Large-scale distributed state estimation: theory, methodology and algorithm

Abstract

In this thesis, the topics of state estimation for large-scale systems (LSSs) with distributed observer design are studied using notions and tools from classical control theory and graph theory. Over the last few decades, there has been a remarkable growth of LSSs which are essential to people’s daily lives, such as smart power grids, water networks, industrial plants, etc. However, these systems are susceptible to faults or attacks, and it is crucial to monitor the status of such systems by estimating the state vector. Due to the vast space that a typical LSS occupies, measurements for such systems are usually distributed over the entire system plant. Our objective is to design a network of observers such that the state vector of the entire system can be estimated, while each observer (node) has access to only local output measurement that may not be sufficient on its own to reconstruct the whole system state. Moreover, we address several categories of faults and disturbances at LSSs and their observers, and the devised distributed estimation schemes are desired to be robust accordingly. Firstly, we consider a scenario that the links among the distributed observers may fail and rebuild over time, which implies that the communication network does not stay connected constantly. We propose a distributed estimation approach with a guarantee on the feasibility of the design such that the state vector of the system is reconstructed by each observer. Then, we assume that the local observer at each node may not be accessible to all input signals, which could be caused by an unknown input fault or disturbance. We propose a distributed observer capable of estimating the overall system’s state in the presence of input, while each node only has some information on input and its local measurements. We provide a design method that guarantees the convergence of the estimation errors under some mild joint detectability conditions, which is also proved to be necessary to obtain asymptotic estimates. After that, we focus on the distributed state estimation with additive fault and noise at the measurements. We assume that local sensor redundancy exists at each node and propose a distributed estimation strategy that exploits this redundancy to provide robustness against faults in the measurement. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of unbounded sensor faults on the state estimation. Finally, we build a simplified heat exchange model to verify the effectiveness of all of the proposed distributed state estimation methods.