Xiuyu Zhang

Adaptive Neural Network Dynamic Surface Control for a Class of Time-Delay Nonlinear Systems With Hysteresis Inputs and Dynamic Uncertainties

In this paper, an adaptive neural network (NN) dynamic surface control is proposed for a class of time-delay nonlinear systems with dynamic uncertainties and unknown hysteresis. The main advantages of the developed scheme are: 1) NNs are utilized to approximately describe nonlinearities and unknown dynamics of the nonlinear time-delay systems, making it possible to deal with unknown nonlinear uncertain systems and pursue the L∞ performance of the tracking error; 2) using the finite covering lemma together with the NNs approximators, the Krasovskii function is abandoned, which paves the way for obtaining the L∞ performance of the tracking error; 3) by introducing an initializing technique, the L∞ performance of the tracking error can be achieved; 4) using a generalized Prandtl-Ishlinskii (PI) model, the limitation of the traditional PI hysteresis model is overcome; and 5) by applying the Youngs inequalities to deal with the weight vector of the NNs, the updated laws are needed only at the last controller design step with only two parameters being estimated, which reduces the computational burden. It is proved that the proposed scheme can guarantee semiglobal stability of the closed-loop system and achieves the L∞ performance of the tracking error. Simulation results for general second-order time-delay nonlinear systems and the tuning metal cutting system are presented to demonstrate the efficiency of the proposed method.

Nonlinear Control of Systems Preceded by Preisach Hysteresis Description: A Prescribed Adaptive Control Approach

When systems are preceded by hysteresis nonlinearities, many controller strategies have been developed with various hysteresis models, especially in the past decade. Among the hysteresis models, the Preisach model has a very general and well-established mathematical structure. However, designs of controllers that guarantee the closed-loop stability of nonlinear systems having the Preisach hysteresis representation are still a challenging issue in the literature. In this paper, we will attempt to demonstrate a solution in which a stable controller can be designed for nonlinear systems that couple with Preisach hysteresis model. The key is that by utilizing the so-called Preisach plane, the Preisach model is reexpressed into a control-oriented form, in which the input signal is explicitly expressed. It is then possible to fuse available control techniques with the Preisach model designing stable controllers. As an illustration to show the advantage of the developed control-oriented form, a prescribed adaptive control approach is adopted to ensure the transient and steady-state performance of the tracking error. The effectiveness of the control scheme is validated by the experimental results.

High-gain observer based decentralised output feedback control for interconnected nonlinear systems with unknown hysteresis input

In this paper, an adaptive dynamic surface control is proposed for a class of interconnected nonlinear systems with inputs preceded by unknown saturated PI hysteresis. By using the proposed dynamic surface control scheme, the explosion of complexity problem when the hysteresis is fused with backstepping design can be eliminated which, together with the estimation of vector norm of the unknown parameters, greatly simplifies the control law and reduces the computational burden. Moreover, by introducing an initialisation technique, the tracking performance of each subsystem can be guaranteed, which, for the first time, establishes the relationship between tracking performance and design parameters in the interconnected system.

Implementable Adaptive Inverse Control of Hysteretic Systems via Output Feedback With Application to Piezoelectric Positioning Stages

This paper aims to develop a neural-network-based robust adaptive output-feedback motion controller for a class of hysteretic nonlinear systems, where the inverse hysteresis approach is adopted. The developed scheme is applied to the piezoelectric positioning stage, showing the advantages of the proposed approach by the experimental results. The main contributions are: 1) by using the neural networks as an approximator, the nonlinear function in the systems can be completely unknown; 2) by designing a high-gain observer to estimate the states of the system and cope with the uncertainties of the system, only the output of the control system is required measurable; 3) experiments on the piezoelectric positioning stage were conducted where the piezoelectric positioning stage is considered as a third-order system under the condition only the output of the system is available; 4) by adjusting the initial conditions of the states observer and adaptive laws of unknown parameters, the arbitrarily small L∞ norm of the tracking error is deviated. It is proved that all the signals in the closed-loop systems are semiglobally ultimately uniformly bounded.

A Comprehensive Dynamic Model for Magnetostrictive Actuators Considering Different Input Frequencies With Mechanical Loads

Magnetostrictive actuators featuring high energy densities, large strokes, and fast responses are playing an increasingly important role in micro/nano-positioning applications. However, such actuators with different input frequencies and mechanical loads exhibit complex dynamics and hysteretic behaviors, posing a great challenge on applications of the actuators. Therefore, it is important to develop a dynamic model that can characterize dynamic behaviors of the actuators, including current-magnetic flux nonlinear hysteresis, frequency responses, and loading effects, simultaneously. To this end, a comprehensive model, which thoroughly considers the electric, magnetic, and mechanical domain, as well as the interactions among them, is developed in this paper. To validate the developed model, the parameters of the model are identified where the hysteresis of the magnetostrictive actuator is described, as an illustration, by the asymmetric shifted Prandtl-Ishlinskii model. The experimental results demonstrate that the comprehensive model presents an excellent agreement with dynamic behaviors of the magnetostrictive actuator.

Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization

This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.

Inverse Adaptive Controller Design for Magnetostrictive-Actuated Dynamic Systems

Magnetostrictive actuators featuring high energy densities, large strokes, and fast responses are playing an increasingly important role in precision positioning applications. However, such actuators invariably exhibit asymmetric hysteresis nonlinearities that could cause oscillations and errors in the micro-positioning tasks. Therefore, in this chapter, an inverse adaptive controller design method is developed for the purpose of mitigating the hysteresis effect in the magnetostrictive-actuated dynamic systems. Focusing on the asymmetric hysteresis phenomenon, an asymmetric shifted Prandtl–Ishlinskii (ASPI) model and its inverse are utilized to describe and compensate the asymmetric hysteresis behaviors in the magnetostrictive actuator, respectively. To guarantee the global stability of the closed-loop system and the transient performance of the tracking error, a prescribed adaptive control method will be applied. The effectiveness of the proposed control scheme is validated on the magnetostrictive-actuated experimental platform.

Adaptive Dynamic Surface Inverse Output Feedback Control for a Class of Hysteretic Systems

In this paper, an robust neural adaptive output-feedback inverse control scheme for a class of hysteretic nonlinear systems is proposed. Firstly, by designing a high-gain observer to estimate the states of the system and cope with the uncertainties of the system, only the output of the control system is required to be measurable. Secondly, the nonlinear function in the systems can totally unknown due to the utilization of the neural networks approximator. Finally, the arbitrarily small \(\mathcal {L}_{\infty }\) norm of the tracking error is achieve by adjusting the initial conditions of the unknown parameters.

A Neural Hysteresis Model for Smart-Materials-Based Actuators

In this paper, a constraint factor (CF) is presented. The CF and an odd m-order polynomial form a new hysteretic operator (HO) together. And then, an expanded input space is constructed based on the proposed HO. In the expanded input and output spaces, the one-to-multiple mapping of hysteresis is transformed into a one-to-one mapping so that a neural network can be used to develop a neural hysteresis model. The model parameters are computed by using the least square method. Finally, the neural hysteresis model is employed to approximate a real data from a magnetostrictive actuator in an experiment. The experimental results demonstrate the proposed approach is effective.