Binary MIMO MRAC using a passifying multiplier — A smooth transition to sliding mode control

Binary Model Reference Adaptive Control (B-MRAC) combines the advantages of Parameter Adaptive Control with those of Variable Structure Control. It was originally proposed for SISO systems. In this paper, a MIMO version of the B-MRAC is proposed for minimum phase uncertain linear plants with uniform relative degree one. In order to guarantee global stability properties, a passifying multiplier is designed so that the recently introduced generalized passivity condition called WASPR is achieved. This allows it to be applicable without the symmetry assumption on the plant uncertain high frequency gain matrix. The B-MRAC is shown to tend to the unit vector control as the adaptation gain increases to infinity. The benefits of the passifying multiplier are assessed in this transition from adaptive to sliding mode control.