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Section: New Results
Applications
Participants : Jean-Pierre Richard, Jean-Pierre Barbot, Mamadou Mboup, Gang Zheng, Denis Efimov, Wilfrid Perruquetti, Olivier Gibaru, Samer Riachy.
As it was mentioned, Non-A is a kind of "method-driven" project, which deals with different aspects of finite-time estimation and control. Thus different applications are possible, ones touched this year are as follows:
The global stabilization of a ball & beam through saturated control, which imposes restrictions on the reactivity of the closed loop, is studied in [91] , [81] . A modified design for the classical ball & beam system is presented. The beam is driven by two actuators. In comparison to the classical system, this design offers an additional degree of freedom, which is the vertical motion of the beam. We show that the new design offers the possibility to get rid of the closed loop low reactivity restriction. Two nonlinear controllers to steer the trajectories of the system towards a final desired position are proposed.
In papers [48] , [49] a new class of power converters is studied (Parallel Multicell Chopper). The topology of these chopper is based on a combination of n switching cells interconnected via independent inductors. This type of choppers is a new DC/DC static power converter which has an output current equals to n times the source current where n is the number of cells . After recalling the dynamical equations of the converter, its hybrid dynamical behavior and properties are highlighted. This particular hybrid system induces new and difficult control problems, such problem can be tackled by a new control concept based on Petri net.
The paper [69] addresses the problem of power management of a hydrogen fuel cell system combined with super capacitors under high load variations in an electric vehicle. The singular perturbation theory is used for the control and coordination of two converters. The Lyapunov theory is used for analysis.
Combined feedforward/feedback control algorithm for highly nonlinear systems was proposed on the basis of the approximating hybrid model in [28] . The designed MIMO controller enables simultaneous control of the air-to-fuel ratio and torque for injector automobile engines. The theoretical results were validated experimentally with physical cars.
A spike sorting method for multi-channel recordings is proposed in [35] . The proposed method uses an iterative application of Independent Component Analysis (ICA) algorithm and a deflation technique in two nested loops. The results suggest that the proposed solution significantly improves the performance of ICA in spike sorting.
In the paper [83] an algorithm for a particular change-point detection problem is proposed, where the frequency band of the signal changes at some points in the time axis. Apart from detecting the change-points, the proposed algorithm is also able to estimate the frequency bands. The main idea of the algorithm is to consider a simple local bandlimited model to represent the input signal in each sliding time window.
The papers [60] , [58] , [59] present a new sensorless parameter identification method for permanent magnet stepper motors. Current sensors are assumed available, but position and velocity sensors are not. Data is obtained with open-loop voltage commands at multiple speeds. A new reference frame is proposed that presents advantages similar to the standard frame, but without the need for a position sensor. The method exploits carefully derived linear parameterizations and a least-squares algorithm. In one case, overparameterization is resolved using elimination theory. Overall, the parameters identified using the new procedure are found to be very close to those obtained with position sensors. The approach is potentially applicable to other types of synchronous motors as well.
In the paper [78] , an improvement of the dynamic accuracy of a flexible robot joint is addressed. Based on the observation of the measured axis deformation, a simplified elastic joint model is deduced. In the first step, the non-linear model component's is analyzed and identified in the cases of the gravity bias and the friction term. In the second step, a non asymptotically algebraic fast identification of the oscillatory behavior of the robot axis is introduced. Finally, the performances of the identification approach are exploited in order to improve the dynamic accuracy of a flexible robot axis. This is done experimentally by the combination of the adaptation of the jerk time profile to reduce the end-point vibration and the model-based precompensation of the end-point tracking error.
Localizability of unicycle mobiles robots is analysed in [82] from an algebraic point of view. A sensibility study leads to a new fusion algorithm in the multi landmark case using as a basis the posture differentiation based estimator.
The problem of early detection of oscillatory failures for aircrafts is addressed in [38] . The proposed solution is based on a finite-time sliding-mode differentiator and a hybrid optimization scheme.
The control design under time-varying delays and uncertainties, which ensures the stability and performance (synchronization/transparency) between the master and slave manipulators, is proposed in [46] , [44] , [45] . The design of the controller based on a proposed control scheme, which is performed by using LMI optimization based on Lyapunov-Krasovskii functionals and control theory.