Finite-time Performance Function Research Articles

Adaptive Fuzzy Prescribed Finite-Time Tracking Control for Nonlinear System With Unknown Control Directions

This article investigates the prescribed finite-time control for the nonlinear system with uncertain nonlinearity and unknown control directions. Different from the existing finite/fixed-time control methods on the basis of the fractional-order state feedback, the proposed finite-time control in this article only employs regular state feedback. The key is that a novel prescribed finite-time performance function is introduced such that the controller design is under the standard Lyapunov stability theoretical framework. A lemma is developed as a tool for coping with the coexistence of multiple Nussbaum gains for the stochastic system with unknown control directions. Fuzzy logic systems are used to approximate the uncertain nonlinear functions. Applying the backstepping structure, an adaptive fuzzy control scheme is developed. The salient characteristic of the proposed control is that the finite convergence time and the accuracy of the tracking error are independent of the initial states and design parameters, and that can be assigned in a prior. Two examples are given to demonstrate the feasibility and effectiveness of the proposed control scheme.

Finite-Time-Prescribed Performance-Based Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems With Dynamic Uncertainty and Actuator Faults.

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.

Event-Triggered Fuzzy Adaptive Leader-Following Tracking Control of Nonaffine Multiagent Systems With Finite-Time Output Constraint and Input Saturation

This article considers the problem of distributed adaptive fuzzy event-based finite-time prescribed performance leader-following tracking control for heterogeneous nonlinear multiagent systems (NMASs) over a directed topology. Each agent is considered in a nonaffine nonstrict-feedback form under input saturation and output constraint which contains unknown dynamics and external disturbances. Fuzzy logic systems (FLSs) are exploited as an effective online approximation tool to tackle system uncertainties. By employing the unique property of FLS, the algebraic loop problem is overcome and by designing novel adaptive laws of the FLS weights, the computation burden is decreased significantly. The threshold of the event-triggered condition is improved compared to the conventional relative-threshold mechanism. A modified performance function called finite-time performance function is introduced to constrain the synchronization errors within the prescribed performance bounds in finite time. The dynamic surface control technique is then developed to avoid the issue of the “explosion of complexity.” Moreover, by developing a new decomposition for the controller gain function resulting from the mean-value theorem and introducing an auxiliary system, the input saturation nonlinearity that affects the nonaffine form stability is handled. Through the Lyapunov stability analyses, it is shown that the developed control algorithm ensures the closed-loop NMAS trajectory to be cooperatively semi-globally uniformly ultimately bounded. Additionally, the tracking errors are driven to a predefined region around zero in finite time. Finally, the efficiency of the established theoretical results is validated by the simulation studies.

Decentralised adaptive prescribed performance finite-time tracking control for a class of nonlinear interconnected systems with unknown control directions

In this paper, the decentralized adaptive prescribed performance finite-time tracking control problem is investigated for a class of interconnected non-affine nonlinear systems with unmodeled dynamics, unknown control direction and unknown dead zone. A novel tracking control strategy combining Nussbaum-gain technique with finite-time control is presented. The designed controller can guarantee that tracking error of each subsystem is constrained by finite-time performance function and converges to the given neighborhood of the equilibrium point within a given arbitrarily settling time. Meanwhile, all the signals in the closed-loop interconnected system are bounded. In addition, the problem that the prescribed performance control method is difficult to realize decentralized control is solved by means of a special mathematical transformation. Specifically, the settling time is a design parameter which is independent of the system initial states in this method. The simulation results are presented to demonstrate the feasibility and superiority of the proposed control method.

Novel finite-time adaptive neural control of flexible spacecraft with actuator constraints and prescribed attitude tracking performance

A novel finite-time neural control strategy is proposed for flexible spacecraft with guaranteed attitude tracking performance subject to parametric uncertainty, uncertain external disturbance, unmeasured elastic vibration and actuator saturation. First, a new finite-time performance function is developed. Then, unlike some existing prescribed performance control methodologies, a novel finite-time controller is derived to guarantee that the attitude tracking errors can converge to a preselected range of the equilibrium within predetermined time independent of the initial conditions. The derived controller is then extended by a neural network compensator to reject the disturbance and overcome the unknown actuator saturation. Specially, the computation burden is reduced by updating the norm of ideal weight vectors rather than their elements with the aid of minimal-learning-parameter technique. Finally, apart from showing the stability of the closed-loop system, numerical simulations demonstrate the effectiveness, robustness and superiority of the proposed approach.

Adaptive fuzzy controller design for dynamic positioning ship integrating prescribed performance

This paper investigates the trajectory tracking control problem of dynamic positioning ship subject to modeling uncertainties, environment disturbances, and unmeasurable velocity. A novel adaptive fuzzy controller is designed to address this challenging problem, by incorporating the prescribed performance control technique and adaptive fuzzy backstepping control method. Specifically, a high-gain observer is constructed to estimate the unmeasurable velocity vector. Then, a special finite-time performance function is introduced to impose performance specifications in advance on the output tracking errors according to the mission requirements (in terms of mission completion time, maximum permitted overshoot, tracking accuracy). Subsequently, through introducing error transformation functions, the tracking control problem with guaranteed transient performance is transformed to the output constrained control problem. In view of this, an asymmetric barrier Lyapunov function is designed to ensure that the transformed errors remain within specified ranges. By virtue of Lyapunov theory, it is shown that all the closed-loop signals are uniformly ultimately bounded and the tracking errors strictly comply with the prescribed performance envelops, despite the presence of modeling uncertainties, environmental disturbances and unmeasurable velocity. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed method.

Adaptive neural network finite-time tracking control for a class of high-order nonlinear multi-agent systems with powers of positive odd rational numbers and prescribed performance

This paper addresses the adaptive finite-time consensus tracking problem for high-order nonlinear multi-agent systems (MASs) with powers of positive odd rational numbers under prescribed performance. Since the virtual and actual control parts of the dynamics of each follower agent are power functions containing positive odd rational numbers, the method of adding a power integrator is used to overcome the controller design difficulties caused by the power functions. With the aid of a finite-time performance function (FTPF) and neural networks (NNs), a distributed adaptive finite-time consensus tracking controller with prescribed tracking performance is properly designed by the backstepping process. It is shown that the proposed control strategy can guarantee that the consensus tracking error converges to an arbitrarily small neighborhood around zero at any settling time, while all signals of the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.

A Novel Adaptive NN Prescribed Performance Control for Stochastic Nonlinear Systems.

This article investigates the problem of neural network (NN)-based adaptive backstepping control design for stochastic nonlinear systems with unmodeled dynamics in finite-time prescribed performance. NNs are used to study the uncertain control plants, and the problem of unmodeled dynamics is tackled by the combination of the changing supply function and the dynamical signal function methods. The outstanding contribution of this article is that based on the finite-time performance function (FTPF), a modified finite-time adaptive NN control design strategy is proposed, which makes the controller design simpler. Eventually, by using the Itô's differential lemma, the backstepping recursive design technique, and the FTPFs, a novel adaptive prescribed performance tracking control scheme is presented, which can guarantee that all the variables in the control system are bounded in probability, and the tracking error can converge to a specified performance range in the finite time. Finally, both numerical simulation and applied simulation examples are provided to verify the effectiveness and applicability of the proposed method.

Finite-time prescribed performance adaptive fuzzy control for unknown nonlinear systems

This paper aims at the problem of finite-time prescribed performance adaptive fuzzy control for a class of unknown nonlinear systems. An adjustable finite-time performance function with faster convergence rate is applied to the procedure of the controller design, whose parameters can be adjusted in real time on the basis of the tracking error. Furthermore, a finite-time prescribed performance adaptive fuzzy tracking controller is designed by the backstepping method, which can guarantee that all the signals in the closed-loop system are bounded. Simultaneously, the output tracking error always stays within an adjustable boundary and converges to a fixed region at finite-time settling time. Besides, the tracking performance in transient state is slightly optimized. Simulation results demonstrate the effectiveness of the proposed controller.

Adaptive neural tracking control for non-affine nonlinear systems with finite-time output constraint

In this paper, an adaptive neural tracking control approach is presented for a class of non-affine nonlinear systems with finite-time output constraint. The non-affine form of the original system is converted to the affine form by means of the mean value theorem. To constraint the output tracking error within a predefined boundary in finite time, a modified performance function, i.e., finite-time performance function, is introduced. During the process of controller design, the dynamic surface control is employed to handle the ‘explosion of complexity’ problem occurred in the conventional backstepping method. According to the approximation of radial basis functions neural networks, an adaptive neural control scheme is developed which guarantees that the output tracking error is preserved within a specified prescribed performance and all the signals in closed-loop system are bounded by appropriately choosing the design parameters. The stability of the closed-loop system is proved by Lyapunov stability analysis and the simulation results are proposed to demonstrate the effectiveness of the developed control approach.

Adaptive finite-time prescribed performance control of switched nonlinear systems with unknown actuator dead-zone

ABSTRACTThis paper focuses on the adaptive finite-time tracking control problem for a class of nonstrict-feedback switched nonlinear systems with unknown nonsymmetric actuator dead-zone. By utilising a novel finite-time performance function (FTPF), the finite-time prescribed performance control (FTPPC) algorithm is first proposed for the considered system. In this design, the neural networks (NNs) are directly utilised to cope with the completely unknown nonlinear functions of the systems. Different from the existing results, the proposed scheme is able to guarantee that the tracking error converges to a prescribed zone at a finite-time and all the signals of the closed-loop system remain semi-globally practical finite-time stable (SGPF-stable). Simulation results are offered to illustrate the feasibility of the newly designed scheme.

Finite-Time Observer-Based Adaptive Control of Switched System with Unknown Backlash-Like Hysteresis

This work investigates a finite-time observer problem for a class of uncertain switched nonlinear systems in strict-feedback form, preceded by unknown hysteresis. By using a finite-time performance function, a finite-time switched state observer (FTSO) is derived using radial basis function neural networks (RBFNNs) to estimate the unmeasured states. An adaptive feedback neural network tracking control is derived based on the backstepping technique, which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to zero, and the observer error converges to a prescribed arbitrarily small region within a finite-time interval. In addition, two simulation studies and an experiment test are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

Direct Adaptive Preassigned Finite-Time Control With Time-Delay and Quantized Input Using Neural Network.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.

Adaptive neural practically finite-time congestion control for TCP/AQM network

Inspired by the prescribed performance control (PPC), a new performance function, called finite-time performance function (FTPF), is first defined in this paper, by which a novel finite-time control design process is introduced. This work is also the first to solve the finite-time control issue for a class of transmission control protocol/active queue management (TCP/AQM) networks. Meanwhile, with the aid of FTPF, PPC and neural networks, a new adaptive practically pre-assigned finite-time controller is designed, which guarantees that the queue length q(t) tracks the desired queue qref in finite-time and all the signals of the closed-loop system are semi-globally practical finite-time stable (SGPFS). Finally, simulation results are shown to illustrate the effectiveness of the proposed method.

A Novel Finite-Time Adaptive Fuzzy Tracking Control Scheme for Nonstrict Feedback Systems

This work investigates a finite-time adaptive fuzzy tracking control problem for a class of nonstrict feedback nonlinear systems from a new point of view. A new concept, named finite-time performance function (FTPF), is defined in this paper for the first time. Moreover, a finite-time adaptive state feedback fuzzy tracking controller is derived based on fuzzy approximation, backstepping technique and prescribed performance control (PPC), which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to a prescribed arbitrarily small region within a finite-time interval, and maximum overshoot is not more than a predefined level. In addition, a controller design process is given which is less complex than the existing finite-time control design methods. Three simulation studies are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

Adaptive fuzzy finite-time stability of uncertain nonlinear systems based on prescribed performance

The semi-globally practical finite-time stability (SGPFS) problem for a class of uncertain strict-feedback nonlinear systems is discussed in this paper. A novel performance function called finite-time performance function (FTPF) is first defined. Moreover, this paper is the first to solve an adaptive semi-globally practical finite-time control issue by combining with backstepping, prescribed performance control (PPC) and fuzzy logic systems. Furthermore, it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite-time, but also all the signals of the closed-loop systems are SGPF-stable. Simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method.

Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems

This work investigates the finite-time tracking control problem for a class of uncertain strict-feedback nonlinear systems from a new perspective. First, a novel concept called finite-time performance function (FTPF) is defined. Further, a new sufficient condition of finite-time stability is derived and the tracking error can converge to a predefined region within a finite-time interval. The design process of the proposed technique is simpler. Finally, four simulation examples are carried out to illustrate the effectiveness of presented method.

Practical finite-time almost disturbance decoupling strategy for uncertain nonlinear systems

A new practical finite-time almost disturbance decoupling result is presented for a class of strict-feedback nonlinear systems with multiple disturbances. Meanwhile, a novel performance function called finite-time performance function is first defined. Further, a practical finite-time tracking controller is designed by means of prescribed performance control, almost disturbance decoupling and backstepping technique. The designed controller makes the output error converge to a predefined arbitrary small area within a finite-time interval. The proposed design method is simpler and is easier to be achieved. Finally, it can be found from simulation examples that the effectiveness and superiority of this work is illustrated well.

Adaptive neural networks finite-time tracking control for non-strict feedback systems via prescribed performance

This paper focuses on the semi-globally practical finite-time tracking control problem for a class of nonlinear systems with non-strict feedback structure. Inspired by prescribed performance control (PPC), a new performance function called finite-time performance function (FTPF) is defined for the first time. With the aid of neural networks and backstepping, an adaptive finite-time tracking controller is properly designed. Different from the existing finite-time results, the proposed method can guarantee that the tracking error converges to an arbitrarily small region at any settling time and all the signals in the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Two simulation examples are given to exhibit the effectiveness and superiority of the presented technique.