Event-Triggered Neural-Network Adaptive Control for Strict-Feedback Nonlinear Systems: Selections on Valid Compact Sets.

In this paper, the problem of adaptive control is investigated for a class of non-strict feedback stochastic nonlinear systems with input delay. First, the effect of the input delay is eliminated by constructing an appropriate auxiliary system with the same order as the considered system. Then, with the help of the backstepping technique and the structural characteristics of the radial basis function (RBF) neural network (NN), an adaptive neural control scheme is extended to non-strict feedback stochastic nonlinear systems with input delay, in which uncertain nonlinear functions are approximated by RBF NN. Furthermore, the proposed adaptive controller ensures that all the closed-loop signals remain bounded in probability. Finally, two examples are provided to confirm the effectiveness of the designed strategy.

This paper is concerned with the problem of adaptive neural control for uncertain nonlinear strict-feedback time-delay systems with unknown virtual control coefficients. Radial basis function (RBF) neural networks are employed to directly approximate unknown virtual control signals, and then the adaptive neural control law is constructed by Lyapunov-Krasovskii functionals and backstepping. In order to avoid encountering a large number of adaptive parameters when using RBF neural networks as function approximators, an unknown constant, instead of unknown neural weights themselves, is employed as the estimated parameter. This technique makes only one adaptive parameter tuned online, thus significantly alleviating the burdensome computation. Meanwhile, some continuous functions are introduced to overcome the design difficulty originating from the use of one adaptive parameter. The proposed adaptive control guarantees the boundedness of all the signals in the closed-loop system. Simulation studies are presented to illustrate the effectiveness of the scheme.

Magnetic levitation system is a typical nonlinear and instable system. Based on the complexity and inaccuracy of modelling, in this paper identified magnetic levitation system using the speciality that neural network(NN) can approach any nonlinear function. A Radial Basis Function neural network (RBFNN) controller is designed based on the neural network adaptive control principle. This paper proposes a control method which combine neural network adaptive control method and state feedback control method based on RBFNN. A simulation of the system is proposed, and the result shows that RBFNN could approach magnetic levitation system very well, neural network adaptive state feedback controller has a good effect on this nonlinear system; this control system has a preferable stability and control property.

Simplified adaptive neural control of strict-feedback nonlinear systems

In this paper, the problem of fixed-time adaptive tracking control for strict-feedback nonlinear systems is studied. By introducing a new tunnel constraint variable, a new adaptive and practical fixed-time controller is constructed based on fuzzy control, fixed-time Lyapunov stability theory and backstepping algorithm. Fuzzy logic system is introduced to approximate the unknown term of the system. Theoretical analysis shows that under the control strategy, and the tracking error converges to a small neighborhood of the origin within fixed-time intervals, where the convergence time is independent of the initial state of the system. At the same time, all the signals of the closed-loop system are bounded. Simulation results show that the proposed controller is effective.

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.

The accuracy of fracture reduction robot is critical factor for clinical application. In this study, a neural network adaptive admittance control (NNAAC) system is proposed to improve the position/force tracking accuracy of the robot under large variable reduction forces and uncertain robot dynamic models. The NNAAC consists of an inner loop and an outer loop. The inner loop combines inverse dynamics control (IDC) and radial basis function neural network (RBFNN) to compensate for inaccuracies in the dynamic model, and an admittance parameter adaptive controller based on the RBFNN in the outer loop improves force tracking accuracy and stability. The performance of the NNAAC is evaluated by fracture model reduction experiments, comparing it with the inverse dynamics control and constant admittance control. The experimental results show that the NNAAC achieves better control effectiveness and high accuracy with a maximum reduction force of 190 N. Specifically, the proposed controller exhibits a maximum position error of less than 1 mm and a maximum orientation error of less than 0.5°.

This article addresses the tracking control problem of uncertain fractional-order nonlinear systems in the presence of input quantization and external disturbance. An adaptive backstepping scheme is proposed by combining with radial basis function (RBF) neural networks (NNs), fractional-order disturbance observer (FODO), and backstepping method. The RBF NNs are used to approximate the unknown nonlinearities of fractional-order systems. The FODO is designed to compensate for disturbance and uncertain parameters. The hysteresis quantizer is used to avoid chattering that possibly appears in actual application. The stability of the proposed controller is proved by fractional-order Lyapunov method. In addition, all the signals in the closed-loop system are bounded. The effectiveness of the proposed method is confirmed by the simulation results.

Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint

Event-triggered adaptive neural network controller for uncertain nonlinear system

Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems

Hydraulic system is widely used in industry where large actuation forces are needed such as electro-hydraulic positioning system, active suspension control, and so on. One of the main problem in hydraulic system is the nontriviality, for instance, the deadbands in valve operation, frictions of links, saturations, pressure dynamics, etc. both system unknown nonlinearities and external disturbances should be considered in controller design. For underwater hydraulic manipulator, because of the environment of sea and the large nonlinearities of the hydraulic manipulator system, both system unknown nonlinearities and external disturbances should be considered in controller design. A lot of control methods have been proposed to solve the problem properly, such as sliding mode control, adaptive control, fuzzy adaptive control, adaptive robust control, ect. However, due to limited knowledge about hydraulic manipulator system, it is hard to precisely estimate the nonlinearities for a possible higher performance. In this paper, a neural network adaptive robust control method is proposed to help control an underwater hydraulic manipulator. In order to achieve better performance using adaptive robust control strategy, unknown nonlinearities in the system are approximated by the outputs of radial basis function neural network (RBFNNs). A projection law has been used to bound the NN weights when they are tuning on-line to avoid possible adaptive divergence, and the tracking transient performance is guaranteed by robust control law. Simulation results illustrate that manipulator has a good tracking performance.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

This paper design an output tracking controller for a class of uncertain nonlinear systems to address the input quantization and output tracking funnel control problem. By the traditional adaptive control and backstepping technique, an adaptive quantized funnel control scheme is designed. It is shown that the presented controller can ensure that arbitrary closed-loop signals are globally uniformly bounded, and the output tracking error is bounded, and held in the prescribed funnel performance functions. The presented control scheme is checked through the simulation result.

In this article, the dynamic surface control (DSC) based on the event-triggered control (ETC) framework is discussed for the states constrained systems in nonaffine form with disturbances. The uncertain smooth nonlinear terms produced at recursive each step are approximated by the radial basis function neural networks (RBFNNs). An invertible symmetric mapping is adopted to deal with the full state constraints. An auxiliary signal is designed to handle the input unmodeled dynamics. The event-triggered input is constructed in the DSC framework. The stability analysis illustrates all the signals are bounded in the controlled system. Each state is strictly limited within the artificially preset boundary restrictions. A simulation is employed to verify the theoretical findings.KeywordsEvent-triggered controlDynamic surface controlFull state constraintsInvertible symmetric mapping