Performance Improvement of Discrete MRAC by Dynamic and Memory Regressor Extension

The paper addresses the problem of performance improvement of direct model reference adaptive control (MRAC) of discrete linear time-invariant (LTI) plants. Two new solutions to the problem are proposed and use the idea of regressor recording together with the principle of augmented error. The recording is provided by means of special filters (linear operators with “memory”) and permits to accelerate the tuning of adjustable controller and, hence to accelerate the transients in the closed-loop system. The first solution is based on dynamical regression extension (DRE) of augmented error invoking its multiple filtering. The second solution is based on memory regressor extension (MRE) of time-varying state matrix $\omega\omega^{\top} (\omega$ is the vector of regressor) of parametric error model by applying one SISO filter. It is shown that adaptation algorithms motivated by DRE and MRE procedures offer potentially fast parametric convergence in comparison with standard gradient-based adaptation algorithm. Moreover, it is proved and demonstrated by examples that new adaptation algorithms provide asymptotic (not exponential) convergence not under persistent excitation (PE) condition, but under weaker, so called, net-in-$L_{1}$, condition. Theoretical results are illustrated via comparable simulation.