An efficient nonlinear channel estimation method for pilot-aided orthogonal frequency division multiplexing system is proposed in this work. The considered channel is selective in time and frequency domain, that is doubly selective channel. Wavelet transform based weighted twin support vector regression is used for channel frequency response estimation, which is suitable for the regression of nonlinear system. Different from traditional support vector regression algorithm, the proposed algorithm gives samples different weights according to their variance calculated based on wavelet transform. The weights are added into both first and quadratic terms of the objective functions to reduce the impact of outliers, which is likely to appear in the received pilot signal polluted by noise. The proposed channel estimation algorithm has good generalization ability and can reduce the influence of overfitting problem. The results of computational tests show that the proposed algorithm is with better estimating performance compared to the classical pilot-aided channel estimation methods. INDEX TERMS Channel estimation, orthogonal frequency division multiplexing, twin support vector regression, wavelet transform.

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In this paper, an adaptive event-triggered tracking control problem is considered for a class of pure-feedback nonlinear systems with output constraints. The mean value theorem is used to transform the pure-feedback system in non-affine form into a system in affine form. In addition, the radial basis function neural network (RBF NN) control is used to approximate the unknown nonlinear function in the system and the tracking error of the controller is limited to a small constant boundary by using the positive obstacle Lyapunov function. An adaptive controller for a class of pure-feedback systems is established, which based on the backstepping control theory and event-triggered control theory, it can ensure all the closed-loop signals are bounded and avoid the Zeno-behavior. The simulation results prove the effectiveness of the controller design.INDEX TERMS Pure-feedback nonlinear systems, event-triggered control, output constraints, RBF neural network.

An active fault-tolerant control (FTC) strategy for a class of switched nonlinear systems in pure-feedback form by using average dwell time method is investigated in this article. The unknown functions in the system are approximated directly by fuzzy logic systems. A fuzzy state observer is designed to estimate the unavailable states, based on which, a fault detection project is designed. In fault-free case, all the signals in the closed-loop system are proved to be bounded under the control of the designed input. The fault estimation and FTC projects will be activated after a fault has been detected. In addition, the active FTC is constructed in the framework of backstepping design technique. The proposed controller guarantee that all the closed-loop signals remain bounded under a class of switching signals with average dwell time. The simulation results show the effectiveness of the proposed method.

This paper investigates estimator-based control problems for pure-feedback nonlinear systems with incomplete measurements due to the transmission packet losing or sensor saturation. The incomplete measurements can cause the state variables unavailable or distorted, which can degrade the performance of the system. To solve these problems, a state estimator is designed for the data-losing case, based on which two backstepping control methods are developed. The output of the system is subject to a prescribed constraint by using an obstacle Lyapunov function. By solving a linear matrix inequality, the stability conditions of the state estimator and closed-loop system are derived. It is proved that the control scheme can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded in mean square. The effectiveness of the proposed methods is confirmed by simulations. INDEX TERMS Cyber-physical system, nonlinear system, pure-feedback, controller design, incomplete measurement I. INTRODUCTION I N recent years, the control theory is making continuous progress, and the controlled system is becoming more complex. The systems integrating physical processes, computation and networking can be described as cyber-physical systems (CPSs) [1]. Many applications such as smart power grids, smart medical devices and complex physical and chemical processes can be interpreted as CPSs [2]-[6]. Because of the information exchange between subsystems, the control performance of the whole complex system has the potential to be improved. However, due to the complexity of the system, the control of the system has become a challenging problem [7]. For example, the interruption of communication between subsystems, the deterioration of communication parameters or sensor saturation will have a serious impact on the control performance and even the stability of the system [8]-[10]. Hence, many works focus on control problems of CPSs. Authors in [11]-[13] concerned about the controller design of CPSs with packet dropouts. Lu [14] proposed an input-to-state stabilizing controller for