This paper considers the problem of distributed control of dynamically coupled nonlinear systems that are subject to decoupled constraints. Examples of such systems include certain large scale process control systems, chains of coupled oscillators and supply chain management systems. Receding horizon control (RHC) is a method of choice in these venues as constraints can be explicitly accommodated. In addition, a distributed control approach is sought to enable the autonomy of the individual subsystems and reduce the computational burden of centralized implementations. In this paper, a distributed RHC algorithm is presented for dynamically coupled nonlinear systems that are subject to decoupled input constraints. By this algorithm, each subsystem computes its own control locally. Provided an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and asymptotic stabilization is established. The theoretical conditions for feasibility and stability are shown to be satisfied for a set of coupled Van der Pol oscillators that model a walking robot experiment. In simulations, distributed and centralized receding horizon controllers are employed for stabilization of the oscillators. The numerical experiments show that the controllers perform comparably, while the computational savings of the distributed implementation over the centralized implementation is clearly demonstrated.

Nanopores are a powerful tool for probing the structure of single molecules, such as a strand of DNA. Acquiring as much information from the output signal generated by a nanopore is essential and ultimately dependent on several factors: offline estimation of pore parameters must be based on a good model; the amplifier that produces the ionic current signal from the pore must be low noise; nanopore experiments must be designed intelligently to properly test hypotheses; and---most importantly---the pore must be the right size. This thesis discusses these topics in four chapters. Chapter 1 discusses the design and validation of a nanopore circuit model used for conductance estimation. Chapter 2 presents research results characterizing noise and signal resolution of a novel patch-clamp amplifier and its implications on next-generation nanopore platforms. Chapter 3 discusses preliminary research on modeling the motion of double-stranded DNA for future experiments with dual solid-state nanopores. Finally, chapter 4, is preliminary research performed with the solid-state nanopore and discussing various pore dimensions. Ultimately, the reader will be presented with research that covers the biochemical and computational ends of nanopore technology and how they are used to obtain as much information as possible from a single current output.

We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled nonseparably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation. (c) 2006 Elsevier Ltd. All rights reserved.

Nanopores are powerful tools for measuring and probing single molecules. A nanopore is a nanometer-sized opening in a membrane that separates two chambers filled with buffered ionic solution. By applying a voltage and measuring the ionic current through the nanopore, it is possible to detect the presence of individual DNA, RNA and proteins as they pass through the pore, and even read the sequence of individual nucleobases that make up a single strand of DNA. However, the speed with which molecules translocate and the size of the sensing region have presented challenges for using nanopores to sequence DNA. Most nanopore-based DNA sequencing research focuses on using biological nanopores paired with an enzyme to slow down the passage of DNA through the pore, but recent advances in solid-state fabrication technology have made it possible to create artificial solid-state nanopores in insulating membranes, typically made of silicon. These pores can be made in a larger range of sizes, are more durable, and are more amenable to large scale fabrication than their biological counterparts. In order to control the rate of molecular translocation through solid-state nanopores, researchers are developing a two-pore architecture, which utilizes time-varying voltage patterns to enable rereading of individual molecules to gain confidence in feature sensing. This thesis presents a numerical study that provides an error analysis of an idealized nanopore sequencing method in which ionic current measurements are used to sequence intact single-stranded DNA in the pore while an enzyme controls DNA motion. This analysis presents examples of systematic and random errors associated with this method of sequencing and demonstrates the necessity of rereading sequences at least 140 times to achieve 99.99% accuracy. Two different methods of parameter estimation are then presented that overcome the problem of contamination of the measured ionic current by capacitive elements in the system and facilitate active control with the two-pore architecture.