Adaptive Backstepping Method Research Articles

Adaptive Fuzzy Tracking Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Systems With Actuator Faults

This paper investigates an adaptive fuzzy tracking control problem for nonlinear stochastic nonstrict-feedback systems with unknown control directions and actuator faults. Based on the monotonically increasing property of system bounding functions, a variable separation scheme is invoked to overcome the research difficulty from nonlower triangular structure. Combining adaptive backstepping method with fuzzy logic system’s approximation capability, an adaptive fuzzy fault tolerant controller is designed. The presented control algorithm makes not only the tracking error as small as possible but also the closed-loop trajectory bounded in the sense of the four-moment. Finally, simulation results are depicted to address the effectiveness of the studied control method.

Neural Network-Based Adaptive Fault-Tolerant Control for Markovian Jump Systems With Nonlinearity and Actuator Faults

The fault-tolerant control (FTC) issue is considered in this article for Markovian jump systems (MJSs) in which both nonlinearity and actuator faults exist simultaneously. The existed nonlinearity in the considered MJSs means that there exist limitations to employ the renown sliding mode control (SMC) method directly. In this work, the radial basis function (RBF) neural network (NN) technique is exploited to model the nonlinearity on which no knowledge whatsoever is available. Then, with the help of the adaptive backstepping method, an NN-based FTC approach is proposed to overcome the considered challenging case. The adverse effects, arising from the nonlinearity and the actuator faults can be completely compensated by the proposed adaptive controller. With the proposed controller and the adaptation laws, the bounded stability of the considered closed-loop plant can be guaranteed. Furthermore, only two types of adaptive parameters are adopted in the proposed approach to achieve the purpose of FTC, and this reduces the computational burden and thus extends its applicability. Finally, the effectiveness of the developed approach is demonstrated on a practical system: a wheeled mobile manipulator.

A High Precision Adaptive Back-Stepping Control Method for Morphing Aircraft Based on RBFNN Method

To overcome the uncertainties of the nonlinear model of a morphing aircraft, this paper presents a high-precision adaptive back-stepping control method based on the radial basis function neural network (RBFNN). Firstly, based on the analysis of static and dynamic aerodynamic parameters of the morphing aircraft, its nonlinear control law is designed by using the conventional back-stepping method. The RBFNN is introduced to approximate online the uncertain terms of the nonlinear control law so as to improve its robustness. The robust term is designed to eliminate the approximation error caused by the RBFNN. Secondly, the tracking differentiator is designed through solving the virtual control variables, thus solving the "differential expansion" problem existing in the traditional back-stepping method. The Lyapunov stability analysis proves that our method can ensure that the tracking error of a closed-loop system converges finally and that its signals are uniformly bounded. Finally, the digital simulation model of the morphing aircraft is established with the MATLAB/Simulink; our method is compared with the conventional back-stepping control method. The simulation results show that our method has a higher control precision and stronger robustness.

Event-Triggered Adaptive Fault Tolerant Control for a Class of Uncertain Nonlinear Systems.

This paper considers an adaptive fault-tolerant control problem for a class of uncertain strict feedback nonlinear systems, in which the actuator has an unknown drift fault and the loss of effectiveness fault. Based on the event-triggered theory, the adaptive backstepping technique, and Lyapunov theory, a novel fault-tolerant control strategy is presented. It is shown that an appropriate comprise between the control performance and the sensor data real-time transmission consumption is made, and the fault-tolerant tracking control problem of the strict feedback nonlinear system with uncertain and unknown control direction is solved. The adaptive backstepping method is introduced to compensate the actuator faults. Moreover, a new adjustable event-triggered rule is designed to determine the sampling state instants. The overall control strategy guarantees that the output signal tracks the reference signal, and all the signals of the closed-loop systems are convergent. Finally, the fan speed control system is constructed to demonstrate the validity of the proposed strategy and the application of the general systems.

Optimal Robust Navigation Control of an Endovascular Microrobot

Microrobots are considered to be a promising solution for complex sequence of operations in biomedical applications. The paper aims to present an algorithm for path planning and control of an endovascular microrobot navigated by a conventional magnetic resonance imaging (MRI) device. The microrobot is a ferromagnetic spherical bead moving through human vascular system; accordingly, the dynamic model is well developed considering the most dominant resistive force, i.e., hydrodynamic drag. An optimal approach considering a power index is used for path planning of the robot from an initial position to the desired destination avoiding collision with boundaries within a generated robust domain based on the unmodeled dynamic of surface forces. Due to the presence of parameter uncertainty and unmodeled dynamics, an adaptive backstepping controller is designed to navigate the bead through the optimal robust path such that the control signal can be implemented via a conventional MRI device. The control method is proved to have stability and convergence as it manages to maintain the estimated parameters and control inputs bounded in the presence of disturbance and uncertainty. The method of path planning explicitly deals with unstructured uncertainties of the surface forces based on developed comparison and reasoning as it maintains minimum effort optimality. The adaptive backstepping method is designed to handle structural uncertainties and disturbances due to pulsatile flow and non-measured velocity. Several simulations were performed to examine navigation of the ferromagnetic microrobot in the circulatory system of human body, and the tracking errors, estimated parameters, and control signal inputs are represented, accordingly. Also, it is shown how wall effect correlation term in the model could increase the control accuracy.

Neural Network Integrated Adaptive Backstepping Control of DC-DC Boost Converter

This paper deals with the output voltage regulation problem of dc-dc boost converter feeding a resistive load. A new control mechanism based on Chebyshev neural network embedded in an adaptive backstepping framework is proposed for the boost converter control. Since the converter is complex, time varying and non-linear in nature, it exhibits high sensitivity to unanticipated disturbances in the load current. Hence, designing a robust control mechanism to attain a satisfactory transient and steady state performance over a wide range of operating points is a challenging task. In this work, a control law is derived based on the systematic and recursive design strategy of adaptive backstepping method. A single layer functional link Chebyshev neural network is employed for a fast estimation of uncertain and time varying load profile of the boost converter. The stability of overall converter equipped with the proposed controller is proved using Lyapunov stability criterion. Further, in order to validate the proposed methodology, the boost converter is simulated in MATLAB/Simulink software and is subjected to different load perturbations. The efficacy of the proposed control is highlighted by evaluating it against the conventional adaptive backstepping control under identical conditions. The results obtained reveals that the proposed control is much faster in estimating the unknown load parameter and offers satisfactory output voltage tracking, yielding fast response and low peak overshoot/undershoot in the event of unknown load perturbations. Experimental investigation using dspace DS1103 controller is further carried out to validate the efficacy of proposed control scheme.

Adaptive sliding-mode-backstepping trajectory tracking control of underactuated airships

The problem of trajectory tracking control for an underactuated stratospheric airship with model parameter uncertainties and wind disturbances is addressed in the paper. An adaptive backstepping sliding-mode controller is designed from the airship nonlinear dynamics model. The proposed controller has a two-level structure for trajectory guidance, tracking and stability, and the developed controller, based on nonlinear adaptive sliding-mode backstepping method, provides airship attitude and velocity control for the entire flight process. Furthermore, an active set based weighted least square algorithm is applied to find the optimal control surface inputs and the thruster commands under constraints of actuator saturation. The closed-loop system of trajectory tracking control plant is proved to be globally asymptotically stable by using Lyapunov theory. By comparing with traditional backstepping control and PID design, the results obtained demonstrate the capacity of the airship to execute a realistic trajectory tracking mission under two cases of lateral- and roll- underactuations, even in the presence of aerodynamic coefficient uncertainties, and wind disturbances.

Event-Triggered Adaptive Neural Network Control for Nonstrict-Feedback Nonlinear Time-Delay Systems With Unknown Control Directions

In this article, the event-triggered-based adaptive neural network control problem is studied for a class of nonlinear time-delay systems with nonstrict-feedback structures and unknown control directions. First, a compensation system is introduced to handle the input delay and an observer is also designed to estimate the unmeasurable states. Then, by employing the neural networks and the variable separation approach, the adaptive backstepping method is applied to control the nonlinear systems with nonstrict-feedback structures. By codesigning the adaptive controller and the triggering mechanism, the input-to-state stability (ISS) assumption with respect to the measurement error is removed. Finally, it is shown that the proposed event-triggered adaptive controller can ensure the semiglobal boundedness of all the states in the closed-loop systems.

An Observer-Based Robust Adaptive Fuzzy Back-Stepping Control of Ball and Beam System

In this paper, an observer-based robust adaptive fuzzy back-stepping control is provided for a ball and beam system while accessible state variables of the system are position and angle of the ball and beam, respectively. Firstly, based on the mentioned measureable signals, a velocity observer is employed to estimate rate of the available states of the system and then a robust adaptive fuzzy back-stepping control is accomplished by the estimated states of the system. Asymptotic stability of the observer-based control system in the presence of un-modeled dynamics and uncertainties is shown by Lyapunov theory. Simulation results illustrate proper functioning of the adaptive fuzzy back-stepping control method on the ball and beam system. Also, the results of the proposed method are compared with an existing method in order to show performance and accuracy of the controller.

Integrated Guidance and Control for Hypersonic Morphing Missile Based on Variable Span Auxiliary Control

The morphing aircraft can improve the flight performance of hypersonic vehicles by satisfying the flight requirements of large airspace and large velocity field. In this paper, for the hypersonic variable span missile, the dynamic model and aerodynamic model are established on the variable span characteristic. The adaptive dynamic surface control back-stepping method is used to establish the integrated guidance and control (IGC) with terminal angular constraint in the dive phase of the hypersonic variable span missile. The span variety is used to assist the lift control to achieve fast and stable control for the centroid motion. The simulation results demonstrate that the feasibility and robustness of the IGC method of the hypersonic variable span missile is better than the invariable span.

Improved adaptive backstepping sliding mode control for a three‐phase PWM AC–DC converter

The stability problem of a three-phase voltage source PWM AC-DC converter is addressed through an improved adaptive backstepping method, which combines the following contents: input-output linearisation, adaptive backstepping method, error compensation and sliding mode control. The state equation of the three phase system is obtained by the power balance relationship between the input current and the output voltage, and then the coordinate conversion is carried out in order to design the controller. When the input-output linearisation method transfers the system model to a strict-feedback form, an improved adaptive backstepping control approach is given to stabilise the converter. Finally, the simulation results show that the improved method has three benefits: retain a faster stability of rectifier, reduce overshoot of DC voltage and bring about a real-time parameter estimation.

A flexible current tracking control of sensorless induction motors via adaptive observer

In this article, an interconnected adaptive observer-based backstepping control method is proposed to achieve sensorless current control without persistent excitation condition. Based on the stability theories of mathematics, an effective observer utilized to estimate the fluxes and external load is given. It has a good foundation for breaking the limitation caused by the coupling between the control process and the parameter estimation course. The characteristic of the uncoupling can make the control range for currents more wider. Due to the effective online tracking and the good adaptability of the designed observers, the control effect shows good robustness to the parameters. Finally, numerical simulations are provided to intuitively illustrate the effectiveness and the superiority of the theoretical results.

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

SummaryA robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.

Strong Robust and Optimal Chaos Control for Permanent Magnet Linear Synchronous Motor

To effectively solve the chaotic phenomenon problem in permanent magnet linear synchronous motor (PMLSM), this paper presents a novel control scheme combining radial basis function neural network (RBFNN), adaptive backstepping method, and particle swarm optimization (PSO) algorithm. By applying a feedback decoupling controller, a decoupled chaotic model of the PMLSM is constituted. In addition, in order to enhance the robustness of the system, the RBFNN is utilized to identify the uncertainties in PMLSM and the convergence of the overall closed-loop system, including unknown parameters is guaranteed based on the adaptive backstepping method. Moreover, the PSO is applied to promote the dynamic performance of the control system. The simulation results demonstrate the existence of chaotic phenomenon in the PMLSM. Besides, PSO-RBFNN controller that has strong robustness can make the motor out of chaos rapidly and smoothly, and identify the unknown parameters quickly and accurately.

Global asymptotic regulation control for MIMO mechanical systems with unknown model parameters and disturbances

A global asymptotic regulation control scheme based on the adaptive disturbance estimation is proposed for the MIMO mechanical systems with unknown model parameters and disturbances. By transforming the motion model of the mechanical system and the disturbances into the parametric forms, respectively, the disturbance rejection control for the MIMO mechanical systems is converted into the adaptive control problem. The robust adaptive control law is then designed using the adaptive backstepping method. Stability analysis shows that the designed control law achieves the global asymptotic regulation of the output vector. Simulations on regulation control of two marine vessels verify the effectiveness of the proposed control scheme.

A Novel Robust Adaptive Backstepping Method Combined with SMC on Strict-Feedback Nonlinear Systems Using Neural Networks

Adaptive backstepping methodology is a powerful tool for nonlinear systems, especially for strict-feedback ones, but its robustness still needs improvements. In this paper, combined with sliding mode control (SMC), a new backstepping design method is proposed to guarantee the robustness. In this method, based on the novel combining method, the auxiliary controller is introduced only in the final step of the real controller, unlike traditional methods, which usually all include an auxiliary controller in every de-signing step to guarantee the robustness of the closed-loop systems. The novel combing methods can avoid calculating multiple and high-order derivatives of the auxiliary controllers in the intermediate steps, low-ering the computational burden in evaluating the controller. The effectiveness of the proposed approach is illustrated from simulation results.

Observer-Based Adaptive Fuzzy Control for Time-Varying State Constrained Strict-Feedback Nonlinear Systems with Dead-Zone

This paper focuses on the problem of adaptive fuzzy control for a class of time-varying state constrained strict-feedback nonlinear systems with dead-zone. Based on the arbitrary approximation of fuzzy logic systems (FLSs), the unknown nonlinear functions in the system are approximated by FLSs. Time-varying barrier Lyapunov functions and a fuzzy observer are designed to dispose the unmeasured time-varying constrained states in the system. Furthermore, combining with the adaptive backstepping method and Lyapunov stability theory, it is testified that the proposed control strategy can ensure system stability and all the signals in the closed-loop system are semi-global uniformly ultimately bounded. Finally, the simulation results are given to demonstrate the effectiveness of the proposed method.

Dynamically Positioned Ship Steering Making Use of Backstepping Method and Artificial Neural Networks

Abstract The article discusses the issue of designing a dynamic ship positioning system making use of the adaptive vectorial backstepping method and RBF type artificial neural networks. In the article, the backstepping controller is used to determine control laws and neural network weight adaptation laws. The artificial neural network is applied at each time instant to approximate nonlinear functions containing parametric uncertainties. The proposed control system does not require precise knowledge of the model of ship dynamics and external disturbances, it also eliminates the problem of analytical determination of the regression matrix when designing the control law with the aid of the adaptive backstepping procedure.

Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone

This paper investigates the problem of adaptive finite-time tracking control for strict-feedback nonlinear continuous-time systems subject to full state constraints and dead-zone. By utilizing the finite-time stability theory, barrier Lyapunov functions and the adaptive backstepping method, a novel adaptive tracking control strategy is proposed. On the basis of the presented method, the finite-time control problem of the nonlinear system with dead-zone is solved. The finite-time controller is designed such that all the signals in the closed-loop system are bounded, the output is driven to track the reference signal to a small neighborhood and all states are ensured to remain in the predefined compact sets. Finally, the effectiveness of the proposed scheme is verified via some simulation results.

Adaptive backstepping approach for dc‐side controllers of Z ‐source inverters in grid‐tied PV system applications

Z -source inverters (ZSIs) are single-stage power converters with both voltage buck and boost capabilities provided by the unique impedance network and the ability to operate during shoot-through states. This study proposes a novel non-linear adaptive backstepping method for dc-side controllers in a multi-loop control scheme of the ZSI in grid-tied photovoltaic (PV) systems. Despite the variability of the capacitor and inductor values in the ZSI impedance network, the proposed controller guarantees robust and stable operation under varying levels of PV irradiance and temperature. The shoot-through duty ratio of the ZSI is obtained directly from the output of an MPPT algorithm and the measured PV and inductor currents. This strategy overcomes the disadvantages of the conventional approach such as the non-minimum phase at the dc side of the ZSI. It also eliminates the need to linearise the voltage/current characteristics of the PV arrays and ZSI model. The ac-side controllers consist of an outer proportional-integral voltage controller and an inner deadbeat current controller to achieve unity power factor and stable capacitor voltage in spite of grid voltage fluctuations. The efficacy of the proposed adaptive backstepping controller and the multi-loop control scheme is validated by offline and hardware-in-the-loop real-time simulations.