ABSTRACT
This chapter introduces the Massachusetts Institute of Technology (MIT) rule, which is an important early landmark in the design of model reference adaptive control (MRAC) systems and discusses the robust Lyapunov approach, which ensures both adaptation and stability. It deals with the hyperstability approach, which includes a comparison between Lyapunov and hyperstability methods. Hyperstability concepts are applied to the MRAC system by recasting it as a "standard" system with a linear time-invariant operator in the forward path and a passive operator in the feedback path. The chapter outlines R. V. Monopoli's augmented error approach, which is conceptually a novel idea and which led to other important techniques such as K. S. Narendra's error model approach. It also deals with some aspects of multivariable MRAC systems and addresses the important problems of stability and convergence considerations. The global stability of MRAC systems had remained a difficult question since adaptive control systems belong basically a special class of nonlinear time-varying systems.
