Adaptive Neural Dynamic Surface Control Research Articles

Adaptive Neural Dynamic Surface Control for the Chaotic PMSM System with External Disturbances and Constrained Output

Background:This article studies the issue of adaptive neural dynamic surface control for the chaotic permanent magnet synchronous motor system with constrained output, external disturbances and parameter perturbations.Methods:Firstly, a virtual controller and two practical controllers are created based on the backstepping framework. In the process of creating controllers, adaptive technique and radial basis function neural networks are used to handle unknown parameters and nonlinearities, respectively. The nonlinear damping items are applied to overcome external disturbances. The barrier Lyapunov function is used to prevent the violation of system output constraint. Meanwhile, the first-order filter to eliminate the “explosion of complexity” of traditional back stepping has been introduced. Then, it is proved that all the closed-loop signals are uniform ultimate asymptotic stability and the tracking error converges to a small set of origin.Results:The effectiveness and robustness of the developed approach are illustrated by numerical simulations.Conclusion:The raised control scheme is a useful tool for enhancing the performance of the chaotic PMSM system with external disturbances, constrained output and parameter perturbations.

Adaptive composite neural network disturbance observer-based dynamic surface control for electrically driven robotic manipulators

This paper presents an adaptive backstepping control scheme for electrically driven robotic manipulator (EDRM) system with uncertainties and external disturbances by using neural network disturbance observer (NNDO) and dynamic surface control (DSC) design technique. NNDO is employed to estimate the uncertainties and external disturbances such that the priori information of the unknown dynamics will not be needed. To overcome the problem of “explosion of complexity” inherent in the backstepping design method, the DSC technique is integrated into the adaptive backstepping control design framework, where the NNDOs with adaptive composite law are utilized to compensate the uncertainties and external disturbances of EDRM. Based on the Lyapunov stability theory, it can be proven that the closed-loop system is stable in the sense that all the variables are guaranteed to be uniformly ultimately bounded. The results of simulation and experimental tests demonstrate the approximation capability of NNDO and the effectiveness of the proposed adaptive DSC scheme.

Distributed Rotating Encirclement Control of Strict-Feedback Multi-Agent Systems using Bearing Measurements

This paper focuses on the distributed multi-target rotating encirclement formation problem of strict-feedback multi-agent systems using bearing measurements. To this end, an estimator is presented to localize agents’ neighbor targets. Then, based on the trajectory planning method, a reference trajectory is constructed by three estimators, which are utilized to obtain the targets’ geometric center, the reference rotating radius and angular. Finally, an adaptive neural dynamic surface control scheme is proposed to drive all agents to move along their reference trajectories, which satisfy the multi-target rotating encirclement formation conditions. A numerical simulation is provided to verify the correctness and effectiveness of our proposed control scheme.

Prescribed performance adaptive DSC for a class of time-delayed switched nonlinear systems in nonstrict-feedback form: Application to a two-stage chemical reactor

This study deals with the tracking problem for a class of nonstrict-feedback switched nonlinear systems (SNSs) with unknown time-delay and unknown functions under arbitrary switching. To achieve this goal, an adaptive neural network-based dynamic surface control (DSC) based on backstepping approach is proposed. A neural network (NN) approximator based on radial basis functions (RBFs) is utilized to approximate unknown functions. Considering properties of Gaussian basis function in RBFNNs, an adaptive neural network DSC for nonstrict-feedback structure has been developed. A Lyapunov-krasovskii functional is applied to compensate the effect of unknown delay terms. Furthermore, a prescribed performance bound (PPB) control strategy is utilized to retain the tracking error within a predefined bound. Finally, a practical example is provided to prove the effectiveness of the proposed method.

Neuroadaptive finite-time output feedback control for PMSM stochastic nonlinear systems with iron losses via dynamic surface technique

In this paper, an observer-based adaptive neural network finite-time dynamic surface control method is proposed for the position tracking control of PMSM stochastic nonlinear systems with iron losses. First, the finite-time technology is used to realize the fast and effective tracking of the desired signal and make the system have better robust performance. Then, the adaptive neural network (NN) technology and state observer are applied to approximating the uncertain nonlinear functions and estimating the immeasurable states, respectively. And, the dynamic surface control (DSC) technology is used to resolve the “explosion of complexity” problem. In addition, the influence of iron losses and stochastic disturbances in the system is considered, and a quartic stochastic Lyapunov function is established to analyze the stability of the system. Finally, the simulation results show the effectiveness of the proposed method.

Finite Time Adaptive Neural Dynamic Surface Control of Nonstrict Feedback Nonlinear Systems Including Dead-Zone and Full State Restrictions

In this paper, finite time adaptive neural network (NN) tracking control is investigated for a class of uncertain nonstrict feedback systems with unknown dead-zone and unmodeled dynamics as well as full state restrictions. Using the linearized representation of dead-zone, finite-time adaptive control is presented by the aid of dynamic surface control (DSC) technique and the property of Gaussian function. By introducing logarithmic function as invertible nonlinear mapping, the full state restriction problem is solved. The dynamic signal generated by the low-pass filter is used to handle unmodeled dynamics. Through finite-time stability theory and introducing the bounded closed set in the proof, all the signals in the closed-loop system are proved to be semi-globally practical finite time stable (SGPFS). The restriction conditions are not triggered for all the states. Finally, two numerical examples are used to illustrate the feasiability of the finite time adaptive control strategy.

Sliding mode based neural adaptive formation control of underactuated AUVs with leader-follower strategy

In this brief, the leader-follower formation control of underactuated autonomous underwater vehicles subject to uncertain dynamics and ocean disturbances is addressed. A robust sliding mode formation control strategy is presented by utilizing backstepping method, adaptive neural network and dynamic surface control technique. The stability of the formation control system is proved based on the Lyapunov's direct method where all the signals are guaranteed to be uniformly ultimately bounded. The main advantages of this control strategy are summarized as: (i) the presented controller only depends on the position measurements of the leader, which is more convenient to implement in practice. (ii) the proposed controller does not require any prior knowledge about the hydrodynamic damping and disturbances from the environment. (iii) a continuous PI function is designed to avoid the effect of inherent chattering in standard sliding mode control. (iv) the computational explosion of the standard backstepping method is avoided by the command filter based on the dynamic surface control technique. At last, the comparative simulations are provided to verify the effectiveness of the presented control strategy.

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.

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 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.

An improved adaptive neural dynamic surface control for pure-feedback systems with full state constraints and disturbance

This paper discusses a neural dynamic surface control (DSC) problem for a class of nonlinear systems in the case of full-state constraints and unknown disturbances. Incorporating an improved DSC method and the neural networks (NNs) approximation with the minimization parameter method, an improved neural DSC approach is constructed for the studied system. By introducing a novel barrier Lyapunov function (BLF) in the design steps, the issue of full-state constraints existing in the system can be solved. The highlighting features of the proposed control method are that only one online estimation parameter should be updated, and the same stability property as the conventional backstepping method can be reserved. The transgressions of full state constraints never occur in the case of disturbances. By the Lyapunov stability analysis, all the signals of the closed-loop system are ultimately bounded. Finally, two simulation examples display the effectiveness of the proposed approach.

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

SummaryThis paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.

State observer-based adaptive neural dynamic surface control for a class of uncertain nonlinear systems with input saturation using disturbance observer

This paper focuses on the problem of tracking control aiming at a class of uncertain nonlinear systems in the presence of input saturation, unknown external disturbances and unmeasured states on the basis of adaptive neural dynamic surface control (DSC) scheme in combination with state and disturbance observers. The unknown nonlinear system functions are approximated by Radial Basis Function Neural Networks, the unmeasured states are estimated by a developed state observer and the unknown compounded disturbances are estimated by nonlinear disturbance observers. In addition, by introducing DSC technique, the problem of “explosion of complexity” inherent in the conventional backstepping method is eliminated. The designed controller ensures the semi-global stabilization of the whole closed-loop system by means of Lyapunov analysis method. The effectiveness of the proposed approach is demonstrated through a numerical example.

FSE-RBFNNs-Based Robust Adaptive DSC Design for a Larger Class of Nonlinear Strict-Feedback Systems

A novel set-invariance adaptive neural dynamic surface (DSC) control scheme is presented for an extended class of the periodically disturbed nonlinear MIMO strict-feedback systems whose control gain functions are possibly unbounded. The most advanced is that the restrictive bounds assumption is removed after introducing appropriate compact sets, which are constructed in such a way that all the closed-loop trajectories stay in those sets all the time. To tackle the tracking control problem in the presence of more general periodic disturbances, a novel function approximator is well constructed by combining the radial basis function neural networks (RBFNNs) with the Fourier series expansion (FSE). In addition, the DSC technique is employed to overcome the problem of “explosion of complexity”. Furthermore, the Lyapunov theory and invariant set theorem are utilized to prove the closed-loop systems semi-globally uniformly ultimately bounded (SGUUB) stability, and the tracking errors can converge to an arbitrarily small residual set after appropriately choosing design parameters. Finally, the simulation results verify the effectiveness of the proposed method.

High-Gain Observer-Based Line-of-Sight Guidance for Adaptive Neural Path Following Control of Underactuated Marine Surface Vessels

This paper presents an adaptive neural network dynamic surface control law with time-varying sideslip compensation, which includes a geometric kinematic control design and a dynamic control design, for path following of underactuated marine surface vessels (MSVs) in the presence of unmeasured states, model uncertainties, unknown ocean environmental disturbances, and input saturation. First, a high gain observer based line-of-sight guidance law, capable of estimating and compensating the time-varying sideslip angle induced by the unknown time-varying ocean disturbances, is proposed to generate the desired heading for the dynamic control system of the MSV. Next, considering the input saturation, adaptive neural network dynamic surface velocity control laws, in which the model uncertainties and unknown ocean environmental disturbances of the system are compensated by adaptive radial basis function neural network and the problem of input saturation is solved by introducing auxiliary dynamic systems, are designed to realize the dynamic control target of the path following. The proposed control strategy of path following compensates the ocean environmental disturbances from the perspective of both the geometric kinematics and the dynamics, and all error signals of a closed-loop control system are proven to be uniformly ultimately bounded. The simulations validate the effectiveness of the proposed control strategy for path following of MSVs.

Adaptive neural dynamic surface control of MIMO pure-feedback nonlinear systems with output constraints

In this work, the problem of adaptive neural dynamic surface control (DSC) with the minimum adjustable parameters is discussed for a class of multi-input multi-output (MIMO) pure-feedback nonlinear systems with unmodeled dynamics and output constraints. An auxiliary signal designed by the characteristics of unmodeled dynamics is used to handle the dynamical uncertainties. The unknown continuous black-box functions produced in the controller design process are approximated by using radial basis function neural networks (RBFNNs). Based on an one-to-one nonlinear mapping(NM), the MIMO nonaffine nonlinear system with output constraints is transformed into a novel block-structure MIMO nonaffine nonlinear system without output constraints. Based on the transformed system and modified DSC, robust adaptive neural tracking control scheme is developed. Through theoretical analysis, all the signals in the closed-loop system are shown to be semi-globally uniformly ultimately bounded (SGUUB). A numerical example is provided to demonstrate the effectiveness of the proposed design strategy.

Decentralized robust adaptive neural dynamic surface control for multi‐machine excitation systems with static var compensator

SummaryFocusing on solving the control problem of the multimachine excitation systems with static var compensator (SVC), this paper proposes a decentralized neural adaptive dynamic surface control (DNADSC) scheme, where the radial basis function neural networks are used to approximate the unknown nonlinear dynamics of the subsystems and compensate the unknown nonlinear interactions. The main advantages of the proposed DNADSC scheme are summarized as follows: (1) the strong nonlinearities and complexities are mitigated when the SVC equipment are introduced to the multimachine excitation systems and the explosion of complexity problem of the backstepping method is overcome by combining the dynamic surface control method with neural networks (NNs) approximators; 2) the tracking error of the power angle can be kept in the prespecified performance curve by introducing the error transformed function; (3) instead of estimating the weighted vector itself, the norm of the weighted vector of the NNs are estimated, leading to the reduction of the computational burden. It is proved that all the signals in the multimachine excitation system with SVC are semiglobally uniformly ultimately bounded.

Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics

This paper solves the problem of adaptive neural dynamic surface control (DSC) for a class of full state constrained stochastic nonlinear systems with unmodeled dynamics. The concept of the state constraints in probability is first proposed and applied to the stability analysis of the system. The full state constrained stochastic nonlinear system is transformed to the system without state constraints through a nonlinear mapping. The unmodeled dynamics is dealt with by introducing a dynamic signal and the adaptive neural dynamic surface control method is explored for the transformed system. It is proved that all signals of the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded(SGUUB) in mean square or the sense of four-moment. At the same time, the full state constraints are not violated in probability. The validity of the proposed control scheme is demonstrated through the simulation examples.