ABSTRACT
This chapter deals with robust Lyapunov design of discrete-time model reference adaptive control (MRAC) and discusses the hyperstability approach. In some cases, Lyapunov design becomes identical to the Massachusetts Institute of Technology rule design, indirectly establishing the fact that a performance index of ISE type is implicitly considered in such Lyapunov designs. The chapter considers the augmented error approach and also discusses unified approaches, also showing the relation to other adaptation algorithms including selftuning algorithms. The augmented error concept circumvents the problems related to system delay and to the inherent one-step delay existing in discrete-time MRAC systems. The chapter also considers multivariable systems and describes that the development of hybrid adaptive control in which discrete-time adaptive control is proposed for continuous-time systems. It offers the proof of the global stability of a hybrid adaptive control system and in the fact that the same algorithms when suitably modified are known to be applicable to both discreteand continuous-time systems with two time scales.
