Multivariable Binary MRAC with Guaranteed Transient Performance Using Non-homogeneous Robust Exact Differentiators

In this paper, we propose an extension of the binary model reference adaptive control (BMRAC) for uncertain multivariable linear plants with non-uniform arbitrary relative degree. The BMRAC is a robust adaptive strategy which has good transient properties and robustness of sliding mode control with the important advantage of having a continuous control signal free of chattering. The relative degree obstacle is circumvented using a multivariable version of a hybrid estimation scheme, named global robust exact differentiator (GRED). The hybrid estimator switches between robust exact differentiators (RED) based on higher-order sliding modes and lead filters in a way that the exact derivatives are globally obtained in finite time. To improve the robustness and the transient performance of the GRED, we propose a modification of the switching scheme replacing the conventional RED with a non-homogeneous one. Global exact output tracking is obtained with robustness and guaranteed transient performance without requiring stringent symmetry assumptions on the plant high-frequency-gain matrix.