Robust decentralized control of large-scale interconnected systems: general interconnections

A decentralized control scheme is developed for a large-scale interconnected nonlinear systems with uncertain but bounded nonlinear interconnections. The interconnections are assumed to be bounded by polynomial type nonlinearities in states. If the interconnections are bounded by a pth-order polynomial in states, then the proposed controller has terms involving pth-order or less. This is in sharp contrast to the existing literature, which use a (2p-1)th-order terms in the controller. We develop robust designs if the coefficients of the bounded polynomial are known, and adaptive designs if the coefficients are not known. We show global exponential convergence of the states for the robust case and global asymptotic convergence of the states for the adaptive case. First, we consider systems that satisfy matching conditions and then extend the designs for systems that do not satisfy matching conditions. We give several examples to illustrate the design methodology. Further, we show how our designs can be extended to interconnections that cannot be bounded by finite length polynomials