Fuzzy Output Feedback Control Approach Research Articles

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

IBLF-Based Finite-Time Adaptive Fuzzy Output-Feedback Control for Uncertain MIMO Nonlinear State-Constrained Systems

This article considers the problem of finite-time adaptive fuzzy output-feedback control design for multi-input–multioutput uncertain nonlinear systems subject to full state constraints. By employing the finite-time stability theory, a new finite-time adaptive fuzzy output-feedback control approach is proposed. An integral barrier Lyapunov functional is utilized to prevent all states from violating their constraints. Fuzzy logic systems are developed to approximate the uncertainties. A fuzzy state observer is constructed to estimate the unmeasurable states. Moreover, to handle the “explosion of complexity” issue in the backstepping control technique, a finite-time convergent differentiator is introduced to estimate the time derivatives of virtual control signals. The stability analysis showed that the control approach guarantees that all closed-loop signals are bounded, and the tracking errors converge to a small neighborhood of the origin in a finite time. Finally, the effectiveness of the proposed control scheme is confirmed by numerical simulations.

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain. In order to better investigate uncertain suspension dynamics, the sampled-data Takagi-Sugeno (T-S) fuzzy half-car active suspension (HCAS) system is considered, which is further modelled as a continuous system with an input delay. Firstly, considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay, a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system. Secondly, since external disturbances often belong to a restricted frequency range, a finite frequency control criterion is presented for control synthesis to reduce conservatism. Thirdly, given a full information of state variables is hardly available in practical suspension systems, a two-stage method is proposed to calculate the static output feedback control gains. Moreover, an iterative algorithm is proposed to compute the optimum solution. Finally, numerical simulations verify the effectiveness of the proposed controllers.

Adaptive Fuzzy Output-Feedback Control for Nonaffine MIMO Nonlinear Systems With Prescribed Performance

This article proposes an adaptive fuzzy output-feedback control approach for a class of nonaffine multi-input multi-output nonlinear systems with prescribed performance and immeasurable states. For most of the existing fuzzy approximation-based approaches, there are many parameters in the fuzzy systems that need to be estimated online with adaptive laws. To overcome this difficulty, we propose a new fuzzy system; the remarkable advantage of this fuzzy system is that only one parameter needs to be estimated online. The fuzzy system is used to approximate the unknown nonlinear function, and an adaptive fuzzy state observer is developed to estimate the unmeasured states. By utilizing the state observer and the prescribed performance control scheme, an adaptive fuzzy prescribed performance output-feedback control method is developed. The number of the adaptive laws both for the state observer and the controller is reduced to the number of subsystems. It is proved that all the signals in the closed-loop systems are semiglobally uniformly ultimately bounded, and that the prescribed performance error constraints can be achieved. Simulation examples are provided to highlight the effectiveness of the proposed approach.

Dynamic surface error constrained adaptive fuzzy output feedback control for switched nonlinear systems with unknown dead zone

This paper investigates the adaptive fuzzy output-feedback dynamic surface control (DSC) approach with prescribed performance for a class of uncertain switched nonlinear systems with unknown dead-zone. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, a fuzzy switched state observer is established to observe the unmeasured states. Based on DSC backstepping control design technique and incorporated by the predefined performance theory and the average dwell time method, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can ensure that all the signals of the resulting closed-loop system are bounded, and the tracking errors are within the prescribed performance bounds for all times. Simulation studies illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control for MIMO switched nonlinear systems with prescribed performances

This paper proposes an adaptive fuzzy output-feedback control approach for a class of uncertain multiple-input and multiple-output (MIMO) switched nonlinear systems with prescribed performance and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, a fuzzy switched state observer is established to observe the unmeasured states. Based on backstepping technique and the prescribed performance theory, a new adaptive fuzzy control method with prescribed performance is developed. It is proved that the proposed control approach can ensure that all the signals of the resulting closed-loop system are bounded, and the tracking errors are within the prescribed performance bounds for all times. Simulation studies illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output-feedback control for a class of nonlinear switched systems with unmodeled dynamics

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of uncertain nonlinear switched systems with unmeasured states, unknown nonlinear functions, unmodeled dynamics, and dynamical disturbances. In the control design, fuzzy logic systems are used to approximate the unknown switched nonlinear functions and a switched fuzzy state observer is designed for estimating the unmeasured states. The problem of unmodeled dynamics and dynamic disturbance are solved by introduce a modified dynamical signals and nonlinear damping terms into the backsteping design procedure. Under the framework of backstepping control design, fuzzy adaptive control and average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop switched system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach.

Observer-based adaptive fuzzy output constrained control for MIMO nonlinear systems with unknown control directions

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems with unmeasured states and unknown control directions. In the control design, by using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed for state estimation as well as system identification, and a Nussbaum gain function is introduced into the control design to solve the unknown control direction problem. By applying the backstepping design techniques, a fuzzy adaptive output feedback control is constructed recursively. To address the problems of output constraint and “explosion of complexity”, the barrier Lyapunov function method and dynamic surface control technique are employed, respectively. It is proved that the proposed control approach can guarantee the semi-globally uniform ultimate boundedness for all the signals and the tracking errors to a small neighborhood of the origin. Simulation studies illustrate the effectiveness of the proposed approach.

Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input

In this paper, an adaptive fuzzy backstepping output feedback control approach is developed for a class of SISO nonaffine nonlinear systems with unknown dead-zone input and immeasurable states. Within this scheme, the original nonaffine system is firstly transformed into an affine-like form by using Taylor series expansion, the unknown dead-zone input is treated as a combination of a linear and a bounded disturbance-like term, and a state observer is introduced to estimate the system states. The fuzzy logic systems are utilized to directly approximate the desire virtual control law, and a novel adaptive fuzzy output feedback controller is designed via backstepping. A main advantage of the proposed controller is that only one adaptive parameter needs to be updated online in backstepping design process. Theoretically, it is proved that the presented adaptive fuzzy controller can guarantee that the tracking error converges to a small neighborhood of the origin and all signals in closed-loop are bounded. Finally, the simulation results validate the effectiveness of the proposed scheme.

Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation.

In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.

Adaptive Fuzzy Output-Feedback Control of Pure-Feedback Uncertain Nonlinear Systems With Unknown Dead Zone

In this paper, an adaptive fuzzy output-feedback control is investigated for a class of pure-feedback uncertain nonlinear systems with unknown dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, and a state filter observer is designed to estimate the unmeasured states. Based on the information of the dead-zone slopes as well as treating the unknown inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. The stability of the resulting closed-loop system is proved and a simulation example is provided to show the effectiveness of the proposed control approach. The important feature of the proposed adaptive fuzzy controller is that it can solve the states immeasurable and the unknown dead-zone problems that exist in the previous publications and extends the existing results on strict-feedback control to the counterpart on pure-feedback control.

Adaptive fuzzy decentralised output feedback control of pure‐feedback large‐scale stochastic non‐linear systems with unknown dead zone

In this study, a robust adaptive fuzzy decentralised backstepping output feedback control approach is proposed for a class of uncertain non-linear stochastic large-scale systems in pure-feedback form. The non-linear large-scale systems under study have unknown non-linear functions, unknown dead-zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown non-linear functions, and a K-filters state observer is designed for estimating the unmeasured states. Based on the information of the bounds of the dead-zone slopes as well as treating the time-varying inputs coefficients as a system uncertainty, a robust adaptive fuzzy decentralised output feedback control approach is constructed via the backstepping recursive design technique. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system can be regulated to a small neighbourhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.

Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics

In this paper, an adaptive fuzzy output-feedback control approach is proposed for a class of uncertain nonlinear systems with unknown nonlinear functions, unmodeled dynamics, and without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. To solve the problem of unmodeled dynamics, the dynamical signal combined with changing supply function is incorporated into the backstepping recursive design technique. Under the framework of the backstepping control design technique and incorporated by the predefined performance technique, a new robust adaptive fuzzy output feedback control scheme is constructed. It is shown that all the signals of the resulting closed-loop system are bounded, and the system output remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach.

Prescribed Performance Fuzzy Adaptive Output-Feedback Control for Nonlinear Stochastic Systems

A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach.

Adaptive Fuzzy Output-Feedback Method Applied to Fin Control for Time-Delay Ship Roll Stabilization

The ship roll stabilization by fin control system is considered in this paper. Assuming that angular velocity in roll cannot be measured, an adaptive fuzzy output-feedback control is investigated. The fuzzy logic system is used to approximate the uncertain term of the controlled system, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the control strategy is effective to decrease the roll motion. Simulation results are included to illustrate the effectiveness of the proposed approach.

Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states. To address output constraint and input constraint, a barrier Lyapunov function and an auxiliary design system are employed, respectively. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the fuzzy state observer, and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the input and output constraints are circumvented simultaneously. A numerical example is provided to illustrate the effectiveness of the proposed approach.

Observer-based fuzzy adaptive control of nonlinear systems with actuator faults and unmodeled dynamics

In this paper, an adaptive fuzzy output feedback fault-tolerant control scheme is developed for a class of nonlinear systems with actuator faults, unmodeled dynamics and without assuming the states being available for control design. Fuzzy logic systems are employed to approximate unknown nonlinear functions, and a fuzzy state observer is established to estimate the unmeasured states. By combining adaptive backstepping technique with changing supplying function technique and the nonlinear fault-tolerant control theory, a novel adaptive fuzzy fault-tolerant output feedback control approach is developed. It is proved that proposed control approach guarantees that all the variables of the closed-loop system are bounded. The simulation results are provided to illustrate the effectiveness of the proposed control approach. Compared with the existing results, the main contributions of this paper are as follows: (1) the proposed control method removes the restrictive assumption that all the states of the controlled system be measured directly; and (2) the proposed control method cannot only compensate for the actuator faults, but also solve the problem of the unmodeled dynamics.

Adaptive fuzzy fault-tolerant control of static var compensator based on dynamic surface control technique

The adaptive fuzzy faults tolerant control problem is investigated for a single machine bus system with static var compensator (SVC). This design does not require that speed of the generator rotor and susceptance of the overall system are measured, and also does not require that the parameters of the controlled system are known accurately. The considered faults are modeled as both loss of effectiveness and lock-in-place. A fuzzy state observer is designed to estimate the speed of the generator rotor and susceptance, by combining the adaptive backstepping technique with a dynamic surface control (DSC) approach, a novel adaptive fuzzy output-feedback faults tolerant control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the angle of the generator rotor follows a desired value. Simulation results are presented to show the effectiveness of the approach.

A Combined Backstepping and Stochastic Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties.