Dead-beat Identification for Model Reference Adaptive Control⋆

In this work, we propose a novel parameter identifier for linear time-invariant systems, which has the fastest possible convergence in principal (i.e., dead-beat). The identifier applies where states and derivatives of states can be measured. The identifier is applied to the certainty-equivalence (indirect) model reference adaptive control that relaxes the conventional assumptions about open-loop stability and persistent excitation in MRAC. Furthermore, in conventional MRAC the parameter convergence rate is proportional to the tracking error, whereas our proposed adaptation law has dead-beat dynamics. This method is previously applied to a Delta robot. In this paper, we present a theoretical analysis of the method by solving the identifier dynamics to get its closed-form solution and examine the effect of perturbations such as white additive noise, uncertainty, and disturbance. The linearized model of an actuated inverted pendulum with unknown parameters is used as a benchmark example.