Finite-time Performance Function Research Articles

Fuzzy wavelet neural adaptive finite-time self-triggered fault-tolerant control for a quadrotor unmanned aerial vehicle with scheduled performance

This paper focuses on fuzzy wavelet neural networks-based adaptive finite-time self-triggered fault-tolerant control design with assured tracking performance for a quadrotor unmanned aerial vehicle subject to unknown actuator faults. First, an improved finite-time performance function is integrated with the command-filtered backstepping control framework to assure the scheduled tracking performance, which can effectively constrain the transient fluctuations of the tracking error at fault occurrence. Then, two compensation mechanisms are developed to weaken the adverse impact induced by actuator faults and filter errors. Further, a fuzzy wavelet neural adaptive self-triggered fault-tolerant controller with guaranteed performance is designed to improve the fault insensitivity and tracking accuracy of the controlled vehicle, where the fuzzy wavelet neural networks are employed to approximate the unknown nonlinearities and the control signals are allowed to achieve irregular updating only when the pre-specified trigger protocol is violated. Stability analysis proves that the designed controller guarantees the attitude and position subsystems are practical finite-time stable, and the tracking errors are strictly confined to a preassigned region and never cross its allowed bounds. Finally, the validity of the developed control scheme is confirmed by the simulation results.

Event‐triggered adaptive tracking control for stochastic nonlinear systems under predetermined finite‐time performance

SummaryIn this paper, an event‐triggered adaptive tracking control strategy is proposed for strict‐feedback stochastic nonlinear systems with predetermined finite‐time performance. Firstly, a finite‐time performance function (FTPF) is introduced to describe the predetermined tracking performance. With the help of the error transformation technique, the original constrained tracking error is transformed into an equivalent unconstrained variable. Then, the unknown nonlinear functions are approximated by using the multi‐dimensional Taylor networks (MTNs) in the backstepping design process. Meanwhile, an event‐triggered mechanism with a relative threshold is introduced to reduce the communication burden between actuators and controllers. Furthermore, the proposed control strategy can ensure that all signals of the closed‐loop system are bounded in probability and the tracking error is within a predefined range in a finite time. In the end, the effectiveness of the proposed control strategy is verified by two simulation examples.

A Novel Communication Time-Delay Cooperative Control Method with Switching Event-Triggered Strategy

A novel communication time-delay classification-based method is designed for nonlinear multiagent systems with the finite-time prescribed performance function. The time-delay phenomenon for communication channels between agents is discussed. Then, an improved time-delay classification method is proposed to broaden the standard of classification mechanism by considering the degree of deviation and relative variation of neighbor agents, rather than classifying the delay time into large time-delay and small time-delay. Based on this, the unified Lyapunov-Krasovskii functional and the finite-time performance function are used to solve the large time-delay phenomenon and ensure that the error is within the preset boundary, respectively. Furthermore, a modified switching event-triggered strategy is put forward to reduce the transmission burden, which considers the impact of tracking error to adjust the threshold condition in real-time. Additionally, all signals of the closed-loop systems are bounded. Eventually, two simulation examples verify the validity of the control strategy.

Safe tracking control based on a secure boundary protection method for nonlinear systems with unknown initial tracking condition

Aiming to the sudden change of the system actual output constraint, a novel safe tracking control strategy is investigated for a class of non-strict feedback nonlinear systems with unknown initial tracking condition in this paper. A secure boundary protection method (SBPM) based on prescribed performance and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can automatically construct two adjustable secure boundaries, so that the system output meets both the control performance prescribed by the PFTPF and the secure boundary constraint. In order to solve the problem of the excessive control input jitter caused by the sudden change of output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed SBPM can effectively ensure the safe tracking control of the system with unknown initial tracking condition when the actual output constraint changes suddenly, and ensure that the system has the prescribed finite-time control performance given by the PFTPF. Differently from the existing works, the system output will be strictly constrained into the actual output constraint without the prediction for the system output value. Finally, the effectiveness of this proposed method is verified by simulations.

Observer-Based Fault-Tolerant Finite-Time Control of Nonlinear Multiagent Systems.

In this article, an adaptive neural containment control for a class of nonlinear multiagent systems considering actuator faults is introduced. By using the general approximation property of neural networks, a neuro-adaptive observer is designed to estimate unmeasured states. In addition, in order to reduce the computational burden, a novel event-triggered control law is designed. Furthermore, the finite-time performance function is presented to improve the transient and steady-state performance of the synchronization error. Utilizing the Lyapunov stability theory, it will be shown that the closed-loop system is cooperatively semiglobally uniformly ultimately bounded (CSGUUB), and the followers' outputs reach the convex hull constructed by the leaders. Moreover, it is shown that the containment errors are limited to the prescribed level in a finite time. Eventually, a simulation example is presented to corroborate the capability of the proposed scheme.

Dynamic Threshold Finite-Time Prescribed Performance Control for Nonlinear Systems With Dead-Zone Output.

This article investigates the tracking control problem for nonlinear systems. An adaptive model is proposed to represent the dead-zone phenomenon and solve its control challenge with a Nussbaum function in conjunction. Drawing inspiration from the existing prescribed performance control schemes, a novel dynamic threshold scheme is developed that fuses a proposed continuous function with a finite-time performance function. A dynamic event-triggered strategy is applied to reduce the redundant transmission. The proposed time-varying threshold control strategy has fewer updates than the traditional fixed threshold and improves the efficiency of resource utilization. A command filter backstepping approach is employed to prevent the complexity explosion faced by the computation. The suggested control strategy ensures that all system signals are bounded. The validity of the simulation results has been verified.

Distributed adaptive sliding-mode control for 2-D plane vehicle platoon with prescribed performance and angle constraint

This paper focuses on the distributed adaptive sliding-mode control problem for two-dimensional (2-D) plane vehicle platoon with prescribed performance, angle constraints, and actuator faults. The quadratic spacing policy (QSP) is first adopted for the 2-D plane vehicle platoon to adjust the inter-vehicle spacing. The spacing error can converge within a finite time to the small region predetermined by a new finite-time performance function (FTPF). Meanwhile, a new transformed error function is introduced to convert the FTPF-constrained spacing errors into equivalent unconstrained ones. Besides, the property of the invertible nonlinear mapping function is used for the original system with the angle constraint to get a new unconstrained system. Moreover, a new controller based on hyperbolic tangent function is designed to handle actuator faults occurring multiple times over a period. Furthermore, the stability and string stability of the 2-D plane vehicle platoon are achieved through sliding-mode control. Finally, the simulation results validate the effectiveness of the proposed techniques.

Adaptive finite-time prescribed performance tracking control for hydraulic servo systems with friction compensation

Hydraulic systems present numerous challenges in the development of high-performance tracking controllers due to their highly nonlinear characteristics and heavy modeling uncertainties. Addressing this issue, this paper presents a friction compensation-based finite-time tracking control strategy with prescribed performance constraints. The system model is first derived, taking into consideration the nonlinear behaviors and potential uncertainties encountered in practical scenarios. Then, an adaptive finite-time prescribed performance controller is synthesized based on the backstepping framework. A novel form of finite-time performance function is introduced to constrain the tracking error, which provides the closed-loop system with a less complex guarantee of finite-time convergence and can also deliver the required transient performance and steady-state accuracy. Additionally, given the impact of uncertainty terms and the difficulty in obtaining the virtual command derivative, we employ neural networks (NNs) to estimate unknown dynamics and introduce command filters to acquire the intermediate signals, simplifying the backstepping control design process. Theoretical analysis indicates that the proposed control strategy can achieve the desired tracking performance and ensure the stability of the entire closed-loop system. Comparative numerical simulations are presented to confirm the usefulness of the suggested approach.

Improved finite-time prescribed performance super-twisting sliding mode united control framework for underwater vehicle-manipulator system

This paper investigates the trajectory tracking control problem for underwater vehicle-manipulator system (UVMS) with model uncertainties, dynamic coupling effects and external disturbances. Firstly, an improved finite-time performance function (IFTPF) is proposed to ensure the prescribed tracking accuracy with predefined convergence time while avoiding singularities in the system and enhancing robustness. Additionally, to reduce the controller’s dependence on the system model and compensate for unknown external disturbances, a neural network (NN) estimator is proposed to estimate the combination of system uncertainties and dynamic coupling effects, while a neural network-based nonlinear disturbance observer (NNDO) addresses the unknown external disturbances. Furthermore, an improved finite-time prescribed performance super-twisting sliding mode control framework using neural network-based disturbance observer (NNDO-IFTPPSTSMC) is proposed to ensure control accuracy and robustness while reducing chattering phenomenon. Theoretical analysis demonstrates that corresponding error variables of the system are bounded, and the trajectory tracking errors satisfy the prescribed performance constraints. Finally, simulation results validate the effectiveness and feasibility of the proposed method.

Adaptive prescribed finite-time asymptotic tracking control for switched systems with unknown initial conditions and full-state constraints

In this paper, an adaptive prescribed finite-time asymptotic tracking control problem is considered for the unknown nonlinear switched systems with unknown initial conditions and full-state constraints. A class of nonlinear mappings (NMs) and a new prescribed finite-time performance function (PFTPF) are introduced so that the control design is independent of initial conditions of the controlled states. Based on the neural network approximation approach, NMs, PFTPF and the Barbalat's lemma, an adaptive prescribed finite-time asymptotic tracking controller with full-state constraints is obtained. To avoid overlarge initial control input, the design method with zero initial control input is adopted, the definition of input tuning function (ITF) is expanded and its effectiveness is proved theoretically. As results, the full-state constraints and the boundedness of all the signals in the closed-loop system are guaranteed, and the tracking error of the system can converge to zero asymptotically. Finally, the effectiveness and superiority of the proposed scheme are verified by the simulation results.

Improved finite-time prescribed performance based adaptive neural control for nonlinear systems with sensor faults

In this article, based on a novel finite-time prescribed performance function, we consider the issue of the adaptive neural fault-tolerant tracking control problem for a type of nonlinear system with sensor faults. The control performance of the system may be affected when sensor faults occur. For the controlled system with sensor faults, an improved finite-time performance function is proposed so that its initial conditions do not need to be set in advance. Compared with existing performance functions, the performance functions in this paper can ensure that the system is always controllable, even if the sensor faults occur suddenly during the steady operation. Moreover, Radial basis function (RBF) neural networks (NNs) are employed to estimate the uncertain smooth nonlinear functions. With the help of the adaptive backstepping control technique, an improved adaptive prescribed performance control technique is developed, which can realize the boundedness of every signal in the closed-loop system, and the tracking error can be limited within the neighborhood near the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive finite-time fault-tolerant control for Robot trajectory tracking systems under a novel smooth event-triggered mechanism

The problem of adaptive finite-time fault-tolerant control with smooth event-triggered mechanism is addressed for quadrotor trajectory tracking systems. In light of recent studies on fault-tolerant control in the field of nonlinear systems, this article focuses on quadrotor trajectory tracking systems with actuator faults and disturbances. Different from the previous works, an ingenious smooth event-triggered mechanism is proposed to circumvent the discontinuous triggered signal and alleviate the communication burden simultaneously, which is of great significance to increase the operation life of the quadrotor. Subsequently, the finite-time performance function is designed to guarantee the prescribed tracking performance. Furthermore, a novel finite-time convergent adaptive fault-tolerant controller is proposed via the time-varying barrier Lyapunov function technique. The radial basis function neural networks are utilized to deal with the nonlinear approximation, and the adaptive laws are developed to accurately estimate the unknown model uncertainty, thus effectively handling the challenge of the controller design caused by the actuator faults and disturbances. Under the developed adaptive fault-tolerant controller, all the closed-loop system signals are bounded and the tracking errors are convergent within finite time. Meanwhile, the Zone behavior can be excluded by the positive sampling intervals. Finally, two examples are employed to verify the effectiveness and advantages of the suggested control scheme.

Finite-time ADRC formation control for uncertain nonaffine nonlinear multi-agent systems with prescribed performance and input saturation

AbstractThis paper explores finite-time formation control of multi-agent systems (MASs) with high-order nonaffine nonlinear dynamics and saturated input. Based on active disturbance rejection control theory, extended state observer is employed to identify unknown nonaffine nonlinear functions in MASs. The proposed control law consisting of backstepping control, tracking differentiator, and finite-time performance function is adopted for MASs to achieve the desired formation while reaching performance requirements. An auxiliary dynamic compensator is introduced to correct the control deviation caused by input saturation. Lyapunov stability theory is utilized to analyze the stability of the closed-loop system, which guarantees that the formation tracking error can asymptotically converge to an arbitrarily small neighborhood around zero in finite time. Finally, the simulation results show that compared to the adaptive, cooperative learning, and virtual structure methods, the proposed control algorithm has stronger tracking ability and faster setting time (1.8 s) under the influence of nonaffine nonlinear uncertainties. The integral square error for the formation control strategy in this paper is 0.16, which is much smaller than the abovementioned methods and is therefore provided to manifest the validity and feasibility of the proposed control strategy.

Reduced-Order Observer-Based Preassigned Finite-Time Control of Nonlinear Systems and Its Applications

In this article, a preassigned finite time control problem of nonlinear systems in strict-feedback form is investigated. From the perspective of arbitrary settling time, an appropriate preassigned finite-time performance function (PFPF) is constructed, and the preassigned finite-time stability (PAFS) is established, where the settling (convergence) time is not only completely unconcerned with initial conditions and design parameters but also more flexible. Furthermore, the backstepping technique and reduced-order observer are used to obtain the preassigned finite-time control scheme. The stability criteria of PAFS are developed to guarantee that the output can quickly converge to an arbitrarily small zone in preassigned time, and all signals of the closed-loop control system are PAFS. In the end, simulation examples verify the effectiveness of the presented method.

Distributed adaptive cooperative control via command filters for multi-agent systems including input unmodeled dynamics and sensor faults

This study focuses on the topic of distributed adaptive cooperative tracking control (CTC) for non-strict feedback multi-agent systems (MASs) including input unmodeled dynamics, prescribed performance, sensor faults and unknown control directions. An adaptive neural CTC tactic is raised via command filtered backstepping technique. With the help of the property of Gaussian function, the barriers produced by the non-strict feedback terms and partial sensor faults are handled. Moreover, the prescribed performance on measured synchronization error is considered by designing a finite-time performance function. By introducing normalization signals and adjusting parameters, the problems caused by input unmodeled dynamics are resolved. The compensation signals and normalization signals are integrated into the whole Lyapunov function in the stability analysis. All the variables in the controlled system are turned out to be semi-globally uniformly ultimately bounded (SGUUB). Meanwhile, the synchronization errors never exceed to predefined boundary. A simulation example is employed to confirm the viability of the constructed control method.

Cooperative learning formation control of multiple autonomous underwater vehicles with prescribed performance based on position estimation

This paper proposes a cooperative learning formation control method with finite-time prescribed performance based on position estimation for parametric path tracking of multiple autonomous underwater vehicles (AUVs) with uncertainties and external disturbances. The parametric path used in the control law permits the velocity to be specified independently while tracking the path accurately. The localized radial basis function neural networks learn the uncertainties cooperatively while tracking the period path, and the knowledge gained from learning is utilized to construct an empirically based formation control law using experience to cope with similar uncertainties rather than repeatedly using adaptive methods, which reduces the computing burden. The position of the leader is assumed to be available only for the leader's neighboring AUV, and a novel finite-time distributed observer is presented for the followers to estimate the leader's position. Based on this, the control law is derived from the prescribed performance control method using a finite-time performance function rather than exponential decaying function to enable the tracking error converges in finite time, which accelerates the learning process. The simulation results confirm the validity of the presented control protocol.

Finite-time prescribed performance trajectory tracking control for the autonomous underwater helicopter

To address the complex trajectory tracking problem of AUH near the seabed when performing high-precision operations such as comprehensive underwater inspections for offshore engineering structures, a prescribed performance control strategy with a finite-time performance function (FTPF) and the fast terminal sliding surface is proposed. The influence of ocean current is fully considered by the combination of ocean current velocity estimated by a current observer and ocean current disturbance in the dynamic model. An arctan-type disturbance observer and neural network are designed to compensate for environmental disturbances, model uncertainty, and thruster failure effects on the system. The system stability is proven by the Lyapunov method, and the numerical simulation shows that the proposed scheme is effective, robust, and efficient, even under disturbances and thruster failure.

Fuzzy-Based Robust Precision Consensus Tracking for Uncertain Networked Systems With Cooperative–Antagonistic Interactions

In bipartite consensus tracking (BCT) tasks for nonlinear multiagent systems, stochastic disturbances and actuator faults are regarded as essential factors that hamper effective controller formulation and tracking precision improvement. To address these difficulties, we design an improved finite-time performance function (FTPF) for a fuzzy fault-tolerant distributed cooperative control scheme to achieve finite-time robust precision BCT tasks for nonlinear multiagent systems. The parameter selection range of the improved FTPF is relaxed, which renders systems to achieve better transient performance. Benefitting from stochastic Lyapunov stability theory, it is shown that all signals of systems are semi-global uniformly ultimately bounded in probability, and bipartite consensus errors can satisfy the arbitrary precision with probability in the predefined time. Finally, to verify its effectiveness, the proposed control scheme is applied to BCT tasks of a group of vehicles, which manifests anticipated control performance under various uncertainties.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

Fixed-Time Fault-Tolerant Formation Control for a Cooperative Heterogeneous Multiagent System With Prescribed Performance

This article investigates the fixed-time fault-tolerant formation control problem of a leader–follower heterogeneous multiagent system (HMAS), including multiple unmanned aerial vehicles (UAVs) and multiple unmanned ground vehicles (UGVs) under loss of effectiveness actuator faults and disturbances. Different from the existing fixed-time formation results, to realize the special application, a finite-time performance function (FTPF) is considered, which can guarantee that formation error converges to a prescribed arbitrarily small region within a known time. Then, based on sliding mode control and bi-limit homogeneity, distributed and decentralized fixed-time formation control algorithms are constructed for the HMAS in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> axis and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> axis, respectively, which can steer the whole system achieving target formation configuration within a scheduled time. In addition, based on local state information, adaptive online updating strategies for unknown actuator efficiency factors and lumped uncertainties are proposed. Then, under the online updating parameters, two novel distributed and decentralized adaptive fault-tolerant formation control laws are presented using practical fixed-time stability theory, which not only achieves stable formation tracking with finite-time prescribed behavioral metrics but also ensures that the formation errors are uniformly bounded within a settling time. Finally, the effectiveness of the developed control schemes is verified by simulation examples.