Adaptive Fuzzy Backstepping Control Research Articles

Command filtering‐based adaptive backstepping control for a class of discrete‐time uncertain nonlinear systems with mismatched disturbances

SummaryThis paper investigates the adaptive fuzzy backstepping control problem for uncertain discrete‐time nonlinear systems with mismatched disturbances. A novel adaptive fuzzy command filtered backstepping approach is proposed, which can overcome the noncausal problem by using the command filter. The filter errors generated by filter are removed by constructing error compensation mechanism. The fuzzy logic systems are used to approximate the uncertain nonlinear dynamics, and the unknown mismatched disturbances are actively attenuated by using adaptive control technique. Based on the proposed new weighed Lyapunov functions, all the signals in the close‐loop system are proved to be uniformly ultimately bounded. The viability of proposed method is demonstrated by simulation results.

Observer-based adaptive fuzzy control of stabilized platform in rotary steerable system with input saturation and output constraint

This paper explores the control strategy for toolface tracking in the stabilized platform of a rotary steerable system, considering both input saturation and output constraint. To mitigate the impact of unknown friction torque and modeling error on the stabilized platform, we propose an adaptive fuzzy backstepping control approach. A fuzzy state observer is specifically devised to handle the uncertain state arising from unknown friction torque and modeling errors. Introducing an auxiliary system effectively compensates for input saturation, and the resolution of the output error constraint is achieved through the construction of a barrier Lyapunov function. Furthermore, employing the Lyapunov method establishes that all signals in the entire closed-loop control system are semi-globally uniformly ultimately bounded. Simulation results confirm the efficacy of the proposed control methodology.

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.

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.

Active disturbance rejection adaptive fuzzy backstepping control of uncertain flexible marine riser system

In this paper, vibration control of a flexible marine riser with uncertain parameters subjected to distributed disturbance and boundary disturbance is studied. The existing vibration control algorithms have the problems of relying on the accurate mathematical model of the system, complex control laws, and need to measure multiple states of the system, which cannot effectively deal with the uncertainty of model parameters and external disturbances. To effectively suppress the vibration of a marine flexible riser system with uncertain parameters, an adaptive fuzzy backstepping control algorithm was designed. First, the backstepping method and Lyapunov function are used to analyze the subsystem and design the virtual control law. On this basis, an adaptive fuzzy system was designed. The fuzzy system was used to approach the unknown nonlinear term in the design process of the control law and the uniform boundedness of the system was proved by the Lyapunov stability theory. The designed control algorithm has a simple structure, and it can effectively restrain the riser vibration and improve the control rate. Finally, the numerical simulation results show that the designed control algorithm is effective in suppressing the vibration of flexible risers and the control effect is better than previous PID control and robust adaptive control.

Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults

In this work, an adaptive fuzzy backstepping fault-tolerant control (FTC) issue is tackled for uncertain fractional-order (FO) nonlinear systems with sensor and actuator faults. A fuzzy logic system is exploited to manage unknown nonlinearity. In addition, a novel FO nonlinear filter-based dynamic surface control (DSC) method is constructed, effectively avoiding the inherent complexity explosion problem in the backstepping recursive process, and in the light of the construction of auxiliary functions, compensating the coupling term introduced by faults. On account of certain assumptions, the stability criterion of the FO Lyapunov function is applied to guarantee the stability of the closed-loop system. Finally, the simulation example verifies the validity of the presented control strategy.

Research on PMSM Speed Performance Based on Fractional Order Adaptive Fuzzy Backstepping Control

A permanent magnet synchronous motor (PMSM) is a nonlinear, strongly coupled, controlled object with time-varying, fractional-order characteristics. It is difficult to achieve the ideal control effect by using the traditional control method when motor parameter changes and load perturbations occur during the operation of the PMSM, so a fractional-order adaptive fuzzy backstepping control method is proposed to improve the system’s fast response and anti-jamming ability in the case of sudden changes in rotational speed, load perturbations and other conditions. Initially, the fractional order theory is introduced, backstepping control is utilized to decompose the system into multiple subsystems, and a fractional order-based Lyapunov function is designed for each subsystem to ensure the system’s stability. Suitable control laws, as well as parameter adaptive laws, are derived through rigorous mathematical derivation. Finally, a fractional order adaptive fuzzy backstepping controller (FOAB-FPID) is designed by combining the advantages of fuzzy control. Then a mechanical simulation model of the PMSM is established to verify the validity of the designed controller, followed by three sets of comparative experiments: PID, fuzzy PID (F-PID), and integer-order adaptive fuzzy backstepping (IOAB-FPID), which are selected to simulate the PMSM under the control of the four controllers. Finally, it is validated on the constructed PMSM experimental platform. Simulation and experimental results show that FOAB-FPID can adaptively adjust system parameters during sudden speed changes, achieve real-time speed tracking, and maintain speed stability under load perturbations and internal parameter uptake. Compared with the three control strategies, reached PMSM system has better acceleration, fast response performance, and better anti-disturbance ability, which proves the rationality and effectiveness of the FOAB-FPID control method.

Adaptive Fuzzy Fault Tolerant Control for Robot Manipulators With Fixed-Time Convergence

This paper aims to resolve the three major issues of fault tolerant control (FTC) for robot manipulators: (i) the faster response, lower tracking errors, lower chattering and higher robustness of the FTC, (ii) the requirement of partial or full knowledge of robot dynamics for the design of model-based FTC, and (iii) the global fixed-time convergence of the system. First, a fixed-time controller based on a backstepping control is designed and its disadvantages are analysed. Then, an adaptive fuzzy backstepping control is developed to enhance the tracking performance of the system. The proposed approach does not require the full prior knowledge of robot dynamic model, thus facilitating implementation of the controller in practical applications. In addition, the tracking errors of the system will be practically convergent within a fixed-time, which provides additional system information in advance. The fixed time convergence of the system is mathematically proved and the performance of the system is demonstrated for FTC of a PUMA560 robot.

ADAPTIVE FUZZY BACKSTEPPING CONTROL FOR BLOOD GLUCOSE REGULATION

In this paper, we propose an adaptive type-2 fuzzy backstepping controller for blood glucose regulation. To mimic at best the behavior of a real pancras, the nonlinear Bergman minimal model is adopted. To deal with the strict feedback form of this model, we use backstepping algorithm. To overcome the knowledge of the several parameters of model to deduce the control laws, we use adaptive type-2 fuzzy systems to obtain the control signals. The stability of the closed loop system is proven using Lypunov theory. A simulation example with a comparative study is given to schow the performances of the proposed approach.

Composite iterative learning adaptive fuzzy control of fractional-order chaotic systems using robust differentiators

In conventional adaptive fuzzy control, to improve the approximation ability of fuzzy logic systems (FLSs), more fuzzy rules should be employed, which will greatly increase the computational burden. This paper investigates the adaptive fuzzy backstepping control of a specific category of incommensurate fractional-order chaotic systems afflicted by functional uncertainties and actuator faults. To address the challenging “explosion of complexity” issue, a novel modified fractional-order robust differentiator is proposed, capable of effectively suppressing noise. Importantly, an iterative learning adaptation law including parameter errors between adjacent periods and prediction errors derived from a series–parallel model is developed to improve the approximation accuracy of FLSs without using abundant fuzzy rules. Utilizing the frequency distribution model and the Lyapunov stability criterion, this approach guarantees the semi-global uniform boundedness of the closed-loop system and facilitates the convergence of tracking errors to a small region. Finally, the effectiveness of theoretical results is demonstrated through numerical simulation examples.

Robust Adaptive Fuzzy Backstepping Control for 2-DOF Laboratory Helicopter System with Improved Tracking Performance

Robust Adaptive Fuzzy Backstepping Control for 2-DOF Laboratory Helicopter System with Improved Tracking Performance

Compound Adaptive Fuzzy Synchronization Controller Design for Uncertain Fractional-Order Chaotic Systems

In this paper, the synchronization of two fractional-order chaotic systems with uncertainties and external disturbances is considered. A fuzzy logic system is utilized to estimate uncertain nonlinearity, and its estimation accuracy is improved by constructing a series-parallel model. A disturbance observer is implemented to estimate bounded disturbance. To solve the “explosion of complexity” problem in the backstepping scheme, fractional-order command filters are employed to estimate virtual control inputs and their derivatives, and error compensation signals are devised to reduce filtering errors. Based on the fractional-order Lyapurov criterion, the proposed compound adaptive fuzzy backstepping control strategy can guarantee that the synchronization error converges to a small neighborhood of the origin. At last, the validity of the proposed control strategy is verified via a numerical simulation.

Extended State Observer-Based Fuzzy Adaptive Backstepping Force Control of a Deep-Sea Hydraulic Manipulator with Long Transmission Pipelines

The force tracking control of deep-sea hydraulic manipulator systems with long transmission pipelines is disposed via fuzzy adaptive backstepping control based on an extended state observer in this paper. The pipeline model is established and then used to estimate the pressures in cylinder chambers, which are used to obtain the output force. In this process, the velocity of the piston, which is unmeasured, is needed, and an extended state observer is constructed to estimate the unmeasurable velocity signal. To cope with parameter uncertainties caused by changes in working depth, an adaptive algorithm is combined with the backstepping controller. Fuzzy logic is employed to design self-tuners that can automatically adjust the control parameters to guarantee force control performance from shallow seas to deep seas. The experimental results illustrate the success of the proposed control method. Comparative experimental results demonstrate that the extended state observer-based fuzzy adaptive backstepping controller has a relatively better tracking performance in different working conditions.

Composite adaptive fuzzy backstepping control of uncertain fractional-order nonlinear systems with quantized input

Composite adaptive fuzzy backstepping control of uncertain fractional-order nonlinear systems with quantized input

A finite‐time adaptive fuzzy backstepping control for multiple‐input multiple‐output coupled nonlinear systems with tracking error constraints

SUMMARYIn this study, a finite‐time adaptive fuzzy backstepping control strategy with tracking error constraints is designed for a class of multiple‐input multiple‐output (MIMO) coupled nonlinear systems with uncertainties. First, the uncertainty of the system is approximated by adaptive fuzzy logic systems (AFLSs), then, the rapidity of the state tracking of the control system are ensured by backstepping and finite time theory. The problem of error constraints is solved by the combination of performance function and simplified barrier Lyapunov function (SBLF). It is proved that the states of a closed‐loop adaptive control system are semi‐globally practical finite‐time stable (SGPFS) by the finite‐time Lyapunov function, and in a finite time, the tracking error of the system state converges to a narrow block of origin with the prescribed bounded. Finally, the scheme's effectiveness is verified by the simulation.

Observer-based finite-time adaptive fuzzy back-stepping control for MIMO coupled nonlinear systems.

An attempt is made in this paper to devise a finite-time adaptive fuzzy back-stepping control scheme for a class of multi-input and multi-output (MIMO) coupled nonlinear systems with immeasurable states. In view of the uncertainty of the system, adaptive fuzzy logic systems (AFLSs) are used to approach the uncertainty of the system, and the unmeasured states of the system are estimated by the finite-time extend state observers (FT-ESOs), where the state of the observer is a sphere around the state of the system. The accuracy and efficiency of the control effect are ensured by combining the back-stepping and finite-time theory. It is proved that all the states of the closed-loop adaptive control system are semi-global practical finite-time stability (SGPFS) by the finite-time Lyapunov stability theorem, and the tracking errors of the system states converge to a tiny neighborhood of the origin in a finite time. The validity of this scheme is demonstrated by a simulation.

Adaptive Fuzzy Backstepping Control Based on Dynamic Surface Control for Uncertain Robotic Manipulator

In the actual operation site, the dynamics of robotic manipulators is affected by two uncertainties, i.e., external disturbances and modeling errors. In this paper, an adaptive fuzzy backstepping controller based on dynamic surface control is proposed to track and control the robotic manipulator while considering both uncertainties and also making a distinction. Firstly, a feedback control technique is used to convert the robotic manipulator dynamics model into two first-order systems, and the control inputs to be designed are introduced. Secondly, the uncertain modeling errors are approximated using two fuzzy networks, and the external disturbances are assumed to be less than some upper limit. Thirdly, in order to weaken the traditional problem of &#x201C;explosion of complexity&#x201D; in the design of the adaptive backstepping controller, a dynamic surface control technique is used in this paper. Then, the stability of the designed controller is demonstrated using Lyapunov theory. Finally, simulations are performed with a two-linked robotic manipulator to show the effectiveness of the designed controller, and then, to show the superiority of the controller, simulation results are compared with the results obtained by other control algorithms.

Robust output regulation for unknown nonlinear strict‐feedback systems with input delay

AbstractThis article investigates the robust output regulation problem for unknown nonlinear strict‐feedback systems with input delay. Nonlinear fuzzy internal model and adaptive fuzzy backstepping control are integrated to obtain a feedforward‐feedback composite controller. As a distinctive feature, Pade approximation technique is introduced to deal with the input delay of nonlinear output regulation problem for the first time. The process of control strategy can be divided into two steps. In the first step, a novel nonlinear fuzzy internal model is designed to get the feedforward compensator. In the second step, an adaptive fuzzy backstepping control scheme is proposed to get the feedback controller, which can guarantee semiglobally uniformly ultimately bounded of the closed‐loop system. Simulation results of an interconnected power system show the validity of the theoretical results.

Adaptive fuzzy control for uncertain switched discrete-time nonlinear systems in a pure-feedback form with state constraints

This paper is concerned with the adaptive fuzzy control for uncertain switched discrete-time nonlinear systems in a pure-feedback form under arbitrary switchings. The design and the stability analysis of the adaptive fuzzy control with state constraints are based on the adaptive fuzzy backstepping control and the Lyapunov function. The feature of the proposed approach is as follows. (i) The proposed adaptive fuzzy control is designed by suppressing the explosion problem of the complexity in the backstepping control, (ii) In the fuzzy inference approach, the nonlinear uncertainties are approximated by using the fuzzy logic systems based on the simplified extended single-input rule modules, and (iii) The proposed estimator to take the estimates for the unmeasurable states, the adjustable parameters and the real control is in a simplified structure designed. The simulation experiment provides that the proposed approach improves the system performance.

Optimal robust adaptive fuzzy backstepping control of electro-hydraulic servo position system

In this paper, an optimal robust adaptive fuzzy backstepping control is presented to the position control of the electro-hydraulic servo (EHS) system in the presence of structured and unstructured uncertainties. Initially, the robust control using the backstepping technique is presented to overcome the existing uncertainties in the dynamic equations. Mathematical proof demonstrates that the closed-loop system in the presence of uncertainties has a global asymptotic stability. Then, to overcome the chattering problem, a very simple fuzzy approximator is presented where it approximates the bounds of the uncertainties. Although the proposed robust fuzzy backstepping control has a desirable performance, it has no mathematical analysis to prove the stability of the closed-loop system. Therefore, to solve this problem, the proposed fuzzy approximator has been transformed into a one-law adaptive fuzzy approximator with a single-input single-output fuzzy rule. Mathematical analysis illustrates that the closed-loop system in the presence of uncertainties has a global asymptotic stability under the proposed robust adaptive fuzzy backstepping control. Furthermore, a novel modified harmony search algorithm (MHSA) has been developed, by using the original harmony search algorithm (OHSA) as an optimization technique, to achieve the optimal values of the membership functions and the control coefficients. Finally, a comparative study has been conducted between the proposed control scheme under the MHSA and the OHSA, and other existing advanced control approaches to verify the effectiveness of the proposed control. Results show that the proposed control scheme under the MHSA can suppress the chattering problem and reduce the disturbances effectively while ensuring that the performance is tracked.