Saman Behtash

Robust output tracking for non-linear systems

The problem of output tracking for a single-input single-output non-linear system in the presence of uncertainties is studied. The notions relative degree and minimum-phase for non-linear systems are reviewed. Given a bounded desired tracking signal with bounded derivatives, a control law is designed for minimum-phase non-linear systems which results in tracking of this signal by the output. This control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors. Two types of uncertainties are considered: those satisfying a generalized matching condition but otherwise unstructured, and linear parametric uncertainties. It is shown that for systems with the first type of uncertainty, high-gain control laws can result in small tracking errors of O(∊), where e is a small design parameter. An alternative scheme based on variable structure control strategy is shown to yield zero tracking errors. Adaptive control te...

Balanced realizations of singularly perturbed systems

Abstract Balanced realizations of linear time-invariant singularly perturbed systems are studied. The reduced model of a singularly perturbed system that is obtained, based on the balanced realization, is compared to that obtained by time-scale considerations. An approximate balancing transformation for singularly perturbed systems is constructed based on balancing transformations of the approximating slow and fast subsystems.