Analysis and design of I/O based variable structure adaptive control

This paper presents an overview of a technique for the design of variable structure model reference adaptive control (VS-MRAC) systems, using only input-output data. The main ideas underlying the design and the analysis, as well as the main properties of the controller, are described having as point of departure a well known parameter adaptive MRAC scheme. Then, asymptotic properties of the VS-MRAC system are established taking into account the effect of the averaging filters necessary to implement some equivalent control signals. In particular, global exponential stability of the associated error system with respect to a small residual set is demonstrated. The effect of linear zones in the relay functions is assessed showing that they can alleviate the chattering phenomena. This is related with the fact that the VS-MRAC has a high-gain stability property. A procedure for noise sensitivity reduction is also proposed. Simulations illustrate the very satisfactory performance of the VS-MRAC in adverse operating conditions