Model reference adaptive control algorithms for decentralized systems

This paper presents two decentralized direct model reference adaptive control (MRAC) algorithms for large-scale interconnected systems having multi-input and multi-output subsystems and subjected to known disturbances. The parameters of each subsystem are assumed to be unknown constants taking values in a known bounded range. These algorithms do not require identification of the system parameters or satisfaction of the perfect model-following conditions (PMFC). The output error and the controller parameters are guaranteed to be bounded using a weighted-sum scalar Lyapunov function. The first algorithm ensures asymptotic stability to a bounded residual set provided that the closed loop transfer matrices of all decoupled subsystems are strict positive real (SPR). The second algorithm relaxes this requirement at the expense of increasing the size of the residual set. Applications to a power system example are presented to demonstrate the effectiveness of the proposed algorithms.