Comparison of concurrent learning and derivative-free model reference adaptive control against parameter variation

Sarsılmaz, Selahattin Burak
For adaptive laws using only instantaneous data, it is well known that parameter convergence is impossible without persistency of excitation. Concurrent Learning Model Reference Adaptive Control (CL-MRAC) is a novel adaptive controller that solves the parameter convergence problem, about forty year old adaptive control problem, without requiring persistency of excitation. This solution relies on the concurrent usage of recorded and current data. Derivative-Free Model Reference Adaptive Control (DF-MRAC) is another novel adaptive controller that challenges the derivative-based adaptive laws and the integral action of them. Instead of constant ideal parameters assumption, DF-MRAC uses less strict assumption which allows time varying ideal parameters. Due to these contributions, both CL-MRAC and DF-MRAC deserve attention. This research mainly addresses their robustness to parameter variation. In this thesis, standard exponential stability theorem of CL-MRAC and uniform ultimate boundedness theorem of DF-MRAC with minor changes in their statements are proved. Some missing parts in these theorems are either filled or emphasized. To make a fair comparison between CL-MRAC and DF-MRAC, constant ideal parameters assumption imposed in CL-MRAC is replaced with time-varying ideal parameters assumption which is similar to the one in DF-MRAC but still stricter than it. Under this relaxed assumption, uniform ultimate boundedness of the solution of the closed-loop system is proved. According to this theorem, existing data recording algorithms are modified and the performances of CL-MRAC with modified algorithms are inspected under time-varying ideal parameters in a sample regulation and tracking problem. The simulation results show that the performance of CL-MRAC is dependent on problems and data recording algorithms. Wing rock problem with time-varying angle of attack is considered a useful benchmark for numerical illustration. Under high level uncertainty and random disturbance, controllers are tested and DF-MRAC performs better than CL-MRAC. Since DF-MRAC suppresses the uncertainty effectively and makes no attempt to learn it in the simulations, its performances with different basis functions are also tested. The simulation results present the excellent performance of DF-MRAC. Although it is shown that both CL-MRAC and DF-MRAC have bounded solutions under parameter variations, their adaptation strategies are completely different and the effect of this difference in the performance is obviously seen in the simulations.