An adaptive variable structure control for fast time-varying unknown plants

In this paper, a combination of adaptive control and variable structure control methodology is proposed to solve the general fast time-varying plants with totally unstructured parameters. We show that the control scheme will work only under the assumptions of known order, relative degree, high frequency gain sign and minimum-phase property. In contrast to the conventional approaches where the variable structure design is applied mainly to the adaptation of some traditional parameters Θ by using the knowledge of unknown bounds on control parameters, a new adaptation scheme for control parameters incorporating the variable structure concept is given. Owing to this new scheme, we forsake the standard requirement of the upper bounds on some unknown parameters, which is frequently adopted in the field of robust linear MRAC using variable structure design. It is shown that without any persistent excitation, the tracking error will converge to zero in finite time for relative degree one plants and to a small residual set exponentially (whose size depends on a design parameter) for plants with any higher relative degree