Distributed observers for LTI systemsan approach based on subspace decomposition

Resumen

When considering large-scale plants, such as factories, water irrigation channels or solar fields, the problem of state estimation is more difficult to solve than in small-scale systems. It should be noted that information from these systems is frequently collected by many individual agents widespread across geographically remote locations, which complicates estimators' designs. Furthermore, these agents are required to communicate with others to achieve system-wide goals, triggering problems derived from the network topology and communication drawbacks such as delays, quantization, limited bandwidth, etc. This thesis aims to provide new solutions for the problem of distributed estimation of the state of a linear time-invariant (LTI) plant with a network of agents. To achieve this goal, several novel structures for agent-based estimators are presented, based on an orthogonal decomposition of the local observable/unobservable subspaces of each agent. First, a novel observer is introduced based on a structure that incorporates consensus among the agents and that can be designed in a distributed fashion, achieving a robust solution with good estimation performance. Furthermore, the structure includes the ability to set the convergence rate of the estimator arbitrarily. Concerning perturbed models, an LQ-based design method for the observer structure is presented, stating stability and optimality conditions and showing in simulation the performance of the algorithm for the unperturbed and perturbed scenarios. The design method presented allows the user, through the use of one scalar parameter, to modify the observer according to their experience with the plant. Finally, a second observer structure is presented based on the same principle of subspace decomposition, but this time, the scenario is a little different. Each of the agents involved in the network must perform real-time monitoring of the plant's state, counting on local measurements of the state taken by the agents and measurements taken by the rest of the network. This interagent communication takes place within a multihop network. Therefore, the transmitted information suffers delay depending on the position of the sender and receiver in a communication graph. A novel data-fusion-based observer structure is presented, and two main subproblems are addressed: the observer design for stabilizing the estimation error and an optimal observer design to minimize the estimation uncertainties when plant disturbances and measurement noise come into play. All contributions of this thesis are theoretical in nature. However, the solutions adopted could be applied to a wide variety of distributed systems.