Adaptive Observer-Based Decentralized Sliding Mode Control for Connected Systems in the Presence of Unknown Interconnection and Bounded Disturbance

Abstract

In this manuscript, the control problem for a class of connected systems with unknown interconnections in the presence of distributed disturbance is studied. For this purpose, an adaptive observer-based decentralized sliding mode controller is proposed to provide the stability of the closed-loop system. In this approach, the connection matrix between subsystems is also assumed unknown, and therefore the dependency to the knowledge of connections is reduced. Due to the lack of availability of most states, a combination of the Luenberger observer and the sliding mode controller is proposed. The observer is to estimate the unmeasurable states, observing the disturbance effects, and thereby facilitating determination of the control law in an adaptive scheme. Furthermore, the effects of unknown interconnections between subsystems are estimated using adaptive laws, to find equivalent of interconnections among subsystems. To control and stabilize the overall system, a decentralized sliding mode controller is designed to stabilize the original system using the estimated disturbance and states. To analyze the stability, based on the proposed observer, direct method of Lyapunov is proposed together with the LMI technique. The stability of system and convergence of the estimation error of each subsystem to zero is guaranteed. The observer-based method is finally applied into two numerical examples to verify the significance of the proposed approach.