Adaptive decentralized control of interconnected systems

This paper presents a decentralized adaptive stabilization scheme for a class of interconnected systems using high-gain adaptive controllers. The nominal subsystems are assumed to satisfy some mild conditions required by standard adaptive control schemes, and the interconnections certain structural conditions. The decentralized controllers are high-gain dynamic systems operating on local outputs to generate local control inputs. Both continuous-time and sampled-data controllers are considered. The idea behind the design of continuous-time controllers is the small-gain theorem. The sampled-data controllers are discrete versions of the continuous-time controllers, where local sampling frequencies of the controllers also serve as their gains. The controllers are synchronized by a careful choice of their sampling frequencies. In order to guarantee closed-loop stability when the interconnection bounds are unknown, controller gains are increased, using simple centralized adaptation rule, to sufficiently high values as required by the strength of interconnections. The results are illustrated by a practical example.