Decentralized adaptive control of interconnected systems

The adaptive control of a class of large-scale systems formed of an arbitrary interconnection of subsystems with unknown parameters, nonlinearities, and bounded disturbances is investigated. It is first shown that no matter how weak the interconnections are, a decentralized adaptive control scheme can become unstable. Approaches are then developed for stabilization and tracking using new decentralized adaptive controllers. In the case where the relative degree
n^{*}
of the transfer function of each decoupled subsystem is less than or equal to two, sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets. In the absence of disturbances and interconnections, the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero. The effectiveness of the proposed adaptive schemes is demonstrated using a simple example.