Transient performance improvement in model reference adaptive control via iterative learning

In this paper, we propose an iterative control strategy for the transient performance improvement of model reference adaptive control (MRAC) for continuous-time single-input single-output (SISO) linear time-invariant (LTI) systems with unknown parameters. The transient improvement is achieved through the introduction of a supplementary discrete-type parametric adaptation law along the iteration-axis, which is obtained in a straightforward manner from the continuous-time parametric adaptation law used in the MRAC scheme. This approach is referred to as the iterative model reference adaptive control (IMRAC). Initially, a standard MRAC scheme is applied to the system under consideration. Thereafter, the parameters are updated iteratively in order to enhance the tracking performance from iteration to iteration. In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time-interval, when the number of iterations tends to infinity. In the general case, i.e., systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. Simulation results are also carried out to support the theoretical development.