Adaptive Dynamic Surface Control Research Articles

Nonlinear gain feedback adaptive DSC for a class of uncertain nonlinear systems with asymptotic output tracking

This paper proposes an adaptive dynamic surface controller with nonlinear gain feedback for a class of uncertain nonlinear systems to achieve the asymptotic output tracking. A nonlinear filter is designed to eliminate the effects raised by the boundary layer error at each step in the dynamic surface control (DSC) procedure. Meanwhile, a new nonlinear gain function, which can regulate the control ability automatically, is designed to improve the dynamic performance of system. Then, an adaptive controller is explicitly designed to achieve the asymptotic output tracking. Moreover, a novel Lyapunov function is designed to analyze the stability of the proposed algorithm. The proposed DSC algorithm not only can avoid the inherent problem of “explosion of complexity” in the back-stepping procedure, but also can achieve the asymptotic output tracking and improve the dynamic performance. Some simulations are shown to demonstrate the effectiveness and advantages of the proposed controller.

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

SummaryThis paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Adaptive neural dynamic surface control of mechanical systems using integral terminal sliding mode

This paper studies the robust tracking control problem of fully-actuated mechanical systems using a novel integral dynamics surface control (DSC) method. We replace the conventional DSC error surfaces with new nonlinear integral surfaces to generate a quasi-terminal sliding mode (TSM) in the tracking error trajectories. Then, we follow the recursive, Lyapunov-based design procedure of the DSC to obtain the control law. The resultant quasi-TSM adjusts the error convergence rate according to the distance from the origin. To achieve robustness against structural variations of the mechanical system as well as external disturbances, we use nonlinear damping combined with a radial basis function neural network (RBFNN) approximator. The RBFNN adaptively identifies the upper-bound of the uncertainty/disturbances to prevent conservative, high-gain control inputs. Moreover, we use raised-cosine basis functions, which have compact supports, to improve the computational efficiency of the RBFNN. Through Lyapunov-based stability analysis, we show the boundedness and ultimate boundedness of the closed-loop system as well as the TSM-induced convergence of the tracking errors. Detailed numerical simulations support the efficacy of the proposed control method.

Uncertainty observation-based adaptive succinct fuzzy-neuro dynamic surface control for trajectory tracking of fully actuated underwater vehicle system with input saturation

In this paper, an uncertainty observation-based adaptive fuzzy neural dynamic surface control (UOB-AFNDSC) is proposed to investigate the problem of high-accuracy trajectory tracking of fully actuated underwater vehicles with respect to unknown uncertainties and input saturation. The control framework of UOB-AFNDSC is constructed using the dynamic surface technique, under which an online-succinct fuzzy-neuro uncertainty observer with both projection-based parameter learning and succinct network structure learning is constructed to online identify the lumped uncertainty term including system uncertainties and external disturbances. To further suppress the effect of uncertainty reconstruction error and input saturation error, two adaptive robust terms are introduced, respectively. To theoretically analyze the stability of the overall closed-loop control system, novel error variables are introduced to ensure the uniform ultimate boundedness of all signals, and the tracking accuracy can be easily adjusted by the width parameter of novel error variables. Finally, some simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

Acceleration-Level Pseudo-Dynamic Visual Servoing of Mobile Robots With Backstepping and Dynamic Surface Control

In this paper, we propose an acceleration-level pseudo-dynamic visual servoing structure for the nonholonomic mobile robots, based on which we design two different adaptive controllers-backstepping and dynamic surface control (DSC) in the presence of unknown depth information. Different from existing kinematic controllers, which directly regard linear and angular velocities as control inputs, this paper designs acceleration control that is integrated to easily obtain smooth velocity signals to be accurately executed by the robot. Two controllers are designed and analyzed with Lyapunov techniques: 1) a backstepping controller yielding asymptotical stability and 2) a dynamic surface controller ensuring system errors to be ultimately uniformly bounded. The unknown depth is handled by designing an adaptive parameter estimation law in both methods. Finally, a comparison between backstepping and DSC is given based on the experimental results and the design procedures.

Adaptive decentralized control for switched nonlinear large-scale systems with quantized input signal

This paper deals with the adaptive fuzzy dynamic surface control (DSC) of a class of switched nonlinear large-scale systems whose input is quantized by a class of sector-bounded quantizers and the quantization parameters are allowed to be unknown. A new control law with hyperbolic tangent function form is introduced to develop a compensation mechanism to remove the restriction of the global Lipschitz condition. By designing switched first-order filters and switched adaptive laws for different subsystems, the switched controllers can not only show the switched systems changes sufficiently but also deal with the problem of “explosion of complexity”. It is shown that the proposed control scheme can ensure that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of the origin regardless of arbitrary switching. The simulation results demonstrate the validity and applicability of the proposed control scheme.

Composite Learning Adaptive Dynamic Surface Control of Fractional-Order Nonlinear Systems.

Adaptive dynamic surface control (ADSC) is effective for solving the complexity problem in adaptive backstepping control of integer-order nonlinear systems. This article focuses on the ADSC design for parametric uncertain fractional-order nonlinear systems (FONSs). In each backstepping step, the virtual controller is driven to pass through a fractional dynamic surface whose fractional-order derivative can be calculated easily. An ADSC law that ensure tracking error convergence is designed. The proposed ADSC requires a stringent condition called persistent excitation (PE) to achieve parameter convergence. To relax this limitation, a prediction error is defined by using online recorded data and instantaneous data, and a composite learning law is proposed to utilize both the prediction error and the tracking error. Then, a composite learning ADSC (CLADSC) method is developed to guarantee tracking error convergence and accurate parameter estimation under an interval excitation condition that is weaker than the PE one. Finally, an illustrative example is presented to show the performance of our methods.

Neuro-Fuzzy-Based Adaptive Dynamic Surface Control for Fractional-Order Nonlinear Strict-Feedback Systems With Input Constraint

This article investigates the issue of neuro-fuzzy-based adaptive dynamic surface control (DSC) for uncertain fractional-order (FO) nonlinear systems in strict-feedback form where input constraint is considered in the systems. In the recursive steps, the neuro-fuzzy network systems are employed to deal with the unknown nonlinear terms existing in systems. Furthermore, based on a DSC scheme, a modified FO filter is constructed to overcome the problem of explosion of complexity caused by the traditional backstepping design. Moreover, according to the FO Lyapunov stability theory, a neuro-fuzzy-based adaptive controller is designed to guarantee all the signals of FO closed-loop systems tend to be bounded. Finally, the three examples are provided to verify the validity and superiority of the presented control scheme.

Pressure Observer Based Adaptive Dynamic Surface Control of Pneumatic Actuator with Long Transmission Lines

In this paper, the needle insertion motion control of a magnetic resonance imaging (MRI) compatible robot, which is actuated by a pneumatic cylinder with long transmission lines, is considered and a pressure observer based adaptive dynamic surface controller is proposed. The long transmission line is assumed to be an intermediate chamber connected between the control valve and the actuator in series, and a nonlinear first order system model is constructed to characterize the pressure losses and time delay brought by it. Due to the fact that MRI-compatible pressure sensors are not commercially available, a globally stable pressure observer is employed to estimate the chamber pressure. Based on the model of the long transmission line and the pressure observer, an adaptive dynamic surface controller is further designed by using the dynamic surface control technique. Compared to the traditional backstepping design method, the proposed controller can avoid the problem of “explosion of complexity” since the repeated differentiation of virtual controls is no longer required. The stability of the closed-loop system is analytically proven by employing the Lyapunov theory. Extensive experimental results are presented to demonstrate the effectiveness and the performance robustness of the proposed controller.

Adaptive prescribed performance control for the post-capture tethered combination via dynamic surface technique

Abstract In this paper, an adaptive dynamic surface controller with prescribed performance is proposed for the stabilization control of the post-capture tethered combination, where the factors such as measurement uncertainties, model uncertainties, external disturbances and input saturation are considered. Compared with the most prescribed performance approaches, the proposed controller has a simple structure, and needs no error transformations. Firstly, we found a dynamic model of the post-capture tethered combination considering the integrated attitudes of the combination. Then, taken the above-mentioned factors into consideration, the dynamics of the post-capture combination can be transformed to a multi-input-multi-output (MIMO) system with mismatched and matched uncertainties. An adaptive approach is proposed for estimating the upper bound of the uncertainties. Furthermore, an auxiliary dynamic system is adopted to deal with the problem of control input saturation, and the bounded assumption of input error is released. All the signals in the closed-loop system are confirmed to be ultimately bounded by the Lyapunov stability theory. Finally, simulation results validate the performance and robustness improvement of the proposed control algorithm.

Neural network based adaptive backstepping dynamic surface control of drug dosage regimens in cancer treatment

This manuscript aims at investigating the neural adaptive control of drug dosage regimens in cancer treatment. The goal of the treatment is to get an appropriate scheme for the drug dosage in order to reduce the tumor cells. To obtain a controller presenting good performances, the cancer immunotherapy system is first described by Caputo fractional differential equations. Second, Nussbaum functions and neural networks are introduced to deal with the unknown control directions and the uncertain nonlinear dynamics, respectively. Then, the backstepping dynamic surface control method is deployed to regulate the updating laws and the control signals, simultaneously. Through rigorous analysis based on the Lyapunov stability theory, it is shown that by means of the proposed adaptive controller, the boundedness of all variables in the closed-loop system and the semi-global asymptotic tracking are well ensured for any bounded initial conditions. It is also demonstrated that the performances of the drug treatment based on our proposed adaptive neural control scheme are better than a number of existing schemes. Finally, simulation results are given to demonstrate the feasibility of the proposed control scheme in the diminution of the number of tumor cells in the cancer model.

Adaptive Neural Network Dynamic Surface Control of the Post-capture Tethered Spacecraft

This paper presents an adaptive neural network dynamic surface control approach for the post-capture tethered spacecraft, where model uncertainties, input saturation, and state constraints exist. First, a dynamic model of the post-capture tethered spacecraft considering the three-dimensional attitude of the target satellite is derived by the Lagrange formalism. Then, the neural network is adopted to compensate the model uncertainties and the effects of input saturation, and a barrier Lyapunov function is employed to prevent the violation of the state constraints. The asymptotic stability of the closed-loop system is guaranteed by the Lyapunov stability theory. Finally, simulation results are given to illustrate the effectiveness of the proposed controller.

Adaptive Fuzzy Dynamic Surface Control of Nonlinear Constrained Systems With Unknown Virtual Control Coefficients

This paper studies the problem of adaptive fuzzy dynamic surface control (DSC) of nonstrict-feedback nonlinear systems subject to unknown virtual control coefficients, dead zone, and full state constraints. The Nussbaum gain technique is used to overcome the difficulty caused by the unknown virtual control coefficients. By utilizing the information of tan-type barrier Lyapunov function, the requirement of full state constraints is successfully achieved. In addition, to handle the problem of “explosion of complexity” resulted from backstepping itself, a DSC approach using the sliding mode differentiator is introduced. Then, based on backstepping control, we develop a new adaptive fuzzy DSC strategy, which ensures that all state constrains are not violated via designing parameters appropriately. Meanwhile, other signals existing in the closed-loop system are bounded. Finally, comparative results are provided to illustrate the effectiveness of the proposed approach.

Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances

In order to stabilize multiple-input–multiple-output uncertain strict feedback nonlinear systems with time-varying full-state constraints and external disturbances, an adaptive neural dynamic surface control method is investigated in this paper. A new compensator is proposed, which combines approximation error based adaptive radial basis function neural networks (RBFNNs) and nonlinear disturbance observer (NDOB) to improve the compensate performance of unmodeled dynamics and external disturbances. To prevent that the time-varying full state constraints are violated, the controller is designed via asymmetric time-varying barrier Lyapunov function (ATBLF). Meanwhile, the dynamic surface control is established to avoid the problem of “explosion of complexity” in traditional backstepping design. All closed-loop signals are proved to be semiglobally uniformly ultimate bounded through stability analysis. Finally, the simulation for six degrees of freedom (6-DOF) model unmanned airship are given to illustrate the effectiveness of the proposed control method.

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

SummaryA robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.

Adaptive neuro-fuzzy backstepping dynamic surface control for uncertain fractional-order nonlinear systems

In this paper, a fractional-order backstepping dynamic surface control (DSC) method is developed to cope with the stabilization problem for fractional-order nonlinear systems with uncertainties and external disturbances. In each step, a neuro-fuzzy network system is employed to approximate the unknown nonlinear function existing in fractional-order subsystem. Furthermore, a modified fractional-order filter is designed to avoid the problem of explosion of complexity caused by the recursive procedure. Then based on the fractional-order Lyapunov stability theory, the corresponding adaptive backstepping DSC controller is proposed to guarantee the stability of the fractional-order closed-loop systems. Finally, three examples are given in simulation part to demonstrate the validity of the proposed control method.

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

ABSTRACTAn adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

SummaryIn this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.

Robust Adaptive Dynamic Surface Control of Nonlinear Time-varying Systems in Strict-feedback Form

In this paper, the problem of robust adaptive control for nonlinear systems with unknown time-varying parameters and disturbance is considered. For this purpose, an indirect adaptive controller based on the Dynamic Surface Control (DSC) is proposed where an adaptive scheme is presented to provide estimations of unknown time-varying parameters. First, the parameters are approximated in terms of polynomials with unknown coefficients using the Taylor series expansion. Then, these unknown coefficients are estimated using a novel adaptive law. It is shown that the proposed control scheme guarantees the stability of the overall system and the tracking error can converge to a desired small residual. Finally, simulation results are given to demonstrate the effectiveness of the proposed method.

Tracking control of MIMO nonlinear systems under full state constraints: A Single-parameter adaptation approach free from feasibility conditions

This paper investigates the tracking control problem of a class of multi-input multi-output (MIMO) nonlinear systems under asymmetric full-state constraints. By integrating a nonlinear transformed function (NTF) with the upper bound estimation technique, we develop a robust adaptive dynamic surface control (DSC) method that exhibits several attractive features: 1) both symmetric and asymmetric state constraints are directly addressed without the need for converting the state constraints into new constraints on tracking errors (as used in the Barrier Lyapunov Function (BLF) in most existing works). Such control scheme (with its structure unchanged) is also applicable to the systems free from state constraints; 2) the undesirable feasibility conditions on virtual control laws commonly involved in most existing works are completely eliminated; and 3) the utilization of NTF-based DSC and upper bound estimation technique not only avoids the explosion of complexity problem in traditional backstepping design, but also allows a structurally simple and computationally inexpensive control scheme to be developed, in which only one single parameter updating is needed, significantly reducing the design complexity and online computation. The effectiveness of the proposed scheme is verified via simulation.