Reduced-Order Observer for Sliding Mode Control of Nonlinear Non-Affine Systems

In this paper nonlinear non-affine systems, for which the state vector is not completely available, are considered. It is assumed that the system's mathematical model is perfectly known and conditions hold, which assure the global injectivity of any required state transformation. The methodology aims at reducing chattering while ruling out possible ambiguous behaviors and considers an augmented state (the state and its first time derivative) and a new control, which is the time derivative of the original one. The proposed procedure combines sliding mode controller/observer and Luenberger like observer. The designed reduced-order observer relies on second order sliding mode differentiators just to provide the necessary, otherwise unavailable, artificial outputs exploited to steer to zero a lower dimensional estimation error vector under a simplified set of convergence conditions.