framework of the backstepping method, a time-varying formation function is introduced in the controller design. To attain the prescribed transient and steady-state performance of MASs, a fixed-time prescribed performance function (FTPPF) is designed and the further coordinate transformation addressing the zero equilibrium point problem is removed. To achieve better approximating performance, a neural network (NN)-based composite dynamic surface control (CDSC) strategy is proposed, where the CDSC scheme is consisted of prediction errors and serial-parallel estimation models. According to the signals generated by the estimation models, disturbance observers are established to overcome the difficulty from approximating errors and mismatched disturbances. Moreover, an improved dynamic event-triggered mechanism and varying threshold parameters are constructed to reduce the signal transmission frequency. Via the Lyapunov stability theory, all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Finally, the simulation results verify the effectiveness of the developed CDSC strategy.

Observer‐based output feedback event‐triggered robust control for heterogeneous vehicular platoon systems

AbstractIn this article, the problem of output feedback robust control for heterogeneous vehicle platoon system (HVPS) is investigated. A novel double‐channel event‐triggered mechanism is designed to reduce the waste of communication resources and unnecessary data transmissions. A neural network state observer is designed by intermittent output signal to estimate unmeasurable states. The prescribed performance function is used to establish a strong string stability condition. Combining backstepping recursive technique and prescribed performance function with its inverse transformation, observer‐based robust adaptive output feedback event‐triggered platoon controller is designed, which can ensure the individual stability, string stability, and strong string stability of HVPS. It is proved that all signals are bounded by Lyapunov stability analysis. Finally, the validity of the proposed results is proved by simulation.

Active underactuation fault‐tolerant backstepping attitude tracking control of a satellite with interval error constraints

AbstractUnderactuation poses a significant challenge to space mission control and performance. This article investigates the non‐linear attitude tracking control problem for a remote sensing satellite underactuated by a reaction wheel (RW) actuator fault. First, a timeline close to the in‐orbit reality of an underactuation fault is presented. Then, the fault detection and diagnosis strategy is performed in a finite‐time decision window. The failed actuator is excluded from the control loop by forming the proposed reconfiguration window to transition from a 3 RWs configuration to 2 RWs. The underactuation fault‐tolerant control is designed according to the active method, where the adaptive robust control law employed for fault‐free conditions is switched to the underactuated attitude tracking control (UATC). The structure of UATC is based on kinematic and adaptive backstepping dynamic controllers. The effect of unknown bounded external disturbances is considered with an adaptive estimation term. The asymptotic stability of the closed‐loop control system is proved via Lyapunov theory in the presence of parametric uncertainty. Due to the underactuation, a new approach proposed in the prescribed performance function is interval error constraints, which include the pointing accuracy and stability requirements in imaging time intervals. Finally, the results of the multidisciplinary simulation and experimental test confirm the applicability of the underactuation fault‐tolerant control.

Fast Finite‐Time Dynamic Surface Synchronization Control for Telerobotics System with Prescribed Performance

AbstractThis study focuses on the fast finite‐time synchronization control problem for nonlinear telerobotics system with asymmetric time‐vary delays and uncertainties. A finite‐time prescribed performance function is incorporated into the backstepping control framework such that the synchronization error will remain within a predefined funnel boundary. To increase the rate of convergence, the selected error transformation function is a arctangent function. The utilization of dynamic surface control method aims to decrease computational complexity by mitigating the need for repetitive differentiation of virtual signals in the conventional backstepping algorithm. In the meantime, the non‐power approximate signals of fuzzy neural network algorithms are utilized to replace the system uncertainties, effectively addressing the passivity issue associated with time‐delayed channels. Both theoretical analysis and experimental results are present to verify that the synchronization error can converge to a small neighborhood around zero in the fast finite time and the closed‐loop system remains stable.

Vision-based finite-time prescribed performance control for uncooperative UAV target-tracking subject to field of view constraints

This paper presents a vision-based finite-time prescribed performance controller for unmanned aerial vehicle (UAV) tracking of uncooperative aerial targets. The relative states between UAV and target are estimated by an onboard monocular camera. The inability of visual measurements to accurately determine the initial state of the target renders conventional prescribed performance controllers ineffective in such situations. As a result, it becomes essential to address the problem of prescribed performance control under conditions of uncertain initial values By utilizing an auxiliary transforming function, an Asymmetric Barrier Lyapunov Function (ABLF) and a finite-time prescribed performance function, a robust adaptive controller based on backstepping framework is proposed to deal with state constraints under unknown initial tracking conditions. It is proved that, the closed-loop relative position is capable of reaching the prescribed performance bound before the preset transforming time and converging to the prescribed steady-state error before a finite setting time. Simulation examples are provided to illustrated the effectiveness of the proposed tracking algorithm.

An adaptive bi-limit homogeneous sliding mode control for 3-DOF stabilized system of ship propulsion-assisted sail with prescribed performance

Sail-assisted ships have garnered widespread interest as a sustainable technology. The three-degree-of-freedom (3-DOF) stabilized system of ship propulsion-assisted sail is used to track the optimal azimuth of the sail and isolate the swaying of the ship's hull. In this paper, the problem of tracking control for the system with prescribed performance is investigated. By using an appointed-time prescribed performance function (APPF), a novel bi-limit homogeneous sliding surface with expected trajectory is proposed to improve the convergence rate, accuracy, and overshoot. Considering the external disturbance, a wind resistance model is established and compensated to reduce the conservatism and chattering. Adaptive extreme learning machines (AELMs) are employed to estimate the mismatch parameters caused by Reynolds number fluctuations and unmodelled dynamics. Finally, an adaptive bi-limit homogeneous sliding mode controller is constructed, by which the system can track the 3-DOF target signals with prescribed performance and suppress disturbances. The fixed-time reachability of the system is verified by Lyapunov analysis and fixed-time theory. To validate the effectiveness of the presented controller, numerical simulations and principle prototype experiments are conducted. The results are compared with other algorithms and show that regardless of the control performance or energy-saving benefits, the proposed method has a better effect.

Command filter-based event-triggered control for stochastic MEMS gyroscopes with finite-time prescribed performance

This paper proposes an adaptive neural control strategy for stochastic microelectromechanical system (MEMS) gyroscopes, aiming to achieve a prescribed performance in a finite time. The radial basis function neural network is introduced to address the system’s unknown nonlinear dynamics and stochastic disturbances. Then, the technology of finite-time prescribed performance function, along with the method of command-filtered backstepping design, is utilized to ensure both transient and steady-state performance and simultaneously solve the problem of "explosion of complexity." Moreover, a switching threshold event-triggered control law is proposed to cut down on communication resources and eliminate corresponding parametric inequality restrictions. The proposed adaptive state feedback control strategy is able to guarantee that the output tracking error converges to a prescribed, arbitrarily small residual set. Additionally, the closed-loop system’s signals can be semi-globally ultimately uniformly bounded in probability. Finally, numerical simulations demonstrate the effectiveness and superiority of the proposed strategy.

Fixed-time adaptive neural quantized formation control of USVs with tunnel prescribed performance

This paper investigates fixed-time adaptive neural quantized formation control of unmanned surface vehicles (USVs) with tunnel prescribed performance in the presence of leader’s information unknown, model dynamic uncertainties and input quantization. Initially, a fixed-time observer is constructed to rapidly estimate the leader’s unknown information. Following this, a control strategy is designed employing a fixed-time sliding mode differentiator-based backstepping technique combined with a neural network-based minimum parameter learning approach (MLP-NN). This strategy addresses the ”complexity explosion” issue arising from the differentiation of the virtual control law and model dynamic uncertainties separately. Moreover, a specialized prescribed performance function is incorporated to ensure that performance specifications of the formation tracking errors meet specific performance criteria. The integration of hysteresis quantizer aids in conserving save communication resources and significantly reduces the detrimental effects caused by quantization errors through the proposed control methodology. It is demonstrated that all closed-loop signals are practical fixed-time stable and formation tracking errors consistently adhere to the predetermined performance envelopes. The efficacy of proposed control strategy is validated through comprehensive numerical simulations.

Event-driven prescribed performance distributed formation control for MSVs based on second-order step response with actuator input saturation

This study aims to investigate the problem of event-driven distributed formation control for marine surface vehicles (MSVs) system, including prescribed performance constraint and actuator input saturation. By constructing a novel prescribed performance function based on second-order step response, the intuitive physical significance is realized, and the performance specifications imposed on the output tracking errors are achieved. Subsequently, a double-layer adaptive sliding-mode disturbance observer (ASMDO) is presented to compensate for lumped uncertain terms. Within the controller design stage, an auxiliary dynamic system is built to introduce the auxiliary intermediate control law, thus avoiding the need to directly design anti-saturation generalized control input for the MSVs system. Then, by incorporating external dynamic variable, a dynamic event-triggered mechanism (DETM) is proposed to regulate the transmission between the controller and actuators. Under the DETM, the designed controller only transmits the control force and torque into actuators at the specified triggering moment, and the trigger moment is independent of the internal state of the system. After that, the minimum inter-event time (MIET) of the proposed DETM is proved to be strictly positive, which ensures Zeno-free behavior. Lastly, the efficiency and advantages of the proposed event-driven distributed formation controller are verified through numerical simulations.

Command filter-based event-triggered fixed-time control for nonlinear systems with prescribed performance and actuator faults

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

Improved Stanley guidance law–based adaptive path-following control of underactuated ship with state-constrained and time-varying drift angle

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path.

Adaptive Attitude Control for QUAVs Using Event-Triggered Control and Optimized Quantized Communication with Prescribed Performance

This paper proposes an appointed-time prescribed performance adaptive attitude controller with an event-triggered (ET) mechanism and optimized quantized communication for quadrotor unmanned aerial vehicles (QUAVs) in an uncertain environment. An appointed-time prescribed performance function is first designed to improve the convergence performance of attitude tracking errors considering different convergence time requirements and the convergence rate. In addition, to reduce the communication burden, a switching threshold ET mechanism and an optimized hybrid quantizer are adopted by using the K-means method. The ET mechanism not only involves the fixed threshold but also refers to the change rate of calculated control law flexibly and predictively. The optimized hybrid quantizer creatively classifies signals by their value and maximizes the advantage of each quantization method to reduce excessive quantization errors. It is shown that the proposed control scheme ensures that the closed-loop signals are uniformly ultimately bounded according to the Lyapunov method. Finally, the simulation experiments are implemented on a QUAV to demonstrate the effectiveness of the presented control scheme.

Time-varying formation for MSVs with input and prescribed performance constraints by fixed-time event-triggered sliding mode control

This work develops a new fixed-time sliding mode time-varying formation control strategy for multiple surface vessels (MSVs) to improve the control performance, ensure the navigation safety and reduce the communication burden. At first, a fixed-time adaptive radial basis function neural network (FxRBFNN) observer is designed to provide the estimations for external environmental disturbances and model parameters uncertainties. Then, observer-based fixed-time distributed time-varying formation event-triggered control law is proposed based on the novel fixed-time auxiliary dynamic system (FxADS), the proposed prescribed performance function, the designed fixed-time nonsingular terminal sliding mode (FxNTSM) manifold and the proposed uniform exact differentiator. Finally, the system stability is proved by Lyapunov theory. The salient features as follows. First, to enhance the convergence performance for time-varying formation control method, a novel hyperbolic cosecant prescribed performance function (PPF) is introduced. Second, a novel FxADS is proposed to confront input constraints. Third, the proposed scheme is combined with a relative threshold event-triggered strategy to reduce the unnecessary updates of actuators under the premise of ensuring the control performance. Fourth, to avoid the proposed formation control law including adjacent vessel accelerations, this work proposed an improved uniform exact differentiator to identify them. Numerical simulations confirm that the proposed scheme has superior control performance.

Nonsingular finite-time heading tracking control of marine vehicles with tracking error constraints

This brief copes with the finite-time heading tracking control for marine vehicles. The tracking error constraints, stochastic disturbance and dead-zone output are simultaneously taken into consideration in the controlled systems. To manage the dead-zone output issue, a smooth approximation model is brought in to offset the nondifferentiable phenomena during the control, besides, the adaptive technique and the Nussbaum function are simultaneously integrated into the design. For the tracking error constraints, the prescribed performance functions (PPF) with error transformations are designed, and novel stochastic Barrier Lyapunov functions are constructed accordingly depending on the newly tracking errors to deal with the constrained tracking control issue. To avert the “differential explosion” issue in the backstepping, the improved first-order filter technique is invoked. The proposed finite-time heading tracking control tactic renders that all variables are bounded, meanwhile, the tracking errors are kept in the pregiven boundaries. The effectiveness of theory results is substantiated via simulations.

A distributed containment tracking control of the UAV formation with prescribed performance subject to collision avoidance

SummaryIn this paper, the issue of finite‐time containment tracking control under collision avoidance constraints for unmanned aerial vehicle (UAV) formation is investigated. To tackle the challenge of collision avoidance in the context of formation containment tracking, combined with a prescribed performance function, a distributed containment tracking control scheme is proposed. Firstly, a UAV formation containment control model from a top view perspective is established. Next, to solve the internal collision avoidance within the formation, a restricted movement region is constructed for each UAV using a distributed prescribed performance function, which guarantees that each UAV's trajectory is maintained within a predefined area. Furthermore, invoking with the finite‐time control theory for the formation, a distributed containment tracking control scheme is developed to complete finite‐time tracking of the formation. Finally, simulation results are carried out to demonstrate the efficacy of the proposed approach.

Optimization-based adaptive trajectory tracking controller design of self-balanced vehicle with asymptotic prescribed performance

To handle with the nonlinear external disturbances and unmodeled dynamics of self-balanced vehicle (SBV), a novel adaptive trajectory tracking controller based on asymptotic prescribed performance is proposed. First, a velocity planner based on kinematic is constructed to control the velocity signal to improve the motion stability of SBV. Second, the prescribed performance function (PPF) is designed to prescribe transient-state and steady-state performances (TSP). Afterwards, an optimization-based predictive control (OPC) is proposed for accurate trajectory tracking of SBV. Furthermore, a modified radial basis function neural network (RBFNN) approximator is developed to compensate the unmodeled dynamics and the nonlinear external disturbances of the SBV. The overall system stability is proved with the help of Lyapunov theorem. Finally, the tracking performance and anti-interference robustness of the proposed control method are verified by comparative numerical simulations.