Decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections

The problem of decentralized control is considered for a class of time-varying large scale systems with uncertainties and external disturbances in the interconnections. In this paper, the upper bounds of the uncertainties and external disturbances are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of the updated values of these unknown bounds, a class of decentralized linear and non-linear state feedback controllers are constructed. It is shown that by employing the proposed decentralized non-linear state feedback controllers, the solutions of the resulting adaptive closed-loop large scale system can be guaranteed to be uniformly bounded, and the states are uniformly asymptotically stable. By using the decentralized linear state feedback controllers, one can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large scale system. Finally, a numerical example is given to demonstrate the validity of the results.