A nonlinear Tracking-Differentiator is one-inputtwo-output system that can generate smooth approximation of measured signals and get the derivatives of the signals. The nonlinear tracking-Differentiator is explored to denoise and generate the derivatives of the walks of the 3-periodicity of DNA sequences. An improved algorithm for gene finding is presented using the nonlinear Tracking-Different...

Abstract: In this paper, a continuous finite-time-convergent differentiator is presented based on a strong Lyapunov function. The continuous differentiator can reduce chattering phenomenon sufficiently than normal sliding mode differentiator, and the outputs of signal tracking and derivative estimation are all smooth. Frequency analysis is applied to compare the continuous differentiator with s...

This paper constructs a relationship between attitude and translational movement of a quadrotor, and presents a PD logic tracking control design algorithm capable of not only stabilizing attitude but also tracking a desired trajectory accurately. In contrast to conventional flight control systems, the artificial inner/outer-loop structure is eliminated via using a third-order time optimal track...

This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state-space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. The improved tracking differentiator (...

We show that the problem "real-time numerical differentiation" of a given noisy signal in time, by supplementing a compensated controller in the second-order robust exact differentiator, the tracking differentiator or the continuous hybrid differentiator, can be viewed as a set of differential algebraic equations (DAEs) to enhance a precise tracking of the given noisy signal. Thus, we are able ...

This paper studies the output tracking control of a class of sandwich-like systems with state-dependent deadzone nonlinearity between two cascaded subsystems (e.g., the gear transmission systems). An exact differentiator-based backstepping control for such a sandwich-like nonlinear system is proposed. The proposed controller utilizes the high-order sliding mode robust exact differentiator to co...

Using Tracking Differentiators in Designing Nonlinear Disturbance Observers for Uncertain SystemsNaser Kazemzadeh, Saeed BarghandanAbstractIn the present paper, a practical designing method has been proposed for a novel class of NDOs based on TD. Such NDOs can nearly estimate all uncertain disturbances (specifically disturbances without prediction information). Regarding the outstanding perform...

On convergence of tracking differentiator Bao-Zhu Guo and Zhi-Liang Zhao* Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, P.R. China; School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa; School of Mathematical Sciences, Shanxi University, Taiyuan 030006, P.R. China; Department of Mathematics, Univer...