This work is devoted to the nonasymptotic and robust fractional derivative estimation of the pseudo-state for a class of fractional-order nonlinear systems with partial unknown terms in noisy environments. In particular, the estimation for the pseudo-state can be obtained by setting the fractional derivative's order to zero. For this purpose, the fractional derivative estimation of the pseudo-state is achieved by estimating both the initial values and the fractional derivatives of the output, thanks to the additive index law of fractional derivatives. The corresponding algorithms are established in terms of integrals by employing the classical and generalized modulating functions methods. Meanwhile, the unknown part is fitted via an innovative sliding window strategy. Moreover, error analysis in discrete noisy cases is discussed. Finally, two numerical examples are presented to verify the correctness of the theoretical results and the noise reduction efficiency.

This paper presents the sliding mode event-triggered control to solve the trajectory tracking problem of robot manipulator systems under state constraints. Through the design of time-varying control gains, a Lyapunov function ensures the fulfilment of the state constraints despite external disturbances. The designed sliding mode event-triggered control ensures that the sliding variable reaches the vicinity of the sliding surface in the finite-time. Furthermore, the proposed method ensures the uniform ultimate boundedness of the tracking error. There is no accumulation of inter-event time, which provides Zeno-free study. Simulation results of two-link robotic manipulator demonstrate the effectiveness of the proposed theory.

Conventional active incremental structure from motion (ISfM) schemes require a precise knowledge of the linear and angular velocities of the vision system to compute the three-dimensional structure of the observed scene. Furthermore, they are generally coupled and nonlinear, which makes the reconstruction inaccurate. In this paper, we present a novel active ISfM scheme to overcome these difficulties. It relies on two appropriate transformations: the first one allows efficient decoupling of the nonlinear model, whereas the second one transforms the decoupled model into the Brunovsky's linear form. We then show that a Luenberger's observer can be designed to estimate the unavailable states, making our scheme globally asymptotically convergent and robust to noise on measurements. We present simulated and experimental results to illustrate the performance of the described methodology.

In this paper we presents two new 0-flat normal forms. It deals with sufficient geometrical conditions which enable us to conclude if a given nonlinear controllable dynamical system can be transformed, by means of change of coordinates, to one of these normal forms. In the same way it gives an algorithm to compute the flat outputs. As an illustration to the proposed approach, a trajectory tracking of a planar manipulator robot is simulated. The results obtained are very satisfactory proving the applicability of the method.