Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

Adaptive neural control for uncertain stochastic nonlinear strict-feedback systems with time-varying delays: A Razumikhin functional method

By the combination of the adaptive backstepping design with the dynamic surface control technique, an novel adaptive neural control approach is investigated for a class of pure-feedback stochastic nonlinear systems with multiple unknown time-varying delays. To overcome the design difficulty arising from the non-affine structure of pure-feedback stochastic systems, the mean value theorem is exploited. The design difficulties due to multiple unknown time-varying delay functions are overcome by using the function separation technique, the appropriate Lyapunov-Krasovskii functionals and the desirable property of hyperbolic tangent functions. The radial-basis-function (RBF) neural networks are utilized to approximate the unknown nonlinear functions. It is shown that the proposed control approach can guarantee that all signals of the closed-loop system are bounded in probability, and the tracking errors can be made arbitrarily small in probability by choosing suitable design parameters. Finally, simulation example is provided to demonstrate the effectiveness of the proposed control scheme.

In this paper, the problem of adaptive neural control is considered for a class of strict-feedback nonlinear systems with unmodeled dynamics, dynamic disturbances and unknown input saturation. During the controller design, radial basis functions(RBF) neural networks are applied to model the unknown nonlinearities, and an adaptive neural control scheme is developed via backstepping, which guarantees that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. A simulation example is provided to show the effectiveness of the proposed control scheme.

This paper focuses on the problem of the adaptive neural control for a class of a perturbed pure-feedback nonlinear system. Based on radial basis function (RBF) neural networks’ universal approximation capability, an adaptive neural controller is developed via the backstepping technique. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood around the origin. The main advantage of this note lies in that a control strategy is presented for a class of pure-feedback nonlinear systems with external disturbances being bounded by functions of all state variables. A numerical example is provided to illustrate the effectiveness of the suggested approach.

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 output-feedback control for a class of nonlinear strict-feedback systems. In this research, radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable state variables. An adaptive neural output feedback control scheme is proposed via backstepping technique. The proposed design method can guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system, and ensures the observer errors converge to a small neighborhood. At last, a simulation example is included to show the effectiveness of the proposed method.

An approximation based adaptive neural decentralized output tracking control scheme for a class of large-scale unknown nonlinear systems with strict-feedback interconnected subsystems with unknown nonlinear interconnections is developed in this paper. Within this scheme, radial basis function RBF neural networks are used to approximate the unknown nonlinear functions of the subsystems. An adaptive neural controller is designed based on the recursive backstepping procedure and the minimal learning parameter technique. The proposed decentralized control scheme has the following features. First, the controller singularity problem in some of the existing adaptive control schemes with feedback linearization is avoided. Second, the numbers of adaptive parameters required for each subsystem are not more than the order of this subsystem. Lyapunov stability method is used to prove that the proposed adaptive neural control scheme guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking errors converge to a small neighborhood of the origin. The simulation example of a two-spring interconnected inverted pendulum is presented to verify the effectiveness of the proposed scheme.

An approximation-based adaptive neural controller is constructed for uncertain stochastic nonlinear systems in nonstrict-feedback form appearing dead-zone and output constraint. Neural networks (NNs) are directly utilized to approximate the unknown nonlinear functions existing in systems. A barrier Lyapunov function is introduced to ensure that the trajectory of output is limited within a predetermined range. By integrating NNs into the backstepping technique, an adaptive neural controller is designed to guarantee all variables existing in the considered closed-loop system are semi-globally uniformly ultimately bounded, and by appropriately tuning several design parameters online, the tracking error can be converged to a small neighborhood of the origin. Simulations on a numerical example are given to demonstrate the effectiveness of the method proposed in this paper.

Deterministic learning-based neural control for output-constrained strict-feedback nonlinear systems

In this paper, an novel adaptive tracking control is developed for a class of completely non-affine pure-feedback nonlinear systems using radial basis function neural networks (RBFNNs). Combining the dynamic surface control (DSC) technique and backstepping method, the explosion of complexity in the traditional backstepping design is avoided. Using mean value theorem and Young's inequality, only one learning parameter need to be tuned online in the whole controller design, and the computational burden is effectively alleviated. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.

Neural network-based adaptive fault-tolerant control for nonlinear systems with unknown backlash-like hysteresis and unmodeled dynamics

Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation

This paper focuses on the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown control coefficients and quantized input. The difficulty from the unknown control direction is solved by using the linear state transformation and the Nussbaum gain function(NGF) approach. Based on the combination of input-driven observer, backstepping technique, neural network(NN) parametrization and variable separation method, a novel adaptive output feedback quantized control scheme involving only one adaptive parameter is developed for such systems. The designed quantized controller ensures that all signals of closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to an adjustable neighborhood of the origin. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed control design.

In this paper, an adaptive neural networks &#x0028 NNs &#x0029 tracking controller is proposed for a class of single-input &#x002F single-output &#x0028 SISO &#x0029 non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real &#x0028 SPR &#x0029 theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.

In this paper, an adaptive neural control scheme is proposed for multi-machine steam-valving power systems. The multi-machine steam-valving power systems consist of interconnected subsystems, with coupling in the form of unknown nonlinearities and parametric uncertainties. Using the adaptive neural control method by S. S. Ge and Cong Wang, A (2004), the coupling problem between subsystems can be solved without linearization treatment. Semi-global ultimate boundedness of all the signals in the closed-loop system are obtained. The outputs of the closed-loop system are proven to converge to a small neighborhood of the desired trajectories. Simulation results of two-machine power systems are presented as an example to show the effectiveness of the approach.