Zhihong Man

Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems

This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Brief paper: Finite-time stability and instability of stochastic nonlinear systems

This paper presents a new definition of finite-time stability for stochastic nonlinear systems. This definition involves stability in probability and finite-time attractiveness in probability. An important Lyapunov theorem on finite-time stability for stochastic nonlinear systems is established. A theorem extending the stochastic Lyapunov theorem is also proved. Moreover, an example and a lemma are presented to illustrate the scope of extension. A useful inequality, extended from Biharis inequality, is derived, which plays an important role in showing the Lyapunov theorem. Finally, a Lyapunov theorem on finite-time instability is proved, which states that almost surely globally asymptotical stability is not equivalent to finite-time stability for some stochastic systems. Two simulation examples are given to illustrate the theoretical analysis.

Finite-time stabilization of stochastic nonlinear systems in strict-feedback form

In this paper, we investigate the problem of almost surely finite-time stabilization of a class of stochastic nonlinear systems. Based on the recently proposed almost surely finite-time stability theorem in Yin, Khoo, Man, and Yu (2011), we prove that, almost surely global finite-time stability of stochastic nonlinear systems in strict-feedback form can be guaranteed by a continuous control law. A systematic design algorithm is developed for the construction of the controller. Simulation results are given to illustrate the theoretical analysis.

Robust sliding mode control for Steer-by-Wire systems with AC motors in road vehicles

In this paper, the modeling of steer-by-wire (SbW) systems is further studied, and a sliding mode control scheme for the SbW systems with uncertain dynamics is developed. It is shown that an SbW system, from the steering motor to the steered front wheels, is equivalent to a second-order system. A sliding mode controller can then be designed based on the bound information of uncertain system parameters, uncertain self-aligning torque, and uncertain torque pulsation disturbances, in the sense that not only the strong robustness with respect to large and nonlinear system uncertainties can be obtained but also the front-wheel steering angle can converge to the handwheel reference angle asymptotically. Both the simulation and experimental results are presented in support of the excellent performance and effectiveness of the proposed scheme.

Technical communique: Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.

Variable step-size LMS algorithm with a quotient form

An improved robust variable step-size least mean square (LMS) algorithm is developed in this paper. Unlike many existing approaches, we adjust the variable step-size using a quotient form of filtered versions of the quadratic error. The filtered estimates of the error are based on exponential windows, applying different decaying factors for the estimations in the numerator and denominator. The new algorithm, called more robust variable step-size (MRVSS), is able to reduce the sensitivity to the power of the measurement noise, and improve the steady-state performance for comparable transient behavior, with negligible increase in the computational cost. The mean convergence, the steady-state performance and the mean step-size behavior of the MRVSS algorithm are studied under a slow time-varying system model, which can be served as guidelines for the design of MRVSS algorithm in practical applications. Simulation results are demonstrated to corroborate the analytic results, and to compare MRVSS with the existing representative approaches. Superior properties of the MRVSS algorithm are indicated.

A new robust training algorithm for a class of single-hidden layer feedforward neural networks

Abstract A robust training algorithm for a class of single-hidden layer feedforward neural networks (SLFNs) with linear nodes and an input tapped-delay-line memory is developed in this paper. It is seen that, in order to remove the effects of the input disturbances and reduce both the structural and empirical risks of the SLFN, the input weights of the SLFN are assigned such that the hidden layer of the SLFN performs as a pre-processor, and the output weights are then trained to minimize the weighted sum of the output error squares as well as the weighted sum of the output weight squares. The performance of an SLFN-based signal classifier trained with the proposed robust algorithm is studied in the simulation section to show the effectiveness and efficiency of the new scheme.

Robust Motion Control of a Linear Motor Positioner Using Fast Nonsingular Terminal Sliding Mode

A robust motion control system is essential for the linear motor (LM)-based direct drive to provide high speed and high-precision performance. This paper studies a systematic control design method using fast nonsingular terminal sliding mode (FNTSM) for an LM positioner. Compared with the conventional nonsingular terminal sliding mode control, the FNTSM control can guarantee a faster convergence rate of the tracking error in the presence of system uncertainties including payload variations, friction, external disturbances, and measurement noises. Moreover, its control input is inherently continuous, which accordingly avoids the undesired control chattering problem. We further discuss the selection criteria of the controller parameters for the LM to deal with the system dynamic constraints and performance tradeoffs. Finally, we present a robust model-free velocity estimator based on the only available position measurements with quantization noises such that the estimated velocity can be used for feedback signal to the FNTSM controller. Experimental results demonstrate the practical implementation of the FNTSM controller and verify its robustness of more accurate tracking and faster disturbance rejection compared with a conventional NTSM controller and a linear H∞ controller.

Design of Robust Repetitive Control With Time-Varying Sampling Periods

This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.

Robust Single-Hidden Layer Feedforward Network-Based Pattern Classifier

In this paper, a new robust single-hidden layer feedforward network (SLFN)-based pattern classifier is developed. It is shown that the frequency spectrums of the desired feature vectors can be specified in terms of the discrete Fourier transform (DFT) technique. The input weights of the SLFN are then optimized with the regularization theory such that the error between the frequency components of the desired feature vectors and the ones of the feature vectors extracted from the outputs of the hidden layer is minimized. For the linearly separable input patterns, the hidden layer of the SLFN plays the role of removing the effects of the disturbance from the noisy input data and providing the linearly separable feature vectors for the accurate classification. However, for the nonlinearly separable input patterns, the hidden layer is capable of assigning the DFTs of all feature vectors to the desired positions in the frequency-domain such that the separability of all nonlinearly separable patterns are maximized. In addition, the output weights of the SLFN are also optimally designed so that both the empirical and the structural risks are well balanced and minimized in a noisy environment. Two simulation examples are presented to show the excellent performance and effectiveness of the proposed classification scheme.