Abstract: This paper investigates the adaptive fuzzy decentralized fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear system contains the unknown nonlinear functions, i.e., unmeasured states and actuator faults, which are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is designed to estimate the unmeasured states. By combining the backstepping technique with the nonlinear FTC theory, a novel adaptive fuzzy decentralized FTC scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and the tracking errors between the system outputs and the reference signals converge to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.

Abstract: This paper studies an adaptive tracking control for a class of nonlinear stochastic systems with unknown functions. The considered systems are in the nonaffine pure-feedback form, and it is the first to control this class of systems with stochastic disturbances. The fuzzy-neural networks are used to approximate unknown functions. Based on the backstepping design technique, the controllers and the adaptation laws are obtained. Compared to most of the existing stochastic systems, the proposed control algorithm has fewer adjustable parameters and thus, it can reduce online computation load. By using Lyapunov analysis, it is proven that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded in probability and the system output tracks the reference signal to a bounded compact set. The simulation example is given to illustrate the effectiveness of the proposed control algorithm.

Abstract: Structured and unstructured uncertainties are the main obstacles in the development of advanced controllers for high-accuracy tracking control of hydraulic servo systems. For the structured uncertainties, nonlinear adaptive control can be employed to achieve asymptotic tracking performance. But modeling errors, such as nonlinear frictions, always exist in physical hydraulic systems and degrade the tracking accuracy. In this paper, a robust integral of the sign of the error controller and an adaptive controller are synthesized via backstepping method for motion control of a hydraulic rotary actuator. In addition, an experimental internal leakage model of the actuator is built for precise model compensation. The proposed controller accounts for not only the structured uncertainties (i.e., parametric uncertainties), but also the unstructured uncertainties (i.e., nonlinear frictions). Furthermore, the controller theoretically guarantees asymptotic tracking performance in the presence of various uncertainties, which is very important for high-accuracy tracking control of hydraulic servo systems. Extensive comparative experimental results are obtained to verify the high-accuracy tracking performance of the proposed control strategy.

Abstract: In this paper, we study a general class of strict feedback nonlinear systems, where the input signal takes quantized values. We consider a stabilization problem for nonlinear uncertain systems via adaptive backstepping approach. The control design is achieved by introducing a hysteretic quantizer to avoid chattering and using backstepping technique. A guideline is derived to select the parameters of the quantizer. The designed controller together with the quantizer ensures the stability of the closed-loop system in the sense of signal boundedness.

Abstract: This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.

Abstract: This paper investigates fuzzy adaptive actuator failure compensation control for a class of uncertain stochastic nonlinear systems in strict-feedback form. These stochastic nonlinear systems contain the actuator faults of both loss of effectiveness and lock-in-place, unmodeled dynamics, and without direct measurements of state variables. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is established to estimate the unmeasured states. By introducing the dynamical signal and the changing supply function technique design into the backstepping control design, a robust adaptive fuzzy fault-tolerant control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded in probability in the presence of the actuator failures and the unmodeled dynamics. Simulation results are provided to show the effectiveness of the control approach.

Abstract: This paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict-feedback form with unknown backlash-like hysteresis nonlinearities. To overcome the design difficulty of nonstrict-feedback structure, variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic. By combining radial basis function neural networks' universal approximation capability with an adaptive backstepping technique, an adaptive neural control algorithm is proposed. It is shown that the proposed controller guarantees that all the signals in the closed-loop system are four-moment semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value. Simulation results further show the effectiveness of the presented control scheme.

Abstract: In this brief, we investigate the control problem of tracking a desired trajectory for a fully actuated marine surface vessel considering multiple outputs constraints. To prevent multiple output constraints violation, a symmetric barrier Lyapunov function (SBLF) is employed. Backstepping, in combination with adaptive feedback approximation techniques, is introduced to design an adaptive neural network control. Experimental simulations are provided to evaluate the feasibility and effectiveness of the proposed controller. Compared to the adaptive neural network control without multiple output constraints, the proposed adaptive neural network using the SBLF can guarantee that all the outputs remain bounded.

Abstract: This paper presents an adaptive position control for a pump- controlled electrohydraulic actuator (EHA) based on an adaptive backstepping control scheme. The core feature of this paper is the combination of a modified backstepping algorithm with a special adaptation law to compensate all nonlinearities and uncertainties in EHA system. First of all, the mathematical model of the EHA is developed. The position control is then formulated using a modified backstepping technique and the uncertainties in hydraulic system are adapted by employing a special Lyapunov function. The control signal consists of an adaptive control signal to compensate the uncertainties and a simple robust structure to ensure the robustness corresponding to a bounded disturbance. Experimental results proved strongly the ability of the proposed control method.

Abstract: In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach.

Abstract: This technical note is concerned with the problem of adaptive tracking control for a class of nonlinear systems with parametric uncertainty, unknown actuator nonlinearity and bounded external disturbance. Two type of actuator nonlinearities, that is, symmetric dead-zone and Bouc-Wen hysteresis, are considered, respectively. First, an adaptive control scheme with positive integrable time-varying function is presented to compensate for the dead-zone nonlinearity. Then, the actuator nonlinearity under consideration is modeled as Bouc-Wen hysteresis, and desired compensation controller is designed based on the backstepping technique and Nussbaum gain approach. In both of the two schemes, the asymptotic tracking is guaranteed with the tracking error converging to zero. Finally, an illustrative example is provided to show the effectiveness of the proposed design methods.

Abstract: This brief considers the problem of trajectory tracking control for marine surface vessels with unknown time-variant environmental disturbances. The adopted mathematical model of the surface ship movement includes the Coriolis and centripetal matrix and the nonlinear damping terms. An observer is constructed to provide an estimation of unknown disturbances and is applied to design a novel trajectory tracking robust controller through a vectorial backstepping technique. It is proved that the designed tracking controller can force the ship to track the arbitrary reference trajectory and guarantee that all the signals of the closed-loop trajectory tracking control system of ships are globally uniformly ultimately bounded. The simulation results and comparisons illustrate the effectiveness of the proposed controller and its robustness to external disturbances.

Abstract: SUMMARY This paper investigates the problem of adaptive neural control design for a class of single-input single-output strict-feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

Abstract: This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

Abstract: In this paper, the authors study the problem of robust adaptive path-following control for underactuated ships with model uncertainties and nonzero-mean time-varying disturbance. A concise adaptive neural network (NN)-based control scheme is proposed using backstepping, feedforward approximations, dynamic surface control, and minimal learning parameter techniques. In addition, to tackle the strong couplings among state variables (including the underactuated state variable) and underactuated characteristics, much effort is put into guaranteeing semiglobal uniform ultimate boundedness of the ship motion control system. The outstanding advantage of this scheme is that the control law has a concise form and is easy to implement in practice due to a smaller computational burden, with only two online parameters being tuned to tackle the uncertainties. The simulation results demonstrate the effectiveness of the proposed algorithm, especially including the experiment in the simulated marine environment.

Abstract: In this paper, an adaptive fuzzy output-feedback control is investigated for a class of pure-feedback uncertain nonlinear systems with unknown dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, and a state filter observer is designed to estimate the unmeasured states. Based on the information of the dead-zone slopes as well as treating the unknown inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. The stability of the resulting closed-loop system is proved and a simulation example is provided to show the effectiveness of the proposed control approach. The important feature of the proposed adaptive fuzzy controller is that it can solve the states immeasurable and the unknown dead-zone problems that exist in the previous publications and extends the existing results on strict-feedback control to the counterpart on pure-feedback control.

Abstract: The flight control problem of a flexible air-breathing hypersonic vehicle is presented in the presence of input constraint and aerodynamic uncertainty. A control-oriented model, where aerodynamic uncertainty and the strong couplings between the engine and flight dynamics are included, is derived to reduce the complexity of controller design. The flexible dynamics are viewed as perturbations of the model. They are not taken into consideration at the level of control design, the influence of which is evaluated through simulation. The control-oriented model is decomposed into velocity subsystem and altitude subsystem, which are controlled separately. Then robust adaptive controller is developed for the velocity subsystem, while the controller which combines dynamic surface control and radial basis function neural network is designed for the altitude subsystem. The unknown nonlinear function is approximated by the radial basis function neural network. Minimal-learning parameter technique is utilized to estimate the maximum norm of ideal weight vectors instead of their elements to reduce the computational burden. To handle input constraints, additional systems are constructed to analyze their impact, and the states of the additional systems are employed at the level of control design and stability analysis. Besides, “explosion of terms” problem in the traditional backstepping control is circumvented using a first-order filter at each step. By means of Lyapunov stability theory, it is proved theoretically that the designed control law can assure that tracking error converges to an arbitrarily small neighborhood around zero. Simulations are performed to demonstrate the effectiveness of the presented control scheme in coping with input constraint and aerodynamic uncertainty.

Abstract: Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances In these systems, it is preferred a formal control approach whose closed-loop system can predict an acceptable performance since deviations may produce instability and may lead to catastrophic results Backstepping provides an intuitive solution since it solves underactuation iteratively through slaving the actuated subsystem so as to provide a virtual controller in order to stabilize the underactuated subsystem However it requires a full knowledge of the plant and derivatives of the state, which it is prone to instability for any uncertainty; and although robust sliding mode has been proposed, discontinuities may be harmful for air- or water-borne nonlinear plants In this paper, a novel robust backstepping-based controller that induces integral sliding modes is proposed for the Newton---Euler underactuated dynamic model of a quadrotor subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics The chattering-free sliding mode compensates for persistent or intermittent, and possible unmatched state dependant disturbances with reduced information of the dynamic model Representative simulations are presented and discussed

Abstract: In this paper, a flight controller with disturbance observer (DOB) is proposed for high-performance trajectory tracking of a quadrotor. The dynamic model of the quadrotor, considering the external disturbances, model mismatches and input delays, is firstly developed. Subsequently, a DOB-based control strategy is designed with the backstepping (BS) technique. In this control scheme, the DOB serves as a compensator, which can effectively reject model mismatches and external disturbances. In this case, the trajectory tracking controller is designed according to the nominal model. Then, the input-to-state stability (ISS) analyses of the developed controllers are presented, which theoretically guarantees the robustness of the developed controller. Finally, comparative studies are carried out. Three types of disturbances including payloads, rotor failures and wind are chosen to verify the effectiveness of the development. The results from simulations and experiments show that the proposed controller provides better performances than the traditional nonlinear controllers.

Abstract: In this paper, global chaos synchronization is investigated for n-scroll Chua (Tang et al. in IEEE Trans Circ Syst I Fundam Theory Appl 48:1369–1372, 2001) and Lur’e (Suykens and Vandewalle in Int J Bifurc Chaos 7:1323–1325, 1997) chaotic systems using backstepping control with recursive feedback. Our theorems on synchronization for n-scroll Chua and Lur’e chaotic systems are established using Lyapunov stability theory. The backstepping scheme is a recursive procedure that links the choice of Lyapunov function with the design of a feedback controller and guarantees global stability performance of strict-feedback chaotic systems. Mainly the backstepping technique gives flexibility in designing a feedback control law. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.

Abstract: A novel guidance algorithm is proposed for the attitude reorientation of a rigid body spacecraft in the presence of multiple types of attitude-constrained zones. In this direction, two types of attitude-constrained zones are first developed using unit quaternions, namely, the attitude-forbidden and -mandatory zones. The paper then utilizes a convex parameterization of forbidden and mandatory zones for constructing a strictly convex logarithmic barrier potential that is subsequently used for the synthesis of feedback attitude control laws while the inevitable unwinding phenomenon is given a simple and effective remedy. Model-independent and model-dependent control laws are then implemented by using the Lyapunov direct method and the modified integrator backstepping method. The paper concludes with a set of simulation results to evaluate the effectiveness and demonstrate the viability of the proposed methodology.

Abstract: This paper studies an adaptive output-feedback control for a class of nonlinear single-input and single-output (SISO) systems with the full-state constraints. A state observer is designed to estimate those unmeasured states. At present, all the results in the output-feedback area ignore the effects of the full-state constraints. The presence of these constraints results in a complicated procedure and the major difficulties in the design. The barrier Lyapunov function (BLF) and a novel design procedure are given to overcome these difficulties. The adaptation law and the controllers are obtained based on the backstepping design procedure. In addition, only one adjustable parameter needs to be updated, and thus, the online computation burden is alleviated. The stability of the closed-loop system is proven by using the Lyapunov theorem. A simulation example is given to verify the effectiveness of the approach.