The relationship between individual tasks and the envisaged applications in this project is summarized in the following table. The project is organized around 4 tasks that foster the theoretical developments required to solve the problems in the four selected applications.

- State estimation for distributed stochastic networked systems. We will focus mainly on the problem of designing observers that can incorporate the stochastic information of the network, possible known moments or confidence intervals of the probability distributions of signals in the model to produce a confidence set estimates for the state. Applications of this stochastic estimation technique include: computing the reliability metrics of not losing a file in a network where nodes are entering and leaving; stochastic communications in Sensor networks; computing the probability of losing a file in a Peer-to-Peer network; or a driver selecting a route and changing the congestions load in a Traffic Network.
- Sensitivity analysis using set-valued observers. A novel approach for performing a sensitivity analysis will be developed using set-valued observers in order to assess how system parameters influence the performance of the network. In particular, how the selection of device communication range, switching-off policies, number of deployed sensors, concentration distribution, etc affects the Sensor Networks lifetime and performance. Sensitivity analysis also plays a key role in other network analysis problems, e.g. how to reduce the number of parameters in a given network model, by finding the relevant ones.
- State estimation for state-dependent dynamics. A study of how to include only the combinations of dynamics that abide to the state-dependent update rule in the state estimation tools will be conducted. The main challenge is to still be able to prove convergence of the estimates, for the cases where most of the tools available in the literature are not applicable. The application of this family of tools is manifold. However, within the scope of this project Traffic Networks constitute the main envisaged application for such techniques as each driver’s decision impacts on the probabilities of other drivers picking a different route.
- Distributed fault detection and isolation. We will build on existing results in order to further develop distributed fault detection and isolation mechanisms having guarantees dependent on characteristics of the system and limited number of false positives. Both in the field of Sensor Networks and Smart Grids, detecting and isolating faulty equipment is a vital task since not detecting and identifying prematurely faults can have a significant impact on the overall performance of the network, leading to high repairing and operational costs.

Artificial Intelligence and Autonomous Systems