طراحي رؤيتگر حالت توزيع شده براي سيستم‌هاي خطي داراي عدم قطعيت

In recent years, considerable attention has been paid to the problem of designing distributed observers for state estimation of linear time-invariant (LTI) systems, in which measurements are collected through a network of sensors. In the classical observer problem, the goal is to find a single observer that receives all measured outputs of the system in order to generate the state estimates. However, in the distributed framework, the objective is to design multiple local observers that can communicate with each other through a predefined network graph. Each local observer in the network receives not only a portion of the system’s measured outputs but also the state estimates from its neighboring observers. Using this information, along with a consensus term in its dynamics, each observer can updat‎e its own estimates an‎d eventually reconstruct the complete system state. Therefore, the problem of finding a distributed observer can be interpreted as designing a single composite observer that consists of multiple interconnected local observers. In most practical control systems, uncertainties, parameter perturbations, an‎d external disturbances are inevitable. Hence, designing distributed observers that are robust against these factors remains a significant challenge. This thesis proposes a robust distributed observer design for uncertain systems, in which some unknown, unstructured, but bounded uncertainties exist in the system matrices, as well as external disturbances in the system dynamics. It is shown that if the LTI system is observable an‎d the communication graph is fully connected, global state convergence can be achieved. In the proposed distributed observer, to mitigate the effect of uncertainties in the system matrices, a new term is introduced into the observer dynamics, providing robust performance against these uncertainties. Then, by analyzing the observer error dynamics using a proposed Lyapunov function, a set of Linear Matrix Inequalities (LMIs) is derived, from which the gains of the robust distributed observer are obtained. Furthermore, to cope with the influence of external disturbances in the system dynamics without the presence of uncertainty, an extended distributed observer is developed. This observer not only estimates the system states at each node but also treats the disturbance as an additional state an‎d estimates it as well. Similar to the previous observer, by analyzing the error dynamics through the proposed Lyapunov function, the gains of this extended distributed observer are also designed. Finally, simulation results are presented to demonstrate the effectiveness of both proposed distributed observers in han‎dling system matrix uncertainties an‎d external disturbances.

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