Discontinuous homogeneous control

Abstract

Control under heavy uncertainty conditions remains among the main topics of the control theory. The sliding-mode control [50, 53, 10] is one of the main tools in the field. This approach is based on exactly keeping a properly chosen constraint by means of control switching of high (theoretically infinite) frequency. Although very robust and accurate, the approach has two basic restrictions. The direct implementation of standard sliding modes requires the relative degree of the constraint to be 1, i.e. control has to appear explicitly already in the first total time derivative of the constraint function. Also, high-frequency control switching may cause the so-called chattering effect [14, 15, 16, 33]. © 2008 Springer-Verlag Berlin Heidelberg.