Backstepping Scheme Research Articles

ADAPTIVE FUZZY-BASED TRACKING CONTROL FOR A CLASS OF STRICT-FEEDBACK SISO NONLINEAR TIME-DELAY SYSTEMS WITHOUT BACKSTEPPING

In this paper, an adaptive fuzzy tracking control is presented for a class of SISO nonlinear strict feedback systems with unknown time delays. The proposed algorithm does not use the backstepping scheme rather it converts the strict-feedback time-delayed system to the normal form. The Mamdani-type fuzzy system is employed to approximate on-line the lumped uncertain system nonlinearity. The developed controller guarantees uniform ultimate boundedness of all signals in the closed-loop system. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector needed to be updated on-line. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. The Lyapunov stability of the fuzzy system parameters and the filtered tracking error is employed to guarantee semiglobal uniform boundedness for the closed loop system. Simulation results are presented to verify the effectiveness of the proposed approach.

Adaptive backstepping synchronization for networked Lagrangian systems

decentralized control law using a backstepping scheme is proposed to deal with a leader follower multiple robots structure. Based on graph theory and Laplacian, the coordination strategy combines the leader follower control with the decentralized control. In fact, in the proposed approach, each follower robot only needs the information exchange with its connected neighbors and does not assume the existence of direct communication channel with the leader, which mitigate the implementation cost, mainly when the cooperative robots number increases. The objective of the designed control law is to synchronize positions and velocities of multiple followers interconnected via the neighbor-based rule with respect to the leader's state. The proposed strategy is further extended to adaptive neural network coordination. The performance of synchronization control system and the nonlinear stability are derived by Lyapunov method. Simulations were performed to demonstrate the effectiveness of the proposed synchronization control approach.

Hybrid Control for an Overhead Crane

One of the common industrial structures that are used widely in many harbors and factories are overhead crane. Overhead cranes are usually operated manually or by some conventional control methods. In this study, a new combination of nonlinear backstepping scheme with fuzzy system is presented to control both position regulation and anti-swing control to avoid collision with other equipments. This study uses two different fuzzy systems: off-line and on-line to consider different concept. The backstepping design procedure consists of two steps. In all steps to design backstepping controller, Lyapunov stability theorem is used to stability analysis and control design problems. Furthermore, the stability of the overhead crane with nonlinear fuzzy backstepping controller is discussed. Simulation results illustrated the validity of the proposed control algorithm. Key words: On-line fuzzy design, off-line fuzzy design, backstepping method, over head crane.

Path tracking control of a spherical mobile robot

The typical dynamic path following method presents a systematic framework for nonholonomic mobile robot and exhibits excellent tracking performance in simulations and experiments. However, it fails to converge the position and pose simultaneously for spherical robot with a 2 DOFs pendulum. This paper discusses the practical path tracking control of a spherical robot, focusing on the simultaneous converges of position and pose. The kinematics and dynamics models of a spherical robot are deduced and regulated to be a canonical form through the null space method and nonlinear feedback. Under the inspiration of human-like tracker-guide mode, a real-time fuzzy guidance scheme for the path tracking control of the spherical robot is proposed. To deal with the dynamics, a hierarchical sliding mode controller is integrated with the fuzzy guidance scheme through a backstepping strategy. The effectiveness of the proposed path tracking method is validated trough MATLAB simulations on both the comparisons with the typical dynamic path following algorithm and several practical cases: effect of initial conditions, complex curves and piecewise continuous paths tracking.

Adaptive Kriging controller design for hypersonic flight vehicle via back-stepping

In this study, the adaptive Kriging controller is investigated for the longitudinal dynamics of a generic hypersonic flight vehicle. For the altitude subsystem, the dynamics are transformed into the strict-feedback form where the back-stepping scheme is used. The velocity subsystem is transformed into the output-feedback form. Considering the non-linearity of the dynamics, the nominal feedback is included in the controller while Kriging system is used to estimate the uncertainty, which is described as the realisations of Gaussian random functions. To eliminate the infinite increase of the data size, the recursive Kriging algorithm is adopted in this study. Under the proposed controller, the almost surely bounded stability analysis is presented. The simulation study compared with neural back-stepping control is presented to show the effectiveness of the proposed control approach.

Decentralized Dynamic Surface Control of Large-Scale Interconnected Systems in Strict-Feedback Form Using Neural Networks With Asymptotic Stabilization

A novel neural network (NN)-based nonlinear decentralized adaptive controller is proposed for a class of large-scale, uncertain, interconnected nonlinear systems in strict-feedback form by using the dynamic surface control (DSC) principle, thus, the "explosion of complexity" problem which is observed in the conventional backstepping approach is relaxed in both state and output feedback control designs. The matching condition is not assumed when considering the interconnection terms. Then, NNs are utilized to approximate the uncertainties in both subsystem and interconnected terms. By using novel NN weight update laws with quadratic error terms as well as proposed control inputs, it is demonstrated using Lyapunov stability that the system states errors converge to zero asymptotically with both state and output feedback controllers, even in the presence of NN approximation errors in contrast with the uniform ultimate boundedness result, which is common in the literature with NN-based DSC and backstepping schemes. Simulation results show the effectiveness of the approach.

Adaptive neural control based on HGO for hypersonic flight vehicles

This paper describes the design of adaptive neural controller for the longitudinal dynamics of a generic hypersonic flight vehicle (HFV) which are decomposed into two functional systems, namely the altitude subsystem and the velocity subsystem. For each subsystem, one adaptive neural controller is investigated based on the normal output-feedback formulation. For the altitude subsystem, the high gain observer (HGO) is taken to estimate the unknown newly defined states. Only one neural network (NN) is employed to approximate the lumped uncertain system nonlinearity during the controller design which is considerably simpler than the ones based on back-stepping scheme with the strict-feedback form. The Lyapunov stability of the NN weights and filtered tracking error are guaranteed in the semiglobal sense. Numerical simulation study of step response demonstrates the effectiveness of the proposed strategy in spite of system uncertainty.

Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties

AbstractThis paper investigates the problem of adaptive stabilization by output feedback for a class of uncertain nonlinear systems. The distinguishing feature of such a class of systems is the presence of uncertain control coefficient and unmeasured states dependent growth with growth rate of polynomial‐of‐output multiplying an unknown constant. First, new high‐gain K‐filters with two dynamic gains are introduced, and an appropriate state observer is constructed based on the K‐filters. Then, motivated by the universal control idea, the backstepping scheme is successfully developed for the adaptive output feedback control design. By appropriate choice of the design parameters, the global stability of the closed‐loop system can be guaranteed. Finally, numerical simulations are provided to illustrate the correctness of the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.

Sensorless Fault Tolerant Control Based On Backstepping Strategy For Induction Motors

AbstractIn this paper, a fault tolerant control for induction motors based on backstepping strategy is designed. The proposed approach permits to compensate both the rotor resistance variations and the load torque disturbance. Moreover, to avoid the use of speed and flux sensors, a second order sliding mode observer is used to estimate the flux and the speed. The used observer converges in a finite time and permits to give a good estimate of flux and speed even in presence of rotor resistance variations and load torque disturbance. The simulation results show the efficiency of the proposed control scheme.

High gain adaptive output feedback control of non-linear systems with a class of control uncertainties

This paper presents a design method of high gain adaptive output feedback controller for non-linear systems with higher order relative degree and some uncertainties in control input term. The controlled system is transformed by two virtual filters and the control input is designed so as to make the virtual filter’s signal a high gain adaptive control signal using backstepping strategy in the filter dynamics. The proposed method is useful in cases where only the output signals are available.

COOPERATIVE ATTITUDE SYNCHRONIZATION FOR RIGID-BODY SPACECRAFT <em>VIA</em> VARYING COMMUNICATION TOPOLOGY

This paper studies the application of nonlinear cooperative control theory to the attitude synchronization problem. To this end, explicit conditions, in terms of vector nonlinear differential inequalities, is presented firstly to ensure both the Lyapunov stability and asymptotically cooperative stability for a certain class of heterogeneous nonlinear system. Then, decentralized control algorithm incorporated with standard backstepping scheme is developed to accomplish attitude synchronization for a group of spacecraft with rigid body dynamics described by unit quaternion. In particular, the proposed control system imposes the least restrictive requirement on the communication, a piecewise constant, intermittently available, and sequentially complete topology is theoretically enough to ensure the asymptotically cooperative stability. Simulation results demonstrate the effectiveness of the proposed control algorithms.

CONTROL AND SYNCHRONIZATION OF CHAOTIC PENDULUM USING BACKSTEPPING

This study presents a backstepping scheme for the control and synchronization of chaos in the damped-driven pendulum. The method is a systematic design approach and consists of a recursive procedure that skillfully interlaces the choice of a Lyapunov function with the control. With this technique, the chaotic dynamics of the pendulum is stabilized to the stable equilibrium point and the arbitrary bounded function of time f(t) is tracked. It is further shown that the complete synchronization between two identical chaotic pendula can be realized using this method. Numerical simulations are also presented to verify the control approach.

A robust control of electro hydrostatic actuator using the adaptive back-stepping scheme and fuzzy neural networks

In general, the position control of electro hydrostatic actuator(EHA) systems is difficult because of the large variation of the effective bulk modulus of the working fluid, which is due to the absence of a heat exchanger like a reservoir tank, the friction between the cylinder and piston, and the external disturbance force. Moreover, it is difficult to identify the values of the effective bulk modulus and friction. In this paper, the variation of the effective bulk modulus, friction, and external disturbance are considered as uncertainties of EHA systems. To solve the problems due to these system uncertainties, an adaptive back-stepping control scheme with fuzzy neural networks(FNNs) is proposed. The effectiveness of the adaptive back-stepping control(ABSC) system with FNNs was compared with those of the standard back-stepping control(BSC) system and the ABSC system through computer simulation.

Adaptive Spacecraft Attitude Tracking Controller Design Based on Similar Skew-symmetric Structure

This article presents an adaptive attitude tracking controller with external disturbances and unknown inertia parameters. The similar skew-symmetric structure is extended from the autonomous case to the non-autonomous case. The non-autonomous similar skew-symmetric is chosen as the desired structure of the closed loop system for attitude controller design. Based on this structure, a novel adaptive backstepping scheme is proposed to design the attitude controller by taking full advantage of the symmetry and the positive definiteness of the inertia matrix. The attitude tracking precision is enhanced by employing the linear parameterized form of the external disturbance torques. Simulation results demonstrate the effectiveness of the proposed attitude controller.

Adaptive neural network tracking control for manipulators with uncertain kinematics, dynamics and actuator model

A neural-network-based adaptive controller is proposed for the tracking problem of manipulators with uncertain kinematics, dynamics and actuator model. The adaptive Jacobian scheme is used to estimate the unknown kinematics parameters. Uncertainties in the manipulator dynamics and actuator model are compensated by three-layer neural networks. External disturbances and approximation errors are counteracted by robust signals. The actuator controller is designed based on the backstepping scheme. Compared with the existing work, the proposed method considers the manipulator kinematics uncertainty, does not need the “linearity-in-parameters” assumption for the uncertain terms in the dynamics of manipulator and actuator, and guarantees the tracking error to be as small as desired. Finally, the performance of the proposed approach is illustrated by the simulation example.

Adaptive Neural Control for Strict-Feedback Nonlinear Systems Without Backstepping

In this brief, a new adaptive neurocontrol algorithm for a single-input-single-output (SISO) strict-feedback nonlinear system is proposed. Most of the previous adaptive neural control algorithms for strict-feedback nonlinear systems were based on the backstepping scheme, which makes the control law and stability analysis very complicated. The main contribution of the proposed method is that it demonstrates that the state-feedback control of the strict-feedback system can be viewed as the output-feedback control problem of the system in the normal form. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Depending heavily on the universal approximation property of the neural network (NN), only one NN is employed to approximate the lumped uncertain system nonlinearity. The Lyapunov stability of the NN weights and filtered tracking error is guaranteed in the semiglobal sense.

Chaos control in AFM system using sliding mode control by backstepping design

This paper presents a robust algorithm to control the chaotic atomic force microscope system (AFMs) by backstepping design procedure. The proposed feedback controller is composed by a sliding mode control (SMC) and a backstepping feedback, so its implementation is quite simple and can be made on the basis of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as system external disturbances. The concept of extended system is used such that a continuous sliding mode control effort is generated using backstepping scheme. It is guaranteed that under the proposed control law, uncertain AFMs can asymptotically track target orbits. The converging speed of error states can be arbitrary turned by assigning the corresponding dynamics of the sliding surfaces. Numerical simulations demonstrate its advantages by stabilizing the unstable periodic orbits of the AFMs and this method can also be easily extended to elimination chaotic motion in any types of chaotic AFMs.

ROBUST ADAPTIVE CONTROL FOR STRICT-FEEDBACK NONLINEAR SYSTEMS

In this paper, we propose a robust adaptive tracking control based on the backstepping strategy for strict-feedback nonlinear systems with nonparametric uncertain nonlinearities. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be decomposed by unknown bounded nonlinear functions and known nonlinear functions. The proposed method can deal with uncertain nonlinearities that appear at the control input term too. It is also shown that suitable choice of design parameters guarantees the convergence of tracking error to any desired bound.

Adaptive Control via Backstepping Technique and Neural Networks of a Quadrotor Helicopter

A nonlinear adaptive controller for the quadrotor helicopter is proposed using backstepping technique mixed with neural networks. The backstepping strategy is used to achieve good tracking of desired translation positions and yaw angle while maintaining the stability of pitch and roll angles simultaneously. The knowledge of all physical parameters and the exact model of the quadrotor are not required for the controller, only some properties of the model are needed. In fact, online adaptation of neural networks and some parameters is used to compensate some unmodeled dynamics including aerodynamic effects. Under certain relaxed assumptions, the proposed control scheme can guarantee that all the signals in the closed-loop system are Uniformly Ultimately Bounded (UUB). The design methodology is based on Lyapunov stability. One salient feature of the proposed approach is that the controller can be applied to any type of quadrotor helicopter of different masses and lengths within the same class. The feasibility of the control scheme is demonstrated through simulation results.

Adaptive Backstepping Control Using Combined Direct and Indirect Adaptation

A new adaptation mechanism is proposed for the tuning functions based adaptive backstepping control for a class of nonlinear systems. The new scheme combines direct and indirect parameter update regimes in an effort to improve the speed and accuracy of the adaptation which in turn leads to increased tracking performance. The parameter update dynamics is driven both by the identification error and the tracking error defined in the backstepping control. The closed loop error dynamics is shown to be globally stable by using a recursive mechanism based on Lyapunov analysis with tracking error convergence along with identification error convergence. The proposed scheme is tested on two benchmark examples in order to demonstrate its performance increase compared to the tuning functions based adaptive backstepping scheme.