Adaptive Neural Tracking Control Research Articles

Adaptive Neural Control of Underactuated Surface Vessels With Prescribed Performance Guarantees.

This paper presents adaptive neural tracking control of underactuated surface vessels with modeling uncertainties and time-varying external disturbances, where the tracking errors consisting of position and orientation errors are required to keep inside their predefined feasible regions in which the controller singularity problem does not happen. To provide the preselected specifications on the transient and steady-state performances of the tracking errors, the boundary functions of the predefined regions are taken as exponentially decaying functions of time. The unknown external disturbances are estimated by disturbance observers and then are compensated in the feedforward control loop to improve the robustness against the disturbances. Based on the dynamic surface control technique, backstepping procedure, logarithmic barrier functions, and control Lyapunov synthesis, singularity-free controllers are presented to guarantee the satisfaction of predefined performance requirements. In addition to the nominal case when the accurate model of a marine vessel is known a priori, the modeling uncertainties in the form of unknown nonlinear functions are also discussed. Adaptive neural control with the compensations of modeling uncertainties and external disturbances is developed to achieve the boundedness of the signals in the closed-loop system with guaranteed transient and steady-state tracking performances. Simulation results show the performance of the vessel control systems.

Prescribed performance global stable adaptive neural dynamic surface consensus tracking control of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics

ABSTRACT This paper focuses on the leader-following consensus control problem of stochastic multi-agent systems with hysteresis inputs and nonlinear dynamics. A leader-following consensus scheme is presented for stochastic multi-agent systems directions under directed graphs, which can achieve predefined synchronisation error bounds. By mainly activating an auxiliary robust control component for pulling back the transient escaped from the neural active region, a multi-switching robust neuro adaptive controller in the neural approximation domain, which can achieve globally uniformly ultimately bounded tracking stability of multi-agent systems recently. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronise with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and all the follower agents can keep consensus with the leader. Two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme.

Adaptive Neural Tracking Control of Robotic Manipulators with Guaranteed NN Weight Convergence

Although adaptive control for robotic manipulators has been widely studied, most of them require the acceleration signals of the joints, which are usually difficult to measure directly. Although neural networks (NNs) have been used to approximate the unknown nonlinear dynamics in the robotic systems, the conventional adaptive laws for updating the NN weights cannot guarantee that the obtained NN weights converge to their ideal values, which could degrade the tracking control response. To address these two issues, a new adaptive algorithm with the extracted NN weights error is incorporated into adaptive control, where a novel leakage term is superimposed on the gradient method. By using the Lyapunov approach, the convergence of both the tracking error and the estimation error can be guaranteed simultaneously. In addition, two auxiliary functions are introduced to reformulate the robotic model for designing the adaptive law, and a filter operation is used to avoid measuring the acceleration signals. Comparisons to other well-recognized adaptive laws are given, and extensive simulations based on a 2-DOF SCARA robotic system are given to verify the effectiveness of the proposed control strategy.

Adaptive neural tracking control for nonstrict‐feedback nonlinear systems with unknown backlash‐like hysteresis and unknown control directions

SummaryIn this paper, a neural network–based adaptive tracking control problem is investigated for a class of nonstrict‐feedback nonlinear systems in the presence of unknown backlash‐like hysteresis nonlinearity, unmodeled dynamics, and unknown control directions. A state feedback controller is developed for the considered system by applying the adaptive backstepping technique and neural networks. The design difficulties exhibited in this paper due to unmodeled dynamics, unknown control directions, and nonstrict‐feedback form are handled by resorting to a dynamic signal, a Nussbaum function, and the variable separation approach, respectively. It is shown that the designed adaptive controller can guarantee that all the signals remain bounded and that the desired signal can be tracked with a small domain of the origin. A numerical example and an example of a real plant for a one‐link manipulator are provided to show the feasibility of the newly designed controller scheme.

Neural adaptive tracking control for a class of high-order non-strict feedback nonlinear multi-agent systems

This research is mainly concerned with the consensus tracking problem for a class of high-order non-strict feedback nonlinear multi-agent systems, in which the virtual and the actual control items of each follower dynamics are the power functions with positive odd integers rather than linear items. Due to this structural feature of the high-order systems, adding a power integrator technique is employed in controller design to overcome the obstacle caused by high power of virtual and real control items. Meanwhile, Radial Basis Function Neural Networks are used to approximate the uncertain nonlinearities. An adaptive tracking strategy is proposed for this type of multi-agent systems. It is shown that the suggested control scheme can guarantee the boundedness of all the closed-loop signals and ensure that all outputs of follower agents track the leader signal synchronously. Since high-order non-strict feedback nonlinear multi-agent systems include some existing nonlinear multi-agent systems as the special case, our result can be used to control more general nonlinear multi-agent systems. Finally, a numerical example is presented to further verify the effectiveness of the proposed algorithm.

Tracking Control of Podded Propulsion Unmanned Surface Vehicle with Unknown Dynamics and Disturbance Under Input Saturation

This paper addresses two interrelated problems concerning the tracking control of podded propulsion unmanned surface vehicle (USV), namely, the modeling of podded propulsion USV, and trajectory tracking controller design. Based on the force analysis, the separation model of podded propulsion USV is established. Furthermore, a practical adaptive neural tracking controller is proposed by backstepping technique, neural network minimum parameter learning method, neural shunting model and auxiliary dynamic system without the exact information of hydrodynamic damping structure and the sea disturbances. Using Lyapunov stability analysis theory, it is proven that all error signals in the system are uniformly ultimately bounded. The advantages of the paper are that first, the underactuated characteristic of podded propulsion USV is demonstrated; then, neural shunting model and neural network minimum parameter learning method are introduced to cope with the problem of "explosion of complexity" and uncertainty factors, respectively; third, auxiliary dynamic system is introduced into controller design to reduce the risk of actuator saturation. Taking into account the above practical problems is helpful to engineering implementation in the marine practice. Finally, numerical simulation has been given to demonstrate the effectiveness of the proposed scheme.

Disturbance observer based adaptive neural control of uncertain MIMO nonlinear systems with unmodeled dynamics

Abstract This paper investigates the disturbance observer-based adaptive neural tracking control of a class of multiple-input multiple-output (MIMO) systems in the presence of unmodeled dynamics, system uncertainties, time varying disturbance and input dead-zone. An adaptive neural control method combined with backstepping technique and the radial basis function neural networks (RBFNNs) is proposed for the systems under consideration. In recursive backstepping designs, neural network (NN) is employed for uncertainty approximation. The disturbance observer is developed to provide efficient learning of the compounded disturbance which includes the effect of time varying disturbance, neural network approximation error. It is shown that by using Lyapunov methods, the developed control scheme can ensure semi-globally uniformly ultimately bounded (SGUUB) of all signals within the closed-loop systems. Simulation results are presented to illustrate the validity of the approach. This paper is novel at least in the two aspects: (1) disturbance observer based tracking control method is developed for MIMO nonlinear systems with unmodeled dynamics and (2) the strong coupled terms is considered in this paper where the interconnections are functions of all states, which is a more general form than existing related results.

Adaptive neural network asymptotical tracking control for an uncertain nonlinear system with input quantisation

In this paper, the problem of adaptive neural network asymptotical tracking is investigated for a class of nonlinear system with unknown function, external disturbances and input quantisation. Based on neural network technique, an adaptive asymptotical tracking controller is provided for an uncertain nonlinear system via backstepping method. In order to reduce complexity of the control algorithm in the backstepping design process, a sliding mode differentiator is employed to estimate the virtual control law and only two parameters need to be estimated via adaptive control technique. The stability of the closed-loop system is analysed by using Lyapunov function method and zero-tracking error performance is obtained in the presence of unknown nonlinear function, external disturbances and input quantisation. Finally, an application example is employed to demonstrate the effectiveness of the proposed scheme.

Neural adaptive tracking control for an uncertain robot manipulator with time-varying joint space constraints

Abstract This paper presents a control design for a robotic manipulator with uncertainties in both actuator dynamics and manipulator dynamics subject to asymmetric time-varying joint space constraints. Tangent-type time-varying barrier Lyapunov functionals (tvBLFs) are constructed to ensure no constraint violation and to remove the need for transforming the original constrained system into an equivalent unconstrained one. Adaptive Neural Networks (NNs) are proposed to handle uncertainties in manipulator dynamics and actuator dynamics in addition to the unknown disturbances. Proper input saturation is employed, and it is proved that under the proposed method the stability and semi-global uniform ultimate boundedness of the closed-loop system can be achieved without violation of constraints. The effectiveness of the theoretical developments is verified through numerical simulations.

Disturbance observer based adaptive neural prescribed performance control for a class of uncertain nonlinear systems with unknown backlash-like hysteresis

Abstract In this paper, an adaptive neural tracking control is studied for a class of strict-feedback nonlinear systems with guaranteed predefined performance subject to unknown backlash-like hysteresis input, uncertain parameters and external unknown disturbance. An adaptive neural control method combined with backstepping technique, and the radial basis function neural networks (RBFNNs) is proposed for the systems under consideration. In recursive backstepping designs, the tracking control performance can be guaranteed by exploiting a new performance function. A disturbance observer is employed to approximate the unknown disturbance. It is shown that by using Lyapunov methods, the designed controller can guarantee the prespecified transient and ensure semi-globally uniformly ultimately bounded (SGUUB) of all signals within the closed-loop systems. Simulation results are presented to illustrate the validity of the approach.

Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

ABSTRACTIn this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.

Adaptive Neural Tracking Control for Interconnected Switched Systems With Non-ISS Unmodeled Dynamics.

The adaptive neural network tracking control problem is investigated for a class of interconnected switched systems. The considered systems are with unmodeled dynamics, some of which do not satisfy the input-to-state stable (ISS) condition. By utilizing the neural network to approximate the composite unknown nonlinear functions, the corresponding decentralized tracking controller is designed for each subsystem with the help of dynamic surface control method. Some subsystems are stable with the designed controller, while other subsystems may not be stable because of non-ISS unmodeled dynamics, but they have some special properties with the designed controller. Then, a novel switching signal scheme is established such that the interconnected switched system is stable in the sense of semi-global boundedness, and the tracking errors can converge to predefined residual sets with prescribed performance index. Moreover, the switching scheme allows the number of switches to grow faster than traditional average dwell time method. Finally, a numerical example is provided to demonstrate the effectiveness of the presented results.

Robust adaptive neural tracking control for a class of nonlinear systems with unmodeled dynamics using disturbance observer

Abstract This paper is concerned with an adaptive neural tracking control for a class of strict-feedback nonlinear systems subject to unmodeled dynamics, system uncertainties, completely unknown external disturbance and input dead zone. An adaptive neural control method combined with backstepping technique and the radial basis function neural networks (RBFNNs) is proposed for the systems under consideration. In recursive backstepping designs, a dynamic signal is introduced to cope with the unmodeled dynamics, a disturbance observer is employed to approximate the unknown disturbance and the dead zone equalled to the sum of the simple linear system and the partial bounded disturbance. It is shown that by using Lyapunov methods, the developed control scheme can ensure semi-globally uniformly ultimately bounded (SGUUB) of all signals within the closed-loop systems. Simulation results are presented to illustrate the validity of the approach.

Adaptive Neural Dynamic Surface Control for Nonstrict-Feedback Systems With Output Dead Zone.

This paper focuses on the problem of adaptive output-constrained neural tracking control for uncertain nonstrict-feedback systems in the presence of unknown symmetric output dead zone and input saturation. A Nussbaum-type function-based dead-zone model is introduced such that the dynamic surface control approach can be used for controller design. The variable separation technique is employed to decompose the unknown function of entire states in each subsystem into a series of smooth functions. Radial basis function neural networks are utilized to approximate the unknown black-box functions derived from Young's inequality. With the help of auxiliary first-order filters, the dimensions of neural network input are reduced in each recursive design. A main advantage of the proposed method is that for an -order nonlinear system, only one adaptation parameter needs to be tuned online. It is rigorously shown that the proposed output-constrained controller guarantees that all the closed-loop signals are semiglobal uniformly ultimately bounded and the tracking error never violates the output constraint.

Neural Observer and Adaptive Neural Control Design for a Class of Nonlinear Systems.

This paper addresses the problem of adaptive neural tracking control for nonlinear nonstrict-feedback systems. The state variables are immeasurable and only the system output is available. A neural observer is constructed to estimate these unknown system state variables. An observer-based adaptive neural tracking control scheme is developed via backstepping approach. It is shown that the designed controller guarantees that the system output well follows the desired reference signal, and meanwhile, other closed-loop signals remain bounded. Finally, two simulation examples are used to test our results.

Adaptive neural control of switched nonstrict-feedback nonlinear systems with multiple time-varying delays

This paper focuses on the problem of adaptive neural tracking control for a class of uncertain switched nonlinear time-varying delay systems in nonstrict-feedback form with arbitrary switchings. Radial basis function neural networks are used to model the unknown redefined continuous functions derived from Young’s inequalities. By combining bounding functions’ monotonously increasing property and variable separation technique, the uncertain system functions with nonstrict-feedback structure are dealt with such that iterative adaptive backstepping approach can be carried out. A newly developed Lyapunov–Krasovskii functional is utilized to compensate for the uncertainties of multiple time-varying delays, which makes the delay nonlinearities free from any assumptions. By introducing novel continuous functions, the problem of circular construction of controller is overcome deduced from employing one common tuning law. It is proved that the tracking error of adaptive neural control systems is semi-globally uniformly ultimately bounded with common Lyapunov function method. Finally, a simulation example is presented to show the effectiveness of the suggested control scheme.

Finite-Time Adaptive Control for a Class of Nonlinear Systems With Nonstrict Feedback Structure.

This paper focuses on finite-time adaptive neural tracking control for nonlinear systems in nonstrict feedback form. A semiglobal finite-time practical stability criterion is first proposed. Correspondingly, the finite-time adaptive neural control strategy is given by using this criterion. Unlike the existing results on adaptive neural/fuzzy control, the proposed adaptive neural controller guarantees that the tracking error converges to a sufficiently small domain around the origin in finite time, and other closed-loop signals are bounded. At last, two examples are used to test the validity of our results.

Adaptive neural control for MIMO stochastic nonlinear pure-feedback systems with input saturation and full-state constraints

Abstract This paper investigates an adaptive neural tracking control problem for a class of multi-input multi-output (MIMO) stochastic nonlinear pure-feedback systems with input saturation and full-state constraints. First, the implicit function and mean value theorems are used to overcome the difficulty in the control of pure-feedback systems. Second, the Gaussian error function is employed to represent a continuous differentiable asymmetric saturation model, the neural network is employed to approximate the unknown nonlinearity, and a barrier Lyapunov function is designed to ensure that the full-state variables are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is obtained, which decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed controller can guarantee that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. The simulation example is given to further illustrate the effectiveness of the proposed approach.

Adaptive neural tracking control for a class of uncertain nonstrict-feedback nonlinear systems

This paper investigates adaptive neural tracking control problem for nonstrict-feedback nonlinear systems with completely unknown uncertainties. Superior to the existing results that only bounded error tracking performance can be achieved, the designed controllers of this paper will guarantee the asymptotic tracking performance under the neural network approximation framework. This is accomplished by using a new control strategy where a proportional-integral (PI) compensator that can be conveniently implemented in practice is introduced. Meanwhile, a novel Lyapunov function is developed, whose upper-right Dini derivative will be used to construct the desired controllers and adaptive laws. Finally, simulation results are given to show the advantages and effectiveness of the proposed new design technique over some existing ones.

Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints

ABSTRACTAn adaptive neural tracking control is investigated for a class of nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints and saturation input. First, the continuous differentiable saturation model is employed to ensure the input constraint, and a barrier Lyapunov function is designed to achieve the full-state constraint. Second, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time-delay terms, and neural networks are employed to approximate the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive controller is proposed to guarantee that all the signals in the closed-loop system are 4-Moment (or 2-Moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin. Two examples are shown to further demonstrate the effectiveness of the proposed control scheme.