Fuzzy Approximation Error Research Articles

Observer-based adaptive interval type-2 fuzzy control of uncertain MIMO nonlinear systems with unknown asymmetric saturation actuators

An observer-based controller is proposed for a class of uncertain MIMO nonlinear systems preceded by actuators with unknown asymmetric saturations. The gains of actuators are unknown nonlinear functions that are generally functions of states. The unknown nonlinearities are approximated by interval type-2 fuzzy systems where the consequent parameters are tuned adaptively. Meanwhile, the interval type-2 fuzzy systems due to their structure can cope with the uncertainties in antecedent membership functions. The states of the system do not need to be known. To tackle the unavailability of states an observer based on strictly positive real (SPR) theory is designed to estimate the states. To cope with the fuzzy approximation error and external disturbances an adaptive continuous robust structure is proposed. The continuous robust structure due to adaptiveness does not need the bound of uncertainties and due to continuity does not have the chattering problem. All the adaptive laws are derived via Lyapunov synthesis approach. Meanwhile, all the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded (SGUUB) and the mean-square tracking error can be made arbitrarily small. Simulation results reveal the effectiveness of the proposed method in terms of coping well with the uncertainties and saturation actuators while maintaining satisfactory performance.

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.

Fractional order fuzzy terminal sliding mode control of aerodynamics load simulator

Fractional order adaptive fuzzy continuous non-singular terminal sliding mode control is proposed for electrical aerodynamics load simulator system which is subjected to extra torque disturbance and parametric uncertainties. A fractional order sliding surface is constructed and a continuous non-singular terminal sliding mode control law is derived to ensure faster convergence and precise control without singularity problem. Fractional order adaptive fuzzy logic system is used to estimate the unknown extra torque disturbance. Moreover, nonlinear friction is compensated using LuGre model. Practically, electrical aerodynamics load simulator system is affected by additional un-modeled dynamics due to uncertainty in system parameters and friction model combined with fuzzy approximation error. The un-modeled dynamics are compensated using fractional order adaptive law which is derived using Lyapunov function. The validity and effectiveness of proposed control scheme are verified using numerical simulations.

Power Control of Wind Turbine Based on Fuzzy Sliding-Mode Control

This paper presents the study of a variable speed wind energy conversion system (WECS) using a Wound Field Synchronous Generator (WFSG) based on a Fuzzy sliding mode control (FSMC) applied to achieve control of active and reactive powers exchanged between the stator of the WFSG and the grid to ensure a Maximum Power Point Tracking (MPPT) of a wind energy conversion system. However the principal drawback of the sliding mode, is the chattering effect which characterized by torque ripple, this phenomena is undesirable and harmful for the machines, it generates noises and additional forces of torsion on the machine shaft. A direct fuzzy logic controller is designed and the sliding mode controller is added to compensate the fuzzy approximation errors. The simulation results clearly indicate the effectiveness and validity of the proposed method, in terms of convergence, time and precision.

A new and robust control strategy for a class of nonlinear power systems: Adaptive general type-II fuzzy

In this article, a robust direct adaptive general type-2 fuzzy logic controller is introduced for a class of nonlinear power systems. The proposed controller uses the advantages of general type-2 fuzzy logic system in handling dynamic uncertainties to approximate unknown nonlinear actions. Implementing general type-2 fuzzy system is computationally costly; however, by using a recently introduced α-plane representation, general type-2 fuzzy logic system can be seen as a composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the controller. In addition, an [Formula: see text] compensator is corrupted to attenuate external disturbance and fuzzy approximation error. General type-2 fuzzy adaptation laws are also derived using Lyapunov approach. It is worth noting that mathematical analysis proves the stability of the closed-loop system. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller, a direct adaptive interval type-2 fuzzy logic controller and adaptive proportional–integral–derivative, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic power system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.

Adaptive fuzzy logic load frequency control of multi-area power system

Abstract Based on indirect adaptive fuzzy control technique, a new load frequency control (LFC) scheme for multi-area power system is proposed. The power systems under study have the characterization of unknown parameters. Local load frequency controller is designed using the frequency and tie-line power deviations of each area. In the controller design, the approximation capabilities of fuzzy systems are employed to identify the unknown functions, formulate suitable adaptive control law and updating algorithms for the controller parameters. It is proved that the proposed controller ensures the boundedness of all variables of the closed-loop system and the tracking error. Moreover, in the proposed controller an auxiliary control signal is introduced to attenuate the effect of fuzzy approximation error and to mitigate the effect of external disturbance on the tracking performance. Simulation results of a three-area power system are presented to validate the effectiveness of the proposed LFC and show its superiority over a classical PID controller.

Composite fuzzy control of a class of uncertain nonlinear systems with disturbance observer

In this paper, a novel composite control, using fuzzy logic system (FLS) and disturbance observer, is proposed for a class of uncertain nonlinear systems with actuator saturation and external disturbances. FLS is employed to approximate the unknown nonlinearities and a serial–parallel identification model is introduced to construct the composite updating law. The disturbance observer is developed to estimate the unknown compounded disturbance composed of the unknown external disturbance, the unknown fuzzy approximation error and the effect of actuator saturation. The uniformly ultimate boundedness of the closed-loop tracking error can be guaranteed rigorously via Lyapunov stability analysis. Simulation results are presented to demonstrate the effectiveness of the proposed method.

Robust Adaptive Fuzzy Control for a Class of Uncertain MIMO Nonlinear Systems with Input Saturation

This paper studies the robust adaptive fuzzy control design problem for a class of uncertain multiple-input and multiple-output (MIMO) nonlinear systems in the presence of actuator amplitude and rate saturation. In the control scheme, fuzzy logic systems are used to approximate unknown nonlinear systems. To compensate the effect of input saturations, an auxiliary system is constructed and the actuator saturations then can be augmented into the controller. The modified tracking error is introduced and used in fuzzy parameter update laws. Furthermore, in order to deal with fuzzy approximation errors for unknown nonlinear systems and external disturbances, a robust compensation control is designed. It is proved that the closed-loop system obtainsH∞tracking performance through Lyapunov analysis. Steady and transient modified tracking errors are analyzed and the bound of modified tracking errors can be adjusted by tuning certain design parameters. The proposed control scheme is applicable to uncertain nonlinear systems not only with actuator amplitude saturation, but also with actuator amplitude and rate saturation. Detailed simulation results of a rigid body satellite attitude control system in the presence of parametric uncertainties, external disturbances, and control input constraints have been presented to illustrate the effectiveness of the proposed control scheme.

Analytic Model Predictive Control of Uncertain Nonlinear Systems: A Fuzzy Adaptive Approach

A fuzzy adaptive analytic model predictive control method is proposed in this paper for a class of uncertain nonlinear systems. Specifically, invoking the standard results from the Moore-Penrose inverse of matrix, the unmatched problem which exists commonly in input and output dimensions of systems is firstly solved. Then, recurring to analytic model predictive control law, combined with fuzzy adaptive approach, the fuzzy adaptive predictive controller synthesis for the underlying systems is developed. To further reduce the impact of fuzzy approximation error on the system and improve the robustness of the system, the robust compensation term is introduced. It is shown that by applying the fuzzy adaptive analytic model predictive controller the rudder roll stabilization system is ultimately uniformly bounded stabilized in theH-infinity sense. Finally, simulation results demonstrate the effectiveness of the proposed method.

Direct adaptive general type‐2 fuzzy control for a class of uncertain non‐linear systems

In this study, a stable direct adaptive general type-2 fuzzy logic controller (DAG2FLC) is introduced for a class of non-linear systems. The proposed controller uses advantages of general type-2 fuzzy logic systems (GT2FLSs) in handling dynamic uncertainties to approximate unknown non-linear actions. Implementing general type-2 fuzzy systems is computationally costly; however, by using a recently introduced α-plane representation, a GT2FLS can be seen as composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the DAG2FLC controller and a H ∞ compensator is added to attenuate external disturbance and fuzzy approximation error. Also general type-2 fuzzy adaptation laws are derived using Lyapunov approach, and the stability of the closed-loop system has been proven by mathematical analysis. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller and a direct adaptive interval type-2 fuzzy logic controller, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic Gyro system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.

Global Asymptotic Stabilization Using Adaptive Fuzzy PD Control

It is well-known that standard adaptive fuzzy control (AFC) can only guarantee uniformly ultimately bounded stability due to inherent fuzzy approximation errors (FAEs). This paper proves that standard AFC with proportional-derivative (PD) control can guarantee global asymptotic stabilization even in the presence of FAEs for a class of uncertain affine nonlinear systems. Variable-gain PD control is designed to globally stabilize the plant. An optimal FAE is shown to be bounded by the norm of the plant state vector multiplied by a globally invertible and nondecreasing function, which provides a pivotal property for stability analysis. Without discontinuous control compensation, the closed-loop system achieves global and partially asymptotic stability in the sense that all plant states converge to zero. Compared with previous adaptive approximation-based global/asymptotic stabilization approaches, the major advantage of our approach is that global stability and asymptotic stabilization are achieved concurrently by a much simpler control law. Illustrative examples have further verified the theoretical results.

Output feedback adaptive fuzzy control of uncertain MIMO nonlinear systems with unknown input nonlinearities

An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.

High performance direct torque control of electrical aerodynamics load simulator using adaptive fuzzy backstepping control

Electrical load simulator is hardware in the loop simulator used to exert real-time aerodynamics loads on the servo actuation system of a flight vehicle under test according to flight conditions. This article investigates direct torque control of electrical load simulator system using adaptive fuzzy backstepping method. To analyze the effect of extra torque disturbance on electrical load simulator system, detailed mathematical formulations are derived. Considering practical aspects of the proposed method, state vector is estimated using a state predictor, and parameters of the system are estimated using algebraic method. Fuzzy logic system is used to estimate extra torque disturbance acting on electrical load simulator system, but the approximation error may not converge to zero, which may affect control performance. Similarly, the parameters of the system may vary with time; thus the lumped disturbance due to time variation of parameters and fuzzy approximation error is compensated using adaptive control law derived based on estimated error dynamics between actual plant and state predictor. Moreover, to improve transient response, a novel saturation function-based transient performance controller is introduced. The performance of the proposed control is verified using extensive numerical simulations.

Fuzzy sliding mode control for the two-link robot

This paper presents the fuzzy logic combined with the sliding mode FSMC to design a robust controller for the two-link robot system. The sliding mode control SMC can be used for a nonlinear system with small uncertainties. However, for complex nonlinear systems, the uncertainties are large and produce higher amplitude of chattering due to the higher switching gain. In this work, the nominal model of the robot is assumed known and the fuzzy logic is used to approximate only the unknown dynamic parts of the system, which are incorporated in the so called equivalent control. A small gain robust control term is added to remove the fuzzy approximation error. The simulation results show the effectiveness of the proposed method.

Design of a unified adaptive fuzzy observer for uncertain nonlinear systems

This paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems. More precisely, we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high-gain or a sliding mode observer by selecting its gain appropriately. Additionally, we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances. We also show that the observation error is ultimately bounded using a Lyapunov approach without having recourse to the usual strictly positive real (SPR) condition or a suitable observation error filtering. The effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature.

Enhanced Adaptive Fuzzy Control With Optimal Approximation Error Convergence

In this paper, an enhanced adaptive fuzzy control (AFC) strategy with guaranteed convergence of an optimal fuzzy approximation error (FAE) is presented for a class of uncertain nonlinear systems in the general Brunovsky form. Based on the fuzzy logic system (FLS) with variable universes of discourse, relaxed sufficient conditions that guarantee the optimal FAE being convergent are given, and the upper bound of the optimal FAE is obtained. The control singularity problem resulting from the unknown affine term is resolved by a novel fuzzy approximation equation, and the parameter adaptive law of the FLS is derived by the Lyapunov synthesis. By means of the optimal FAE bound result, it is proved that the closed-loop system achieves partially asymptotic stability under a certain selection of control parameters. The proposed approach retains all advantages of a previous similar approach under relaxed constraint conditions. Thus, it provides a more flexible solution to the AFC with optimal FAE convergence. Simulation studies have demonstrated high-precision tracking performance with smooth control input of the proposed approach.

State Observer Based Dynamic Fuzzy Logic System for a Class of SISO Nonlinear Systems

This paper presents an observer based dynamic fuzzy logic system (DFLS) scheme for a class of unknown single-input single-output (SISO) nonlinear dynamic systems with external disturbances. The proposed approach does not need the availability of the state variables. Within this scheme, the DFLS is employed to identify the unknown nonlinear dynamic system. The control law and parameter adaptation laws of the DFLS are derived based on Lyapunov synthesis approach. The control law is robustfied in H8 sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions, it guarantees the boundedness of all the signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. The proposed method is applied to an inverted pendulum system to verify the effectiveness of the proposed algorithms.

An Optimal Fuzzy High-Gain Observer for an Uncertain Nonlinear System

This paper proposes an alternative optimal fuzzy high-gain observer design scheme. The structure of the proposed observer is represented by the Takagi-Sugeno fuzzy model and has the integrator of the estimation error. It improves the performance of a high-gain observer and makes the observer robust against noisy measurements, uncertainties and parameter perturbation. The proposed observer adopts the [Formula: see text] control technique and an adaptive projection algorithm. This technique results in a reduction of both the fuzzy approximation error and time-varying disturbances. In addition, the proposed observer accomplishes a fast transient response and parameter convergence. Some simulation results are given to present the validity of the theoretical derivations and the performance of the proposed observer.

A Novel Robust Decentralized Adaptive Fuzzy Control for Swarm Formation of Multiagent Systems

In this paper, a novel decentralized adaptive control scheme for multiagent formation control is proposed based on an integration of artificial potential functions with robust control techniques. Fully actuated mobile agents with partially unknown models are considered, where an adaptive fuzzy logic system is used to approximate the unknown system dynamics. The robust performance criterion is used to attenuate the adaptive fuzzy approximation error and external disturbances to a prescribed level. The advantages of the proposed controller can be listed as robustness to input nonlinearity, external disturbances, and model uncertainties, and applicability on a large diversity of autonomous systems. A Lyapunov-function-based proof is given of robust stability, which shows the robustness of the controller with respect to disturbances and system uncertainties. Simulation results are demonstrated for a swarm formation problem of a group of six holonomic robots, illustrating the effective attenuation of approximation errors and external disturbances, even in the case of agent failure. Moreover, experimental results confirm the validity of the presented approach and are included to verify the applicability of the scheme for a swarm of six real holonomic robots.

Adaptive fuzzy H∞ control strategy for a micro-electromechanical system gyroscope based on the linear matrix inequality approach

In this paper, an adaptive fuzzy logic controller is proposed to create a H∞ tracking performance for a micro-electro-mechanical system gyroscope with system non-linearity consisting of parameter uncertainties and external disturbances. An adaptive fuzzy logic system is used to approximate the non-linear function to compensate the system’s non-linear behavior. Riccati-type equations and the linear matrix inequality technique are incorporated into the direct adaptive fuzzy H∞ control. The influence of both fuzzy logic approximation error and external disturbances on the tracking error is attenuated to a prescribed level. Simulation results confirm that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the proposed methods. Compared with the Riccati-type equation-based approach, the linear matrix inequality-based approach creates a better tracking performance.