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This article presents a decentralized design of a distributed state observer for a continuous-time linear time-invariant plant. The plant is monitored by a group of agents and each agent's measurement of the plant's state suffers from lack of detectability with the plant dynamics. Then the missing information (i.e., the undetectable portion) is compensated by a local communication with the neighboring agents. In particular, when the local observer for each agent is designed, no global information such as the structure of network and the number of agents is needed, and so, the decentralized design is achieved. Therefore, the plug-and-play operation is enabled; that is, during the operation, a new agent can design a local observer for itself without any global information and join the network, and any agent may leave the network without hampering the operation as long as the rest of the agents remain detectable. The main idea is to let each agent recover its own detectable part while the undetectable part is compensated by a projection of the neighbors' estimates into the receiver's undetectable subspace. An adaptive algorithm for individual agent is designed in order to find suitable gains for compensating the undetectable portion. Simulation results confirm the effectiveness of the proposed design.
Kim et al. (Wed,) studied this question.