In this study, a class of linear interconnected systems with unknown interconnections between subsystems is considered. Primarily, an observer is designed to reconstruct an equivalent of unknown interconnections that are considered uncertain. A decentralized controller will be thereafter designed to keep the stability of the original system when the estimated system is at risk of instability due to the lack of information on interconnections. To design a decentralized observer and to estimate states of each subsystem, without knowing the relations between subsystems, a combination of Luenberger observer along with the adaptive sliding mode technique is used. Because the interconnected system might generally be unstable, a state feedback controller is used to stabilize each subsystem using estimated states together with the output of other subsystems. The stability of the system and the convergence of the discrepancy between real states and that of estimated are guaranteed, gaining the Lyapunov theory. Simulation results signify that the proposed decentralized controller based on a new adaptive sliding mode observer is highly efficient for linear interconnected systems with unknown interconnections.
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.
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