Single particle tracking has become a ubiquitous class of tools in the study of biology at the molecular level. While the broad adoption of these techniques has yielded significant advances, it has also revealed the limitations of the methods. Most notable among these is that traditional single particle tracking is limited to imaging the particle at low temporal resolutions and small axial ranges. This restricts applications to slow processes confined to a plane. Biological processes in the cell, however, happen at multiple time scales and length scales. Real-time feedback-driven single particle tracking microscopes have emerged as one group of methods that can overcome these limitations. However, the development of these techniques has been ad-hoc and their performance has not been consistently analyzed in a way that enables comparisons across techniques, leading to incremental improvements on existing sets of tools, with no sense of fit or optimality with respect to SPT experimental requirements. This thesis addresses these challenges through three key questions : 1) What performance metrics are necessary to compare different techniques, allowing for easy selection of the method that best fits a particular application? 2) What is a procedure to design single particle tracking microscopes for the best performance?, and 3) How does one controllably and repeatably experimentally test single particle tracking performance on specific microscopes?. These questions are tackled in four thrusts: 1) a comprehensive review of real-time feedback-driven single particle tracking spectroscopy, 2) the creation of an optimization framework using Fisher information, 3) the design of a real-time feedback-driven single particle tracking microscope utilizing extremum seeking control, and 4) the development of synthetic motion, a protocol that provides biologically relevant known ground-truth particle motion to test single particle tracking microscopes and data analysis algorithms. The comprehensive review yields a unified view of single particle tracking microscopes and highlights two clear challenges, the photon budget and the control temporal budget, that work to limit the two key performance metrics, tracking duration and Fisher information. Fisher information provides a common framework to understand the elements of real-time feedback-driven single particle tracking microscopes, and the corresponding information optimization framework is a method to optimally design these microscopes towards an experimental aim. The thesis then expands an existing tracking algorithm to handle multiple particles through a multi-layer control architecture, and introduces REACTMIN, a new approach that reactively scans a minimum of light to overcome both the photon budget and the control temporal budget. This enables tracking durations up to hours, position localization down to a few nanometers, with temporal resolutions greater than 1 kHz. Finally, synthetic motion provides a repeatable and programmable method to test single particle tracking microscopes and algorithms with a known ground truth experiment. The performance of this method is analyzed in the presence of common actuator limitations. / 2024-01-16T00:00:00Z

<p> The dual configuration is innovated as a new approach in sensitivity reduction. Three types of sensitivity due to variations in plant parameters are discussed. It has been shown that cost insensitive and terminal insensitive designs are indeed achievable by applying the dual configuration to implement the optimal control. </p> <p> The theory has been developed for a general class of optimal systems and the linear systems with quadratic cost functionals have been analytically evaluated to illustrate the theory. </p> / Thesis / Master of Engineering (ME)

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The goal of an optimal control algorithm is to improve the performance of a system. For a stochastic system, a typical optimal control method minimizes the mean (first cumulant) of the cost function. However, there are other statistical properties of the cost function, such as variance (second cumulant) and skewness (third cumulant), which will affect the system performance. In this dissertation, the work on the statistical optimal control are presented, which extends the traditional optimal control method using cost cumulants to shape the system performance. Statistical optimal control will allow more design freedom to achieve better performance. The solutions of statistical control involve solving partial differential equations known as Hamilton-Jacobi-Bellman equation. A numerical method based on neural networks is employed to find the solutions of the Hamilton-Jacobi-Bellman partial differential equation. Furthermore, a complex problem such as multiple satellite control, has both continuous and discrete dynamics. Thus, a hierarchical hybrid architecture is developed in this dissertation where the discrete event system is applied to discrete dynamics, and the statistical control is applied to continuous dynamics. Then, the application of a multiple satellite navigation system is analyzed using the hierarchical hybrid architecture. Through this dissertation, it is shown that statistical control theory is a flexible optimal control method which improves the performance; and hierarchical hybrid architecture allows control and navigation of a complex system which contains continuous and discrete dynamics. / Electrical and Computer Engineering

In motorsport, simulating road vehicles driving at the limit of handling is a valuable tool to study and optimize their overall performance during the design and set-up phases. Along with Quasi-Steady-State optimization, optimal control (OC) is the most utilized technique to simulate the control and states of a vehicle during minimum-time maneuvers and has been used for offline lap-time optimization for more than twenty years now. Since the first applications of optimal control in this field, it has been clear that the solution of the minimum-time optimization does not represent a model of the human driver but instead substitutes him/her. However, the common points or divergences between the minimum-time strategy of human race drivers and the OC one are still unclear. Moreover, it seems that in the literature there is no agreement about what vehicle models must be used, and in general the choice of one model or the other is not clearly justified. Finally, thanks to the rise in popularity of autonomous driving and racing, optimal control has been used as path planner for automated vehicles: %nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are directly fed to the vehicle, is still an unexplored topic. nonetheless, the application of free-trajectory real-time nonlinear optimal control in Model Predictive Control (MPC) schemes, where the optimal controls are computed from a single optimization and directly fed to the vehicle, is a topic still open for exploration. The first aim of this thesis is to provide an objective comparison of several vehicle, tire, powertrain and road models to be used in minimum-time OC. In the first part of this work we thus detail several models of the vehicle and its subsystems. We then solve minimum-time OC problems on a series of test tracks adopting most of the model combinations and discuss the differences in the solutions. We then draw conclusions on the best model combinations to obtain realistic and reliable minimum-time maneuvers. The second part of the thesis aims to prove that the solutions of minimum-time OC problems are indeed different from the driving behavior of professional drivers, but they can be employed to coach the human driver and improve his/her racing performance. After modeling a high-performance vehicle manufactured by Ferrari, we again use optimal control to compute minimum-time maneuvers on two different tracks. A professional racer driving is then coached in following the OC strategy on the Ferrari driving simulator, and we objectively prove that the driver can outperform his previous lap times. In the third and last part of the thesis, we aim to prove that free-trajectory real-time optimal control is a valid alternative to hierarchical MPC frameworks based on high-level path planning and low-level path tracing. We first develop a novel kineto-dynamic vehicle model able to satisfy the trade-off between computational lightness and accuracy in representing the vehicle's pure and combined dynamics. Then, by solving a minimum-time OC in real-time, we are able to autonomously drive a real scaled vehicle around a track at the limits of tire adherence.

The use of autonomous underwater vehicles (AUVs) for oceanic observation and research is becoming more common. Underwater gliders are a specific class of AUV that do not use conventional propulsion. Instead they change their buoyancy and center of mass location to control attitude and trajectory. The vehicles spend most of their time in long, steady glides, so even minor improvements in glide range can be magnified over multiple dives. This dissertation presents a rigid-body dynamic system for a generic vehicle operating in a moving fluid (ocean current or wind). The model is then reduced to apply to underwater gliders. A reduced-order point-mass model is analyzed for optimal gliding in the presence of a current. Different numerical method solutions are compared while attempting to achieve maximum glide range. The result, although approximate, provides good insight into how the vehicles may be operated more effectively. At the end of each dive, the gliders must change their buoyancy and pitch to transition to a climb. Improper scheduling of the buoyancy and pitch change may cause the vehicle to stall and lose directional stability. Optimal control theory is applied to the buoyancy and angle of attack scheduling of a point-mass model. A rigid-body model is analyzed on a singular arc steady glide. An analytical solution for the control required to stay on the arc is calculated. The model is linearized to calculate possible perturbation directions while remaining on the arc. The nonlinear model is then propagated in forward and reverse time with the perturbations and analyzed. Lastly, one of the numerical solutions is analyzed using the singular arc equations for verification. This work received support from the Office of Naval Research under Grant Number N00014-08-1-0012. / Ph. D.