Abstract: This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Abstract: This paper presents an active disturbance rejection adaptive control scheme via full state feedback for motion control of hydraulic servo systems subjected to both parametric uncertainties and uncertain nonlinearities. The proposed controller is derived by effectively integrating adaptive control with extended state observer via backstepping method. The adaptive law is synthesized to handle parametric uncertainties and the remaining uncertainties are estimated by the extended state observer and then compensated in a feedforward way. The unique features of the proposed controller are that not only the matched uncertainties but also unmatched uncertainties are estimated by constructing two extended state observers, and the parameter adaptation law is driven by both tracking errors and state estimation errors. Since the majority of parametric uncertainties can be reduced by the parameter adaptation, the task of the extended state observer is much alleviated. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically achieves an asymptotic tracking performance in the presence of parametric uncertainties and constant disturbances. In addition, prescribed transient tracking performance and final tracking accuracy can also be guaranteed when existing time-variant uncertain nonlinearities. Comparative experimental results are obtained to verify the high tracking performance nature of the proposed control strategy.

Abstract: This paper proposes an fuzzy adaptive output-feedback stabilization control method for nonstrict feedback uncertain switched nonlinear systems. The controlled system contains unmeasured states and unknown nonlinearities. First, a switched state observer is constructed in order to estimate the unmeasured states. Second, a variable separation approach is introduced to solve the problem of nonstrict feedback. Third, fuzzy logic systems are utilized to identify the unknown uncertainties, and an adaptive fuzzy output feedback stabilization controller is set up by exploiting the backstepping design principle. At last, by applying the average dwell time method and Lyapunov stability theory, it is proven that all the signals in the closed-loop switched system are bounded, and the system output converges to a small neighborhood of the origin. Two examples are given to further show the effectiveness of the proposed switched control approach.

Abstract: Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.

Abstract: This paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict-feedback systems with input delay and output constraint. Input delay is handled based on the information of Pade approximation and output constraint problem is solved by barrier Lypaunov function. Some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub-vectors. A novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed-loop systems are semiglobally uniformly ultimately bounded, and the tracking error can be adjusted around the origin with a small neighborhood. The stability of the closed-loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach.

Abstract: This paper investigates the problem of adaptive fuzzy state-feedback control for a category of single-input and single-output nonlinear systems in nonstrict-feedback form. Unmodeled dynamics and input constraint are considered in the system. Fuzzy logic systems are employed to identify unknown nonlinear characteristics existing in systems. An appropriate Lyapunov function is chosen to ensure unmodeled dynamics to be input-to-state practically stable. A smooth function is introduced to tackle input saturation. In order to overcome the difficulty of controller design for nonstrict-feedback system in backstepping design process, a variables separation method is introduced. Moreover, based on small-gain technique, an adaptive fuzzy controller is designed to guarantee all the signals of the resulting closed-loop system to be bounded. Finally, two illustrative examples are given to validate the effectiveness of the new design techniques.

Abstract: The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Abstract: This paper presents a path following controller of a surface vessel with a prescribed performance in the presence of input saturation and external disturbances. Based on the three degrees-of-freedom model of the surface vessel, the designed backstepping control scheme features three functional parts, namely, guidance, attitude control, and velocity control. To guarantee that the position errors are confined within the prescribed convergence rates and maximum overshoot, a performance constrained guidance law is formulated with an error transformed function. Command filters are incorporated in the control subsections to limit the magnitude of the virtual controls and simultaneously avoid arduous computations involving their time derivatives. Subsequently, auxiliary systems that are governed by smooth switching functions are developed in an unprecedented manner to compensate for the saturation constraints on actuators. Nonlinear disturbance observers are concurrently introduced to estimate the unknown external disturbances for increasing system's robustness. It is demonstrated that under the proposed control, the prescribed transient and steady tracking performance bounds are never violated, and all closed-loop signals remain uniformly ultimately bounded, despite the presence of input saturation and disturbances. Results from a comparative simulation study illustrate the effectiveness and advantages of the proposed method.

Abstract: In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.

Abstract: This paper studies an adaptive fuzzy tracking control problem for nonlinear stochastic systems with input saturation and nonstrict-feedback form. We use fuzzy logic systems to approximate unknown nonlinear functions. A novel approach is introduced to tackle unknown functions with nonstrict-feedback structure in the design process. By introducing an auxiliary system, the input saturation problem can be solved. Moreover, based on backstepping control design approach, a novel adaptive fuzzy tracking controller is designed to guarantee all signals in the closed-loop system to be bounded, and the system output can be driven to track the trajectory of a given reference signal. Finally, some simulation results are given to confirm the effectiveness of the proposed approach.

Abstract: In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called “explosion of complexity” problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

Abstract: This paper considers the problem of adaptive neural control of nonlower triangular nonlinear systems with unmodeled dynamics and dynamic disturbances. The design difficulties appeared in the unmodeled dynamics and nonlower triangular form are handled with a dynamic signal and a variable partition technique for the nonlinear functions of all state variables, respectively. It is shown that the proposed controller is able to ensure the semi-global boundedness of all signals of the resulting closed-loop system. Furthermore, the system output is ensured to converge to a small domain of the given trajectories. The main advantage about this research is that a neural networks-based tracking control method is developed for uncertain nonlinear systems with unmodeled dynamics and nonlower triangular form. Simulation results demonstrate the feasibility of the newly presented design techniques.

Abstract: In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4 ), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers’ outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Abstract: A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example.

Abstract: In this technical note, the problem of adaptive tracking control is investigated for a class of stochastic uncertain nonlinear systems in the presence of input saturation. To analyze the effect of input saturation, an auxiliary system is employed. With the help of backstepping technique, an adaptive stochastic tracking control approach is developed. Under the proposed adaptive tracking controller, the boundedness of all the signals in the closed-loop system is achieved almost surely. Moreover, distinct from most of the existing results, the ultimate tracking error can be bounded by an explicit function of design parameters and input saturation error (the error between the control input and saturated input) in the mean quartic sense. Finally, an example is given to show the effectiveness of the proposed scheme.

Abstract: This paper presents a six-degree-of-freedom relative motion control method for autonomous spacecraft rendezvous and proximity operations subject to input saturation, full-state constraint, kinematic coupling, parametric uncertainty, and matched and mismatched disturbances. Relative rotational and relative translational controllers are developed separately based on a unified adaptive backstepping technique. Both element-wise and norm-wise adaptive estimation techniques are used for handling parametric uncertainties, kinematic couplings, and matched and mismatched disturbances, where the bounds of disturbances are unknown. Two auxiliary design systems are employed to deal with input saturation in the relative rotational and relative translational control designs, and the stability of the saturated control solution is verified. Full-state constraint of the relative pose motion is handled by using barrier Lyapunov functions while achieving a satisfactory control performance. All signals in the closed-loop system are guaranteed to be uniformly ultimately bounded, and the relative motion states are all restricted within the known constraints. Compared with the previous control designs of spacecraft rendezvous and proximity operations, the proposed control strategy in this paper can simultaneously deal with input saturation, full-state constraint, kinematic coupling, parametric uncertainty, and matched and mismatched disturbances. Experimental simulation results validate the performance and robustness improvement of the proposed control strategy.

Abstract: This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems’ universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.

Abstract: This paper studies the problem of adaptive fuzzy control for a category of single-input single-output nonlinear networked control systems with network-induced delay and data loss based on adaptive backstepping control approach. Fuzzy logic systems are used to approximate the unknown nonlinear characteristics existing in the system, while Pade approximation is introduced to handle network-induced delay. Data loss occurs intermittently and stochastically in the data transmitting process, which is regarded as the delay in the controller design. In the framework of adaptive fuzzy backstepping technique, a novel state-feedback adaptive controller is constructed to ensure all signals in the resulting closed-loop system to be bounded and the state variables can be regulated to the origin. Finally, two examples are given to show the validity of the proposed results.

Abstract: This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

Abstract: Recently, an adaptive backstepping quantized control scheme was proposed. In this note, for a class of general nonlinear systems, it is shown that with a simple yet novel transformation of the control signal, all the strict assumptions on the system in early works can be relaxed, a coarser quantization can be achieved, and the stabilization error can be steered to within an arbitrarily small neighborhood of the origin.

Abstract: This paper proposes an active disturbance rejection adaptive controller for tracking control of a class of uncertain nonlinear systems with consideration of both parametric uncertainties and uncertain nonlinearities by effectively integrating adaptive control with extended state observer via backstepping method. Parametric uncertainties are handled by the synthesized adaptive law and the remaining uncertainties are estimated by extended state observer and then compensated in a feedforward way. Moreover, both matched uncertainties and unmatched uncertainties can be estimated by constructing an extended state observer for each channel of the considered nonlinear plant. Since parametric uncertainties can be reduced by parameter adaptation, the learning burden of extended state observer is much reduced. Consequently, high-gain feedback is avoided and improved tracking performance can be expected. The proposed controller theoretically guarantees a prescribed transient tracking performance and final tracking accuracy in general while achieving asymptotic tracking when the uncertain nonlinearities are not time-variant. The motion control of a motor-driven robot manipulator is investigated as an application example with some suitable modifications and improvements, and comparative simulation results are obtained to verify the high tracking performance nature of the proposed control strategy.

Abstract: In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Abstract: For a class of stochastic nonlinear time-delay systems with multiple constraints—predefined tracking constraint, input saturation, and output dead zone—the output tracking control problem is addressed in this paper. By expressing the saturated actuator as a smooth nonlinear function and employing the Nussbaum function technique, the input and output constraints problems are solved. The tracking performance is achieved under the predefined tracking constraint by utilizing the backstepping recursive design technique and the approximation property of neural networks. Then, based on the utilization of the Lyapunov–Krasovskii functional, the stochastic stability of the closed-loop system is achieved. Finally, the proposed control method is verified through a simulation example.

Abstract: In this paper, adaptive neural dynamic surface control (DSC) is developed using radial basis function neural networks (NNs) for a class of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties. Based on a one-to-one nonlinear mapping, the pure-feedback system with full state constraints is transformed into a novel pure-feedback system without state constraints. The dynamic uncertainties are dealt with using a dynamic signal. Using modified DSC and mean value theorem as well as Nussbaum function, two adaptive NN control schemes are proposed based on the transformed system. The designed control strategy removes the conditions that the upper bound of the control gain is known, and the lower bounds and upper bounds of the virtual control coefficients are known. It is shown that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the full state constraints are not violated. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Abstract: In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of switched nonlinear systems. A new switched adaptive output feedback control method is presented where the changes of plant can be considered explicitly. Mode-dependent fuzzy logic systems are employed to approximate the switching nonlinear functions in system. To reduce the conservativeness caused by adoption of a common adaptive law for all subsystems, the switching optimal weight vectors are directly estimated via switched adaptive laws at each step of backstepping. However, the difficulties are how to ensure the estimation performance subject to persistent switchings, and how to design common virtual controls based on switching parameters. Further, based on the estimation of optimal weight vectors, the switched fuzzy state observer can be also applied to obtain the unmeasured states. By designing a novel Lyapunov function, the improved dynamic surface control incorporated by prescribed performance technique guarantees all the total state tracking errors, not partial ones, within predefined performance bounds. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Abstract: In this paper, an image-based visual servoing control law is proposed for a quadrotor unmanned aerial vehicle using an on-board monocular camera and an inertial measurement unit sensor. Based on the perspective projection model, suitable image features are defined on a rotated image plane called virtual image plane, thus a decoupled image feature dynamics is achieved. Then, a translational velocity observer is presented using these image features. The image feature dynamics and quadrotor dynamics are combined to derive a nonlinear controller. The controller is based on backstepping technique to account for the underactuation of the quadrotor. The image-based visual servoing controller only needs three point features, which make it useable in general environment. The closed-loop system is proved globally asymptotic stable by means of Lyapunov analysis. Computer simulations that regulate a quadrotor to a desired position with respect to (w.r.t.) four points lying on a horizontal plane and three points lying on a full rotated slope are conducted separately. Smooth and efficient trajectories are obtained both in virtual image plane and Cartesian space. Finally, experimental tests including pushing and pulling the visual target are conducted to verify the validity and robustness of the proposed controller. The proposed control law regulates the quadrotor to a desired position, defined by desired image, from an unknown initial position, which can be used in monitoring, landing, and other applications.