Section: New Results

Sliding mode control estimation

Participants : Jean-Pierre Barbot, Wilfrid Perruquetti, Denis Efimov, Thierry Floquet.

Sliding mode algorithms are very popular for finite-time estimation and regulation. The recent results obtained by the group are as follows:

• The issues of a higher order sliding mode controller realization under actuator saturation and quantization have been analysed in [37] . The zig-zag solutions are introduced and analysed.

• The problem of design of interval observers for linear-parameter-varying systems, containing non detectable or non strongly observable parts, is addressed in [18] , [63] , [62] applying the higher order sliding mode algorithms. Application of sliding mode observers leads to accuracy improvement in the system.

• In [32] an anomaly signal detection in communication networks is studied by control theory techniques. Several classes of sliding mode observers are proposed for a fluid flow model of the transmission control protocol (TCP)/internet protocol network. Comparative simulations via network simulator NS-2 show the enhancement brought by a higher order sliding mode observer. The efficiency of this observer opens the way toward observing traffics with real TCP flow characteristics.

• In [80] , [42] , [41] the problem of continuous and discrete state estimation for a class of linear switched systems is studied. The class of systems under study can contain non-minimum phase zeros in some of their "operating modes". The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state-space is decomposed into the strongly observable part, the nonstrongly observable part and the unobservable part, to analyze the effect of the unknown inputs. A state observer based on high-order sliding-mode and Luenberger-like observers is proposed. For the case when the exact reconstruction of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. In [41] this technique has been applied to fault detection in switched systems.

• The paper [55] aims, firstly to highlight the possibility of recovering a message included in a chaotic continuous time delay system, secondly to show that it is possible to use the third order sliding mode in order to recover directly all the states and the unknown input (message), thirdly to illustrate the robustness of the proposed observer with respect to a noisy signal. This work is based on the concept of left invertibility and recent advances in sliding mode observers.

• The problem of estimation of discrete and continuous states for switched systems applying higher order sliding mode observers and projection is investigated in the papers [68] , [67] .