New Adaptive Laws for Model Reference Adaptive Control Using Non-Quadratic Lyapunov Functions

摘要

In the design of model reference adaptive control (MRAC) schemes, adaptive laws have been developed based on Lyapunov stability theory. Over the past few decades, it has been a common practice to use Quadratic Lyapunov Functions (QLF). In contrast to such development, using a new Non-Quadratic Lyapunov Function (NQLF), this paper presents new adaptive laws for the MRAC. These new laws have the same advantage of assurance of stability of the overall system, as the earlier adaptive laws developed using the QLF. Over and above, they have an additional advantage of improved performance: in fact, the use of NQLF improved the system output error signal converging to zero. Finally, this paper also presents simulation results supporting the arguments.%Za projektiranje sustava adaptivnog upravljanja referentnim modelom (MRAC) razvijeni su adaptivni zakoni koji se zasnivaju na Ljapunovijevoj teoriji stabilnosti. U zadnjih se nekoliko desetljeća uobičajeno koristi kvadratna Lja-punovljeva funkcija (QLF). Suprotno tome, u ovome se radu zakoni upravljanja referentnim modelom izvode na osnovi nove nekvadratne Ljapunovljeve funkcije (NQLF). Za izvedene je nove zakone upravljanja cjelokupni sustav stabilan, kao i kod prijašnjih zakona adaptivnog upravljanja kvadratnom Ljapunovljevom funkcijom. Povrh toga predloženim novim zakonima upravljanja NQLF funkcijom poboljšava se konvergencija izlaznog signala pogreške prema nuli. Na kraju su u radu predstavljeni rezultati simulacija koji podupiru navedene tvrdnje.