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.

Decentralized observer‐based integral sliding mode control design of large‐scale interconnected systems and its application to doubly fed induction generator‐based wind farm model

“…Here, various types of observers are proposed, such as output feedback, sampled‐data, and event‐triggered feedback based observers for the estimation of system states. As an example, the authors in References 34 and 35 have designed sliding mode observer‐based decentralized control for linear interconnected systems in the presence of unknown interconnected and bounded disturbance based on combination of the Luenberger observer and the sliding mode controller. Besides that, the stability conditions have been derived based on the direct method of Lyapunov.…”

Unknown Input Observer-Based Decentralized PID- BFO Algorithm for Interconnected Systems Against Fault Actuator

“…Various control schemes such as decentralized, centralized, and distributed controls have been adopted for such systems [3]. Generally, exchanging information between subsystems is a significant challenge in controller design for large-scale systems [4]. Such a challenge attracts researchers to decentralized control to avoid information exchange between subsystems, making the controller more straightforward to design.…”

Decentralized adaptive terminal sliding mode control design for nonlinear connected system in the presence of external disturbance

“…The order of the control system is reduced to cope with external disturbances and uncertainties. [11][12][13] Despite of the advantages of the sliding mode technique, the chattering phenomenon, as a real challenge in physical applications, 14 degrades performance of the control system. 15 Indeed, the chattering is the high-frequency oscillations that sometimes make the system unstable.…”