ITS Berkeley

Bacteria such as Rhodobacter sphaeroides use a single flagellum for propulsion and change of orientation. Simple organisms such as this have inspired nanorobotic designs with potential applications in medicine which motivates the present work. In this article, an elastic model for a single flagellum bacterium is presented and followed by an analysis of the system based on optimization. The model is based on the method of Regularized Stokeslet which allows for a discretization of the system into particles which are connected by spring forces. An optimal elasticity distribution that...

A robust control problem for distant downstream control of a reservoir-canal system modeled by Saint-Venant equations is investigated. The problem is to regulate the release of water at the upstream end such that the measured water level (or stage) at the downstream end does not deviate outside of prescribed bounds under the effect of downstream perturbations. Under the assumption of small perturbations, the Saint-Venant model is linearized around a steady state flow. The resulting linear model is discretized to obtain a linear state-space model using a method of characteristics based...

A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a spatially dependent transfer matrix relating the input variables to the output variables is obtained. It is shown that by considering a finite number of dominant oscillatory modes of the input, an...

We investigate a class of hybrid systems driven by partial differential equations for which the infinite dimensional state can switch in time and in space at the same time. We consider a particular class of such problems (switched Hamilton-Jacobi equations) and define hybrid components as building blocks of hybrid solutions to such problems, using viability theory. We derive sufficient conditions for well-posedness of such problems, and use a generalized Lax-Hopf formula to compute these solutions. We illustrate the results with three examples: the computation of the hybrid components of a...