Switching structure state and parameter estimator for MIMO non-linear robust control

In this paper the problem of simultaneous robust state and parameter estima tion for a class of MIMO non-linear systems under mixed uncertainties (unmo delled dynamics as well as observation noises) it tackled. A switching gain robust 'observer-identifier' is introduced to obtain the c orresponding estimates. This is achieved by applying an observer to the so- called nominal extended system, obtained from the original system without a ny uncertainties and considering the parameters as additional constant stat es. As it is shown, in general the extended system can lose the global obse rvability property, supposed by valid for the original non-extended system, and a special procedure is needed to provide a good estimation process in this situation. The suggested adaptive observer has the Luenberger type obs erver structure with switching matrix gain that guarantees a good enough up per bound for the identification error performance index. The Van der Monde generalized transformation is introduced to derive this bound which turns out to be 'tight' (it is equal to zero in the absence of both noises and un modelled dynamics). The example dealing with an inverted pendulum illustrat es the high effectiveness of the suggested approach.