UC Berkeley

This dissertation is mainly focused on assimilation of data into hydrodynamic models of water flow in open channel networks which is motivated by the need for accurate flow models in various applications such as emergency response and flood monitoring systems, automated gate systems and hydrological studies. We investigate application of different data assimilation techniques in different scenarios to incorporate the available flow measurements obtained from sensors into flow models to improve their accuracy.

Water flow in open channels is an instance of the so-called distributed parameters systems in which the dynamics of the system is described by a set of partial differential equations. As the flow model, the Saint-Venant equations, also known as shallow water equations, which are a set of first-order hyperbolic nonlinear partial differential equations are used. Different practical scenarios are considered. In a case in which streaming measurements of the flow are available and real-time estimation of the flow state is desired, we present how standard state estimation techniques such the Kalman filter, the Extended Kalman filter and the Unscented Kalman filter can be applied to integrate the available measurements into the shallow water equations. It is also shown how these techniques can be adapted to a case in which some of the model parameters are unknown to estimate unkown parameters along with the state of the system.

For data assimilation in large-scale networks which lead to high dimensional models, application of two sequential Monte Carlo methods, the optimal sampling importance resampling and the implicit particle filters, is considered. The computational cost of propagating each particle is higher in implicit particle filters, however, they provide more accurate results with smaller number of particles by choosing the particles in a way that they belong to the high probability regions of the posterior density function. We also propose a maximum-a-posteriori-based method to perform the state estimation which is shown to perform better in terms of both accuracy and computational cost for the application of interest.

For flow estimation in tidally influenced channels, an efficient estimation method which takes advantage of spectral decomposition of the state is proposed. The estimation problem is formulated as a least squares regression with an $l_1$-norm regularization, known as the LASSO, and a homotopy-based algorithm is implemented to solve the resulting optimization problem recursively as new measurements become available.

Finally, we consider the problem of optimal topology design in multi-agent systems for efficient average consensus. The network design problem is posed in two different ways. (1) Assuming that the maximum communication cost, i.e. the maximum number of communication links, is known, the goal is to find the network topology which results in the fastest convergence to the consensus (in presence of communication time delays on the links). (2) If a minimum performance of the protocol is required, the design problem is posed as finding the network with lowest possible communication cost which fulfills the required performance. The design problem is formulated as an optimization problem which is finally transformed to a mixed integer semidefinite program.