Adaptive control of a large-scale system

The authors present two direct model reference adaptive control (MRAC) algorithms for a class of large-scale interconnected systems that have multi-input, multi-output subsystems and are subjected to a known disturbance. The parameters of each subsystem are assumed to be unknown constants or unknown time-varying in a known bounded range. These algorithms do not require identification of system parameters or satisfaction of the perfect model-following conditions. The output error and the controller parameters are guaranteed to be bounded using a Lyapunov stability theorem. The first algorithm ensures asymptotic stability to a bounded residual set provided that the decoupled subsystem transfer matrix is strict positive real (SPR). The second algorithm relaxes the requirement of the SPR condition at the expense of increasing the size of the residual set. Illustrative examples are presented.