Fuzzy Finite-time Control Research Articles

Combining finite-time control and prescribed tracking performance for uncertain PMSM driven steer-by-wire system with unknown disturbance

To solve the uncertainties in permanent magnet synchronous motor (PMSM) driven steer-by-wire (SbW) system, a prescribed-performance-control (PPC) based finite-time fuzzy controller is proposed. Specifically, the dynamics of SbW system driven by PMSM is analyzed, and combine PPC technology to transform the tracking error coordinates. Then, the velocity signal is obtained from the sigmoid function-based tracking differentiator by using the position signal. To solve the problem of mismatched disturbance, fuzzy logic system (FLS) are used as a universal approximator to estimate the lumped nonlinear friction and other unknown functions, the boundary of lumped disturbance is estimated by the designed adaptive updating law. By fusing the designed virtual controller and the intermediate control law, the controller needs no precise parameters of system, under which the effect of uncertainty of control gain can be compensated completely. Finally, rigorous theoretical analysis based on the Lyapunov stability theory is provided to demonstrate the finite-time stability of the closed-loop system under consideration. Simulation and experiment results are presented to show the effectiveness of the developed control approach, and some comparisons are given to show the rapid and accurate position tracking control performance.

Event-Triggered Adaptive Fuzzy Finite-Time Control for Steer-by-Wire Vehicle Systems

Event-Triggered Adaptive Fuzzy Finite-Time Control for Steer-by-Wire Vehicle Systems

Approach to Gait Coordination: Adaptive Fuzzy Finite-Time Control of a Stochastic Prosthesis-Human Symbiosis With Intentional Delay

The generation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">intentional delay</i> in response to the stride frequency is seldom considered in prosthesis-human symbiosis. Unfortunately, such intentionally delayed human-robot interaction poses a new challenge to their gait coordination in stochastic environments. Utilizing fuzzy logic systems (FLSs), we investigate an adaptive fuzzy finite-time control of a stochastic prosthesis-human symbiosis with intentional delay to address this issue. Noting that the intentional delay is related to walking velocity, this work conducts experiments on ten healthy subjects to identify the intentional delays at different velocities using the FLS. Introducing the FLS-identified delay and contralateral healthy limb gaits, we propose a prosthetic gait planner to simultaneously determine the reference stride frequency and stride length, thus properly regulating the desired velocity. Considering the adverse effects of the required intentional delay and state constraints in the stochastic framework, we propose a new statistical Lyapunov-Krasovskii functional, together with a Tan-type barrier Lyapunov function. Correspondingly, an adaptive fuzzy controller is developed via a backstepping design, thus solving the semi-global finite-time stable in probability with intentional delay, unknown nonlinearities, and state constraints. Application studies validate the efficacy of the proposed approach. The results show that our approach can predict walking behavior while performing gait coordination.

Adaptive Finite-Time Fuzzy Control for Uncertain Nonlinear Systems with Asymmetric Full-State Constraints

This paper studies the adaptive finite-time fuzzy control issue associated with uncertain nonlinear systems that exhibit asymmetric constraints on the full state. A distinct function, constrained by nonlinear states, is designed to mitigate the excessive breach of these full-state boundaries. Unlike the standard barrier Lyapunov function (BLF) method, this approach solves symmetric and asymmetric full-state constraints without modifying the controller structure, and it does not require any additional assumptions about virtual control to be met. Simultaneously employing approximating functions using fuzzy logic systems and incorporating dynamic surface control technology integrated with a first-order filter, the unknown nonlinear functions emanating from the suggested controller strategy are estimated. Additionally, this approach addresses the prevalent problem of complexity explosion observed in conventional backstepping techniques. An adaptive finite-time fuzzy tracking control strategy is introduced, ensuring that all signals and tracking errors of the controlled system remain bounded in finite time. Finally, two simulation examples are given to illustrate the effectiveness of the proposed control scheme, confirming that all states remain within the predefined regions.

Event-triggered finite-time fuzzy control approach for fractional-order nonlinear chaotic systems with input delay

In this paper, a novel fuzzy event-triggered control approach with guaranteed performance of practical finite-time tracking convergence is constructed for uncertain fractional-order nonlinear chaotic systems in the presence of time-varying input delay. Firstly, fuzzy logic systems are employed to deal with immeasurable systematic information. Secondly, fractional-order command filters are incorporated to circumvent the problem of “complexity explosion” in backstepping controller construction. Meanwhile, a sequence of fractional-order finite-time compensation signals are introduced to counteract the adverse influence of time-varying input delay rapidly. Furthermore, a novel practical finite-time chaos control approach based on event-triggered strategy is proposed, which not only facilitates the decrease of sampling frequency and controller burden dynamically, but also ensures the convergence of all tracking errors towards a small region around the origin in finite time. Finally, through the simulation research, the transient response performance and the chaos-suppression ability of fractional-order chaotic systems stabilized via the suggested approach are rigorously testified.

Continuous finite-time fuzzy control of mechanical systems via non-Lipschitz membership functions

This document presents a method to construct continuous fuzzy controllers that yield finite-time stability of the closed-loop system. The proposed approach allows the user to follow classical design procedures for fuzzy systems without using other finite-time techniques such as sliding modes. The finite-time stability property is a consequence of a special kind of input membership function of the fuzzy inference system.The continuity properties of the fuzzy inference system are studied. Sufficient conditions for the output of the fuzzy inference system to be Lipschitz continuous are stated.A comparison with the asymptotic counterpart of the controller is also presented. The results support the hypothesis that finite-time controllers provide improved robustness to the steady state response.

Event-Based Design for Decentralized Fuzzy Finite-Time Control of Interconnected Switched Nonlinear Systems Against Sensor Failure

Event-Based Design for Decentralized Fuzzy Finite-Time Control of Interconnected Switched Nonlinear Systems Against Sensor Failure

Adaptive finite-time fuzzy control for hybrid levitation system of maglev trains with active anti-lock constraints

The great risk of the suspension contact tremendously restricts the practical public service of hybrid maglev trains. If an operational train contacts to the guideway resulting in the “lock” state, it would cut down its lifetime or even endanger passenger safety. To address the deadlock problem of hybrid maglev trains, a novel adaptive finite-time fuzzy control with active anti-lock constraints is proposed in this paper. First, an efficient fuzzy-logic system is applied to approximate the hybrid levitation dynamics, not only precisely describing the system but also reducing computation burden. Moreover, by a novel nonlinear coordinate transformation, an anti-lock levitation controller is designed to prevent suspension contact between trains and guideways via the back-stepping technique. In the process, command filtering is utilized to circumvent the derivatives of virtual control variables and to address practical input constraints. Differing from the barrier Lyapunov function technique, the proposed nonlinear transformation helps to directly address both positive lower and upper boundaries. In addition, finite time convergence is achieved by the proposed scheme, which enjoys the characteristics of a fast and quantifiable response. Numerical simulations verify the theoretical results.

Command Filter-Based Adaptive Fuzzy Finite-Time Tracking Control for Uncertain Fractional-Order Nonlinear Systems

In this article, we focus on the issue of adaptive fuzzy finite-time tracking control for a class of uncertain fractional-order nonlinear systems with external disturbance. A new finite-time fractional-order command filtered implementation scheme is presented for the adaptive backstepping method. In the command filtered implementation approach, analytical computation of the fractional derivatives of the stabilizing functions is not necessary. Therefore, the controller and adaptive law of the systems are easier to derive and implement. Based on the proposed command filter, adaptive backstepping technique, and fractional Lyapunov’s direct method, a novel adaptive fuzzy finite-time controller is designed, which can guarantee that the tracking error converges to a small neighborhood of the origin in finite time, and other signals of the closed-loop systems are semiglobal uniform ultimate bounded. In the design process of the controller, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions, and an auxiliary function is adopted to compensate for the unknown external disturbance and approximation errors of FLSs. Finally, a simulation example is given to show the effectiveness and availability of the proposed control strategy.

Fast Finite-Time Fuzzy Control for a Class of Nonstrict Feedback Systems with Input Quantization

Fast Finite-Time Fuzzy Control for a Class of Nonstrict Feedback Systems with Input Quantization

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.

Command Filter Approximation-Based Finite-Time Fuzzy Control for Induction Motor with Full State Constraints

Command Filter Approximation-Based Finite-Time Fuzzy Control for Induction Motor with Full State Constraints

Adaptive fuzzy finite-time control with prescribed performance for waverider vehicles

This paper proposes an adaptive fuzzy control method with prescribed performance for Waverider Vehicles (WVs), being able to guarantee finite-time convergence and small overshoot for tracking errors. Firstly, we design a new type of performance function that is independent of the initial error, and possess finite-time convergence and small overshoot. Then, we transform the inequality constraints on tracking errors into an unconstrained equation by introducing a transformed error. On this basis, we design a prescribed performance control (PPC) approach to limit the tracking errors within prescribed funnels utilizing the transformed error and fuzzy approximation, which ensures that satisfactory transient performance and steady-state accuracy can be guaranteed for tracking errors. Compared with the existing PPC, the improvement is to assure finite-time convergence of tracking errors with almost zero overshoot. Finally, compared simulations are given to verify the advantage.

Adaptive Fuzzy Finite-Time Control for a Class of Stochastic Nonlinear Systems with Input Saturation

Adaptive Fuzzy Finite-Time Control for a Class of Stochastic Nonlinear Systems with Input Saturation

Finite-Time Fuzzy Control for Nonlinear Singularly Perturbed Systems With Input Constraints

Singularly perturbed systems have found widespread applications in practice. The existing results on singularly perturbed systems mainly focused on the Lyapunov asymptotic stability, which are unable to deal with the cases that the system states cannot exceed a given threshold during a fixed time interval. This article addresses the finite-time fuzzy control issue for discrete-time nonlinear singularly perturbed systems with input constraints. The aim is to guarantee the boundedness of the states of singularly perturbed systems during a finite-time interval. Based on the matrix inequality technique, some conditions are established to guarantee the finite-time boundedness of the fuzzy singularly perturbed systems, where the singularly perturbed parameter is independent so as to avoid the ill-conditioned problem caused by the small singularly perturbed parameter. The gains of the finite-time fuzzy controller can be obtained by solving some singularly perturbed parameter independent linear matrix inequalities. Finally, the proposed finite-time fuzzy controller design approach for nonlinear singularly perturbed systems is illustrated via the Van der Pol circuit.

Adaptive Fuzzy Finite-Time Control for Nonstrict-Feedback Nonlinear Systems.

This article presents an adaptive fuzzy finite-time control (AFFTC) method for nonstrict-feedback nonlinear systems (NFNSs) with unknown dynamics. With the aid of the backstepping technique, by establishing the smooth switch function (SSF), a novel C1 AFFTC strategy is recursively constructed, which counteracts the effect of nonstrict-feedback structure and unknown dynamics. Different from the reporting finite-time control achievements, the singularity hindrance derived from the differentiating virtual control law is availably surmounted. Moreover, the developed AFFTC strategy can drive the tracking error to converge into a small neighborhood of the origin in a finite time. Simulation results are conducted to substantiate the efficacy of theoretical findings.

Adaptive fuzzy finite-time control of stochastic nonlinear systems with actuator faults

This paper considers the finite-time control problem for a class of nonlinear stochastic systems with actuator faults/failure. A fast convergence feedback control algorithm based on backstepping finite-time command filtering is proposed. Under the framework of adaptive feedback, the fuzzy logic system is used to deal with the uncertainties of the system. Taking into account the actuator faults of both loss of effectiveness and lock-in-place, an adaptive fuzzy controller is developed. Since there is no need to calculate the derivative of the virtual control signal, the presented scheme overcomes the “explosion of complexity” problem inherent in conventional methods. A compensation mechanism is also introduced to compensate for errors caused by the filter. The proposed method ensures not only that all signals of the closed-loop system are finite-time bounded, but also that the tracking error converges to a small neighborhood around the origin. The effectiveness of the proposed method is demonstrated in the simulation results.

Fault-tolerant finite-time fuzzy control for nonlinear power systems with time delays and actuator faults

To ensure the stability of nonlinear power systems with actuator faults and time delays, this study aims to design an adaptive fuzzy finite-time control scheme. To deal with this control issue, firstly, we propose an adaptive fault-tolerant finite-time controller using backstepping technique. To aid the controller design, fuzzy logic systems are applied to approximate the uncertain nonlinear terms without the prior information. Then, it is proved that the designed controller can ensure the stability in a finite time for the nonlinear power systems with actuator faults and time delays using Lyapunov–Krasovskii method. Finally, numerical simulations of a 4-machine power system with Thyristor Controlled Series Compensation (TCSC) illustrate the applicability of the proposed control methodology.

Disturbance Observer-Based Adaptive Fuzzy Control for Strict-Feedback Nonlinear Systems With Finite-Time Prescribed Performance

This article studies the disturbance observer-based adaptive fuzzy finite-time control issue of strict-feedback nonlinear systems. Specifically, to meet practical application requirement, the finite-time prescribed performance is considered, which can guarantee the tracking error enters into the prescribed bounded set in a known time. A disturbance observer is proposed to estimate the external disturbance. It is proved that the closed-loop system is semi-globally practically finite-time stable. Finally, simulation studies for a one-link manipulator are shown to verify the effectiveness of the proposed approach.

Observer-Based Adaptive Fuzzy Finite-Time Control Design With Prescribed Performance for Switched Pure-Feedback Nonlinear Systems

In this paper, an adaptive fuzzy finite-time control problem for pure-feedback switched nonlinear systems with prescribed performance is investigate. By utilizing the prescribed performance technique, we mean that the system output is converge to the predefined bounds. By using the dynamic surface control (DSC) and the backstepping technique, we establish a novel adaptive fuzzy finite-time pure-feedback switching control method. In such a scheme, the Butterworth low-pass filter (LPF) is used to construct the fuzzy observer, which can estimate the immeasurable states and avoid algebraic loop problem. In accordance with the stability theory of common Lyapunov function (CLF), the designed controller can ensures that the tracking error converges to a small neighborhood of the origin in finite time. Finally, an example is given to illustrate this method and verify its validity and effectiveness.