Reduced-Order Observer for Dynamic Output Feedback of Variable-Structure Control Systems
by
Giorgio Bartolini
University of Cagliari - DIEE
Coauthors: Elisabetta Punta (National Research Council of Italy - ISSIA)

We consider nonlinear non-affine systems, for which the state vector is not completely available. These systems are characterized by a precise and known mathematical model and by a set of assumptions assuring the global injectivity of any required state transformation.

A possible approach is a generalization to nonlinear systems of the well known Luenberger observer for linear ones. The considered problem, which is non trivial even in the case of affine systems, has been dealt within the sliding mode context by the Authors.

In recent literature a common method for the class of systems transformable into the Brunowsky canonical form, is to estimate the unavailable states by means of sliding mode differentiators and high-gain observers; this strategy has been proven to be effective even in presence of large uncertainties in the mathematical model. In spite of this great advantage, the differentiation procedure results not to be reliable as the order of the involved output derivative increases, therefore the methodology appears not suitable for large scale systems.

The two approach feature different properties, which could be regarded, in some situations, as complementary.

The first method is differentiator free, but requires perfect modeling and additional constraints and conditions to be satisfied in order to fulfill both the the approximability property and the convergence of the estimation error; the second one suffers of the previously outlined accuracy problem when the output derivatives to be estimated is high.

The proposed strategy is a compromise between the two approaches aimed at building reduced-order observers using differentiators just to provide the necessary, otherwise unavailable, artificial outputs exploited to steer to zero a lower dimensional estimation error vector under an often simplified set of convergence conditions.

Date received: March 14, 2008