Abstract: A mobile robot is one of the well-known nonholonomic systems. The integration of a kinematic controller and a torque controller for the dynamic model of a nonholonomic mobile robot has been presented (Fierro and Lewis, 1995). In this paper, an adaptive extension of the controller is proposed. If an adaptive tracking controller for the kinematic model with unknown parameters exists, an adaptive tracking controller for the dynamic model with unknown parameters can be designed by using an adaptive backstepping approach. A design example for a mobile robot with two actuated wheels is provided. In this design, a new kinematic adaptive controller is proposed, then a torque adaptive controller is derived by using the kinematic controller.

Abstract: A controller is proposed for the robust backstepping control of a class of general nonlinear systems using neural networks (NNs). A tuning scheme is proposed which can guarantee the boundedness of tracking error and weight updates. Compared with adaptive backstepping control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed, so no preliminary dynamical analysis is needed. One salient feature of our NN approach is that there is no need for the off-line learning phase. Three nonlinear systems, including a one-link robot, an induction motor, and a rigid-link flexible-joint robot, were used to demonstrate the effectiveness of the proposed scheme.

Abstract: This paper presents a novel speed control technique for an interior permanent-magnet synchronous motor (IPMSM) drive based on newly developed adaptive backstepping technique. The proposed stabilizing feedback law for the IPMSM drive is shown to be globally asymptotically stable in the context of Lyapunov theory. The adaptive backstepping technique takes system nonlinearities into account in the control system design stage. The detailed derivations of the control laws have been given for controller design. The complete IPMSM drive incorporating the proposed backstepping control technique has been successfully implemented in real-time using digital signal processor board DS1102 for a laboratory 1-hp motor. The performance of the proposed drive is investigated both in experiment and simulation at different operating conditions. It is found that the proposed control technique provides a good speed tracking performance for the IPMSM drive ensuring the global stability.

Abstract: In this paper we present a tracking controller for a class of underactuated mechanical systems, based on a backstepping procedure. This class includes an approximation of small helicopter dynamics. The need to avoid artificial singularities due to the attitude representation is the main driver behind the control design presented in this paper: to achieve this goal, we will operate directly in the configuration manifold of the vehicle. The control design provides asymptotic tracking for an approximate model of small helicopters, and bounded tracking when more complete models are considered. Simulation examples, including both point stabilization and aggressive maneuver tracking, are presented and discussed.

Abstract: Presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large-scale systems using nonlinear output feedback. The proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities. Any decentralized system in the family may have an unknown, nonzero equilibrium point. Partially decentralized reduced-order filters are presented to recover the unmeasured states. The recursive, decentralized, output-feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements. The effectiveness of the decentralized algorithm is supported by simulation results.

Abstract: This paper deals with the robust adaptive control of a class of nonlinear systems in the presence of parametric uncertainties and dominant uncertain nonlinearities. The proposed controller utilizes the robust adaptive control to guarantee uniform boundedness and convergence of tracking errors. In addition, an adaptive fuzzy logic system is used as a universal approximator to reduce the model uncertainties coming from uncertain nonlinearities and to improve tracking performance. The approach does not require the matching condition imposed on control systems by using the backstepping design procedure, and provides boundedness of tracking errors under poor parameter adaptation. The method can be applied to a class of single-input single-output (SISO) nonlinear systems, transformable to a parametric-strict-feedback form.

Abstract: This paper is concerned with the control of a class of chaotic systems using adaptive backstepping, which is a systematic design approach for constructing both feedback control laws and associated Lyapunov functions. Firstly, we show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the so-called nonautonomous "strict-feedback" form. Secondly, an adaptive backstepping control scheme is extended to the nonautonomous "strict-feedback" system, and it is shown that the output of the nonautonomous system can asymptotically track the output of any known, bounded and smooth nonlinear reference model. Finally, the Duffing oscillator with key constant parameters unknown, is used as an example to illustrate the feasibility of the proposed control scheme. Simulation studies are conducted to show the effectiveness of the proposed method.

Abstract: We propose, from an adaptive control perspective, a neural controller for a class of unknown, minimum phase, feedback linearizable nonlinear system with known relative degree. The control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural-network structure. The resulting controller, however, moves the complex mechanics involved in a typical backstepping design from off-line to online. With appropriate choice of the network size and neural basis functions, the same controller can be trained online to control different nonlinear plants with the same relative degree, with semi-global stability as shown by the simple Lyapunov analysis. Meanwhile, the controller also preserves some of the performance properties of the standard backstepping controllers. Simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller.

Abstract: In this correspondence, Nussbaum gains (1983) are introduced in the backstepping design to obtain adaptive controllers for systems with unknown high-frequency gain. Two kinds of modified backstepping control design schemes are developed. It is shown that both schemes can give asymptotic tracking.

Abstract: For a class of nonlinear systems, a robust backstepping design achieves both local optimality and global inverse optimality. The design is robust in the sense that it achieves a prescribed level of disturbance attenuation with stability margins. An analytic example illustrates the performance of the locally optimal control design.

Abstract: Develops a systematic methodology for the control of a class of nonlinear systems and applies it to an electrohydraulic system. The class of systems to be dealt with are those that are single input and can be put in strict feedback form. The approach is conceptually similar to previously developed integrator backstepping methodologies. However, unlike some previous investigations which have relied exclusively on a Lyapunov analysis, this work presents a stability analysis using a passivity formulation. There are two main advantages of the proposed approach which become significant during implementation. One practical advantage is that the resulting controller leads to synthetic inputs that are decoupled in a certain sense. This leads to a compartmentalization of modeling error effects associated with the controller. A second advantage of this method is that the system model need not be differentiated in the control formulation. A class of modeling error is introduced and compensated for with the resulting control able to guarantee specified boundary layer tracking. A nonlinear model is developed and verified for an electrohydraulic testbed consisting of a cylinder governed by an electronically controlled servovalve. Finally, the control algorithm is implemented on the testbed and a comparison is made with existing integrator backstepping algorithms. The comparisons demonstrate the benefits of the presented approach.

Abstract: The output-feedback global tracking problem is solved for the well-known nonlinear benchmark RTAC (rotational-translational actuator) system, in which one of the unmeasured states appears quadratically in the state equations. Our observer/controller backstepping design yields a nonlinear output-feedback controller that forces the translational displacement to globally asymptotically track an appropriate time-varying signal. The proposed solution is new even for the case of global output-feedback stabilization, namely when the reference signal is zero.

Abstract: An adaptive backstepping controller is proposed to control the mover position of a linear induction motor (LIM) drive to track periodic reference inputs in this study. First, the feedback linearisation theory is used to decouple the thrust force and the flux amplitude of the LIM. Then, an integral-proportional (IP) position controller is designed according to the estimated plant model to match the prescribed periodic step-command tracking specifications for the LIM drive. Moreover, a feedforward control is added to the IP control system for the tracking of periodic sinusoidal and triangular reference inputs. Although theoretically the feedforward control can track any time-varying reference, the robust control performance is degenerate when the uncertainties occur in the controlled plant. Therefore, an adaptive backstepping approach is proposed to obtain the robustness for uncertainties. With the proposed adaptive backstepping controller, the mover position of the LIM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference inputs. The effectiveness of the proposed control scheme is verified by both the simulated and experimental results.

Abstract: The control problem of a hydraulic servo-system is addressed. The performance achievable by classical linear controllers, e.g. PD, are usually limited due to the highly nonlinear behavior of the hydraulic dynamics. This paper adopts the backstepping design strategy to develop a Lyapunov-based nonlinear controller for a hydraulic servo-system. Load, hydraulic and valve dynamics are incorporated in the design process. An adaptation law is also proposed to deal with uncertainties in hydraulic parameters. The approach can be further extended to the control of hydraulically driven manipulators. Both simulation and experimental results are provided to show the effectiveness of the proposed method.

Abstract: A wide class of mechanical systems with uncertainties can be modeled through a state equation in parametric-pure-feedback form. Thus, in principle, the well-known backstepping design procedure can be applied to solve a regulation or a tracking problem. Yet, this is no more possible if a clear parametric dependence on the control signal (torque or force) cannot be established. Systems to which this happens can be efficaciously controlled via the proposed approach which inherits n-1 steps of the classical backstepping procedure. This latter procedure is used to attain a partial system state transformation, completed with the construction of a suitable sliding manifold upon which a second order sliding mode is enforced.

Abstract: This paper deals with state feedback adaptive control of parametric-strict-feedback (triangular) non-linear systems with unknown virtual control coefficients. A priori knowledge of the signs of the virtual coefficients is not required, and control signals and adaptive laws are smooth. Asymptotic tracking of smooth reference signals is achieved while all the variables remain bounded. The proposed algorithms make use of backstepping and tuning functions, and enlarge the class of non-linear systems with unknown parameters for which asymptotic output tracking can be achieved. Copyright (C) 2000 John Wiley & Sons, Ltd.

Abstract: We consider feedback design for nonlinear, multi-input affine control systems with disturbances and present results on assigning, by choice of feedback, a desirable upper bound to a given control Lyapunov function (clf) candidate's derivative along closed-loop trajectories. Specific choices for the upper bound are motivated by ℒ2 and ℒ∞ disturbance attenuation problems. The main result leads to corollaries on “backstepping” locally Lipschitz disturbance attenuation control laws that are perhaps implicitly defined through a locally Lipschitz equation. The results emphasize that only rough information about the clf is needed to synthesize a suitable controller. A dynamic control strategy for linear systems with bounded controls is discussed in detail.

Abstract: In this paper the problem of automating the gearshift process of a manual transmission without synchronizers is investigated. The application is very interesting from an integrated powertrain control point of view, since it includes many different control tasks and encourages the use of the engine as an actuator to the rest of the powertrain. A model-based control law for the task of gearshifting is presented. The controller is designed based on the backstepping methodology. It includes control laws for transmission torque control as well as for engine speed control. Simulations have shown good results for the gearshift controller.

Abstract: A novel nonlinear controller, backstepping control with integral function, is proposed for high performance motion control systems. Backstepping control utilizes Lyapunov function to guarantee the convergence of the position tracking error from all possible initial conditions. An integral action is integrated in the backstepping design. The added integrator improves the system's robustness against modeling uncertainties and external disturbance, thus improving steady-state control accuracy. The proposed novel scheme has been implemented and tested on an actual industrial product platform. Experimental results and performance comparison confirm that the proposed backstepping control scheme offers significantly improved performance in terms of the trajectory tracking ability to time-varying reference input, system control bandwidth, and robustness against external disturbances.

Abstract: This paper studies the problem of adaptive control for a class of nonlinear time-varying discrete-time systems with nonparametric uncertainties. The plant parameters considered here are not necessarily slowly time-varying in a uniform way. They are allowed to have a finite number of big jumps. By using the backstepping procedures with parameter projection update laws, a robust adaptive controller can be designed to achieve adaptive tracking of a reference signal for this class of systems. It is shown that the proposed controller can guarantee the global boundedness of the states of the whole adaptive system in the presence of parametric and nonparametric uncertainties. It can also ensure that the tracking error falls within a compact set whose size is proportional to the size of the uncertainties and disturbances. In the ideal case when there is no nonparametric uncertainties and time-varying parameters, perfect tracking can be achieved.

Abstract: Two nonlinear lateral control algorithms are designed for a tractor-semitrailer type commercial heavy vehicle. The baseline steering control algorithm is designed utilizing input-output linearization. To enhance the lateral stability and furthermore reduce tracking errors of the trailer, braking forces are independently controlled on the inner and outer wheels of the trailer. The coordinated steering and braking control algorithm is designed based on the multivariable backstepping technique. Simulations conducted using the complex model show that the trailer yaw errors under coordinated steering and independent braking force control are much smaller than those without independent braking force control.

Abstract: Sufficient conditions ensuring that a nonlinear system with disturbances having a delay is delay independent globally asymptotically stable, are given. The proof carried out relies extensively on a characterization of the stability property in terms of the Lyapunov function. The result is applied to some biological systems and neural networks. It is also used to construct a stabilizing memoryless controller for a second order system with state-delay.