Fuzzy Output Feedback Tracking Control Research Articles

Adaptive Fuzzy Output-Feedback Tracking Control for Nonlinear Time-Varying State-Constrained Systems Without the Feasibility Condition

Adaptive Fuzzy Output-Feedback Tracking Control for Nonlinear Time-Varying State-Constrained Systems Without the Feasibility Condition

Optimal fuzzy output feedback tracking control for unmanned surface vehicles systems

This study investigates an optimal fuzzy output feedback tracking control problem with a Q-learning algorithm on unmanned surface vehicles (USVs) with immeasurable velocities information. Firstly, the USVs are modeled by a Takagi–Sugeno (T–S) fuzzy system. Based on the fuzzy system, an ideal optimal fuzzy output feedback tracking controller is proposed by utilizing reconstruction states, measured output and input data. Theoretically, the analytical solution of the designed optimal controller is reduced to solving the algebraic Riccati equations (AREs). Due to the difficulty of solving AREs directly, a Q-learning value iteration algorithm is proposed to obtain its approximation solution. Furthermore, it is rigorously mathematically proved that the proposed Q-learning algorithm can approximate the ideal solution and guarantee the USVs output to track the desired reference signal. Ultimately, the simulation and comparison results with the existing control method verify the efficacy and advantage of the presented fuzzy optimal output feedback tracking control approach with a Q-learning algorithm.

Optimal Fuzzy Output Feedback Control for Dynamic Positioning of Vessels With Finite-Time Disturbance Rejection Under Thruster Saturations

This paper focuses on the problem of optimal fuzzy output-feedback tracking control for dynamic positioning of marine vessels simultaneously with model uncertainties, unknown disturbances, unavailable velocities and thruster saturations. The control scheme is built by integrating a fuzzy velocity observer, a finite-time disturbance observer, a dynamic auxiliary system, the optimal control strategy with the dynamic surface control. The fuzzy velocity observer is constructed to obtain the unavailable velocities without requiring the certain model dynamics. The finite-time disturbance observer is established to estimate the unknown disturbances. The dynamic auxiliary system is designed to compensate for thruster saturations effects. By incorporating these methods, a disturbance rejection adaptive controller is designed with dynamic surface control. The optimal compensation term is inserted to minimize the cost function of the tracking error system by adaptive dynamic programming. It is shown that the optimal control consisting of the adaptive controller and the optimal compensation term guarantees that all signals in the closed-loop dynamic positioning system are bounded. Finally, simulation results demonstrate the effectiveness of the proposed optimal control scheme.

Adaptive Fuzzy Output-Feedback Tracking Control for Switched Nonstrict-Feedback Nonlinear Systems with Prescribed Performance

In this article, an adaptive fuzzy output-feedback tracking control scheme is proposed for a class of single-input and single-output uncertain switched nonlinear systems in nonstrict-feedback form with prescribed performance and arbitrary switching. By using the concept of prescribed performance, we mean that the tracking error converges to the predefined performance bounds. The unknown nonlinear functions are approximated by utilizing the fuzzy logic systems. For the systems under study, unavailable states are taken into account, which are estimated by constructing a fuzzy state observer. In order to overcome the difficulty arising from the nonstrict-feedback form, an effective adaptive parameter is introduced. By using the common Lyapunov function method and backstepping design approach, an adaptive control algorithm is presented for the considered system. The designed controller can guarantee that all the signals within closed-loop systems are semi-globally uniformly ultimately bounded. The effectiveness of the control strategy put forward in this paper is demonstrated by the simulation results.

Adaptive Fuzzy Output Feedback Simultaneous Posture Stabilization and Tracking Control of Wheeled Mobile Robots With Kinematic and Dynamic Disturbances

This article proposes a simultaneous posture (i.e., position and heading direction angle) stabilization and tracking control for differential-drive wheeled mobile robots (WMRs) using an adaptive fuzzy output feedback tracking control (AFOFTC) method and a fuzzy basis function network (FBFN). Existing studies on simultaneous posture stabilization and tracking control of WMRs do not compensate for the uncertainties and disturbances caused by kinematics and dynamics (i.e., kinematic and dynamic disturbances). To inhibit the performance degradation caused by these disturbances, an FBFN-based adaptive fuzzy output feedback posture stabilization and tracking control of WMRs is proposed considering the unavailable velocities of the WMR. In this approach, i) kinematic error equations are derived in polar coordinates, ii) a nonlinear velocity observer for WMRs containing the kinematic and dynamic uncertainties is designed, iii) a backstepping-like feedback linearization controller is designed based on the kinematics in polar coordinates to generate a reference trajectory, and iv) an AFOFTC law is proposed based on the dynamics to ensure that the WMR follows the generated reference trajectory. The proposed method can maintain satisfactory posture stabilization and tracking control performance despite the kinematic and dynamic disturbances. A stability analysis as well as the simulation and experimental results are provided to validate the proposed scheme.

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.

Observer-based adaptive fuzzy tracking control of MIMO switched nonlinear systems preceded by unknown backlash-like hysteresis

This paper considers the problem of adaptive fuzzy output feedback tracking control for a class of multi-input and multi-output (MIMO) switched nonlinear systems with hysteresis nonlinearities, where the hysteresis nonlinearities are described by a set of differential equations with unknown parameters. Fuzzy logic systems, as specialized function approximators, are employed to approximate the unknown nonlinear functions of the system under study. A MIMO switched fuzzy observer is constructed to tackle the problem of unmeasured states, and the dynamic surface control technique is introduced to avoid the appearance of repeated differentiations existing in most traditional backstepping designs. Based on the multiple Lyapunov function approach, an adaptive fuzzy output feedback controller is developed. The proposed control scheme can guarantee that all the signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) under a class of switching signals with average dwell time, and the outputs to track given reference signals exactly. Simulation results demonstrate the validity of the control scheme.

Adaptive Fuzzy Prescribed Performance Control for Nonlinear Switched Time-Delay Systems With Unmodeled Dynamics

This paper considers the adaptive fuzzy output feedback tracking control problem for a class of uncertain nonlinear switched systems with time delay and unmodeled dynamics. Based on a kind of switched K-filters, a prescribed performance control scheme is proposed to guarantee the tracking performance and restrain the fluctuation caused by switches between submodes as well. In addition, fuzzy logic systems (FLSs) are use to approximate unknown nonlinear functions and dynamic surface control (DSC) method is employed to eliminate the explosion of complexity problem inherent in traditional backstepping method. The proposed controllers of corresponding subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time (ADT). A numerical simulation is performed to illustrate the effectiveness of the proposed approach.

Adaptive output feedback tracking control for non‐linear switched stochastic systems with unknown control directions

The problem of adaptive fuzzy output feedback tracking control for a class of switched stochastic non-linear systems with time-varying delay and unknown control directions is addressed in this study. During the adaptive controller design procedure, a state observer is introduced to estimate the unmeasurable system states, an appropriate stochastic Lyapunov-Krasovskii functional is utilised to compensate the time-varying delay terms, and fuzzy logic systems are employed to approximate a suitable unknown function which is composed of all the unknown non-linearities of the switched systems. In addition, the Nussbaum-type function is used to detect the unknown control directions. With the help of the designed controller independent of switching signals, the semi-globally uniformly ultimately boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighbourhood of the origin. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

Adaptive decentralized fuzzy output feedback tracking control for a class of nonlinear large-scale systems with input delays

In this paper, the decentralized tracking control problem of nonlinear large-scale systems with immeasurable states and unknown nonlinearities in each subsystem and their interconnections subject to input delays is proposed. Based on the universal approximation properties of fuzzy systems, a fuzzy observer is designed to estimate the inaccessible states of the system. Subsequently, by defining the appropriate change of coordinates and employing the backstepping technique, an adaptive fuzzy backstepping output feedback control scheme is proposed for nonlinear interconnected systems subject to input delays. Owing to the problem of so-called explosion of complexity that inherently arises in the design procedures of the traditional backstepping technique, an adaptive fuzzy dynamic surface output feedback control approach is also presented for this class of large-scale systems. Moreover, it is shown that the two proposed adaptive decentralized fuzzy observer-based control approaches ensure all the signals of the closed loop system uniformly ultimately bounded and the norms of the tracking errors as well as the norms of the observation errors can converge to small desired values by proper selection of the design parameters. Finally, the theoretic achievements are carried out on the chemical reactor recycle system to illustrate and compare the effectiveness of the two proposed approaches.

Adaptive Fuzzy Output Feedback Control for Switched Nonstrict-Feedback Nonlinear Systems With Input Nonlinearities

This paper studies adaptive fuzzy output feedback tracking control problem for nonstrict-feedback switched nonlinear systems. The switched systems under consideration contain unknown nonlinearities, unmeasured states, and unknown deadzones. Fuzzy logic systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state observer is designed, and thus, the immeasurable states are estimated via it. In the framework of observer-based output feedback control, and by using the certainty equivalence deadzone inverse, a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed. The stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods. Two simulation examples are provided to check the effectiveness of the proposed approach.

Adaptive Fuzzy Output-Feedback Tracking Control for a Class of Switched Stochastic Nonlinear Time-Delay Systems

In this paper, a design scheme for an adaptive fuzzy tracking controller is proposed for a class of switched stochastic nonlinear time-delay systems via dynamic output-feedback. First, a reduced-order observer is introduced to estimate the unmeasurable states of the switched system. During the adaptive controller design procedure, an appropriate stochastic Lyapunov---Krasovskii functional deals with the time-delay terms, and fuzzy logic systems are employed to approximate the unknown nonlinearities. Based on the designed controller, the semi-globally uniform ultimate boundedness of all the closed-loop signals is guaranteed and the tracking error converges to a small neighborhood of the origin. Finally, a simulation example is given to illustrate the validity of the proposed approach.

Fuzzy Adaptive Output Feedback Tracking Control of VTOL Aircraft With Uncertain Input Coupling and Input-Dependent Disturbances

This paper proposes fuzzy adaptive output feedback tracking control method for VTOL (vertical takeoff and landing) aircraft. Since uncertainties exist in the input coupling parameter due to its dependence on the physical parameters, and unknown disturbances can occur as well in the form of input-dependent accelerations in dynamics, which should be compensated at the same time. To this end, the dynamics with input-dependent disturbances are first rigorously derived based on the general form of acceleration disturbance vector in VTOL system. Second, the nonlinear velocity observer is designed to estimate the velocity information not available in the actual situation such that the output feedback tracking control can be achieved even in the presence of uncertain input coupling and disturbances, which is not possible in the case of previous works. Third, fuzzy adaptive observer is designed to estimate both unknown input coupling coefficient and input-dependent disturbances. Finally, the fuzzy adaptive output tracking controller is designed based on the nonlinear velocity observer and the fuzzy adaptive observer. The trajectory tracking errors can be guaranteed to be globally ultimately bounded and their ultimate bounds can be adjusted appropriately. Both stability analysis and simulation results demonstrate the effectiveness of the proposed method against uncertainties and disturbances in VTOL system.

Observer-Based Adaptive Fuzzy Tracking Control of MIMO Stochastic Nonlinear Systems With Unknown Control Directions and Unknown Dead Zones

In this paper, an adaptive fuzzy backstepping output-feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) stochastic nonlinear systems. The MIMO stochastic nonlinear systems under study are assumed to possess unstructured uncertainties, unknown dead-zones, and unknown control directions. By using a linear state transformation, the unknown control coefficients and the unknown slopes characteristic of the dead-zones are lumped together, and the original system is transformed to a new system on which the control design becomes feasible. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By introducing a special Nussbaum gain function into the backstepping control design, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The main features of the proposed adaptive control approach are that it can guarantee the stability of the closed-loop system, and the tracking errors converge to a small neighborhood of zero. Moreover, it can solve the problems of unknown control direction, unknown dead-zone, and unmeasured states simultaneously. Two simulation examples are provided to show the effectiveness of the proposed approach.

Fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization

In this paper, the problem of adaptive fuzzy quantized output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form. The considered switched systems contain unknown nonlinearities, hysteretic quantized input and without requiring the system states being available for measurement. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a switched fuzzy state observer is designed to estimate the unmeasured states. The hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions. Based on the estimated states and using the backstepping design principle, an adaptive fuzzy quantized output feedback control scheme is developed. It is proved that whole adaptive fuzzy quantized control scheme 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 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.

Fuzzy adaptive output feedback DSC design for SISO nonlinear stochastic systems with unknown control directions and dead-zones

In this paper, the adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems unknown dead-zones and unknown control direction. In the design, by using a linear state transformation, the unknown control coefficient and the unknown slope characteristic of the dead-zone are lumped together, and the original system is transformed to a new system. Fuzzy logic systems are employed to identified the uncertain nonlinear systems, a nonlinear fuzzy state observer is constructed to solve the problem of unmeasured states, and a special Nussbaum function is introduced into the control design to solve the unknown control direction problem, respectively. To address the problem of “explosion of complexity”, the dynamic surface control (DSC) technique is employed, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The stability is proven based on Lyapnov theory, and it can guarantee that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed method.

Adaptive fuzzy output feedback tracking control with prescribed performance for chemical reactor of MIMO nonlinear systems

In this paper, a fuzzy adaptive control approach with prescribed performance is developed for a chemical reactor of multi-input and multi-output nonlinear systems with unmeasured states. Using fuzzy logic systems to model the uncertain nonlinear systems, a fuzzy adaptive observer is designed for immeasurable states estimations. Under the framework of the backstepping design and incorporated by the predefined performance technique, a new fuzzy adaptive output feedback control is developed. It is shown that all the signals of the resulting closed-loop systems are bounded, and the tracking errors remain within an adjustable neighborhood of the origin with the prescribed performance bounds. The detailed simulation results and performance comparisons are provided to demonstrate the effectiveness of the proposed control approach.

Adaptive fuzzy control design and applications of uncertain stochastic nonlinear systems with input saturation

In this paper, the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain stochastic nonlinear systems. The stochastic nonlinear systems under study have unknown nonlinear uncertainties, unmodeled dynamics, input saturation and without the direct measurement of state variables. Fuzzy logic systems and a smooth function are first utilized to approximate the unknown nonlinear functions and the input saturation, respectively, and then a fuzzy state observer is designed to estimate the unmeasured states. By combining the adaptive backstepping design technique with the dynamic surface control (DSC) design technique and using the concept of the dynamical signal, a new adaptive fuzzy output feedback tracking control approach is developed. It is proved that all the variables involved in the closed-loop system are semi-globally uniformly ultimately bounded (SUUB) in probability, and also that both observer errors and tracking errors converge to a small neighborhood of the origin by appropriate selecting the design parameters. The proposed adaptive fuzzy control approach is finally applied to the two-stage chemical reactor with recycle streams, and achieves the satisfactory control performance.

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.