Quantum mechanics

Algorithm

Control (management)

Wireless sensor network

Engineering

Linear system

Network topology

Mathematical physics

Control engineering

Computer science

Distributed computing

Computer network

LTI system theory

Physics

Nonlinear system

State observer

Mathematics

Invariant (physics)

Mathematical analysis

Artificial intelligence

Observer (physics)

Combinatorics

Topology (electrical circuits)

Control theory (sociology)

State (computer science)

IEEE Transactions on Automatic Control

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of LTI systems, sensor network topologies, and sensor measurement structures. Our analysis builds upon the following key observation—a given node can reconstruct a portion of the state solely by using its own measurements and constructing appropriate Luenberger observers; hence, it only needs to exchange information with neighbors (via consensus dynamics) for estimating the portion of the state that is not locally detectable. This intuitive approach leads to a new class of distributed observers with several appealing features. Furthermore, by imposing additional constraints on the system dynamics and network topology, we show that it is possible to construct a simpler version of the proposed distributed observer that achieves the same objective while admitting a fully distributed design phase. Our general framework allows extensions to time-varying networks that result from communication losses, and scenarios including faults or attacks at the nodes.

Distributed Observers for LTI Systems