Prospective Doctoral Students
Please send me the following information via email:
- A short statement of interest, detailing why you are interested in my research and/or what particular research problem you would be interested in pursuing as a member of the group.
- Your CV, with undergraduate GPA.
- A list of mathematics, dynamics, controls, and computer science coursework you have completed.
Prospective Undergraduate and Master's students
Since its introduction in the 1960's, input-output stability analysis has had a vast impact on the study of control systems, especially areas of robust and optimal control. The seminal work of Zames provided stability criteria for conic systems and Hill and Moylan later proposed even more general stability criteria in terms of QSR-dissipativity. These properties can be used to ensure stability in the most challenging of control problems, even when confronting uncertain, nonlinear, open-loop unstable, MIMO, nonminimum phase, or delayed systems. However, only special cases of conic sectors, such as gain, passivity, and passivity indices have found common use, obscuring much of their utility.
The Bridgeman Lab is currently seeking students to help increase the practical applicability of these powerful control tools. Interested students need not be familiar with conic sectors, dissipativity, or even input-output stability (yet). Undergraduates or master's students can build upon their knowledge from a first course in controls, dynamics, or analysis. Multiple projects, tailored to your skills and interests are possible.
Design of novel controller synthesis methods - One reason why conic sectors and QSR-dissipativity are used infrequently is that there are relatively few methods to synthesize conic or QSR-dissipative controllers. In this project, students will investigate how to design controllers that simultaneously meet design objectives and guarantee stability that is robust to uncertainty. Some knowledge of control or analysis will be crucial to this project.
Experimental use of conic-sector-based control - Despite being introduced about 50 years ago, conic sectors have rarely been used to design controllers that are used in practice. This project would involve the application of conic controllers to regulate either a robotic testbed or a quadcopter. Programming experience, experience with the control of robotic systems or knowledge of basic control theory, Matlab, and/or ROS would be assets.
Identification of conic bounds or QSR-dissipativity - One stumbling-block hindering the use of input-output stability theory is the lack of methods to identify input-output properties for nonlinear systems. This project would involve the identification of input-output properties of either a specific system, such as a robot or quadcopter, or more general systems subject to delays, saturation, sensor or actuator noise, discretization, events, or varying parameters. Knowledge of dynamics (ideally Lagrangian or analytical mechanics) is a ‘must’ for these projects. Knowledge of analysis is an asset.
Implementation of algorithms to identify and impose conic properties - Reliable programs to execute existing stability analysis and controller synthesis methods will greatly facilitate their use. This project would involve the development of these vital programs, ideally in Matlab. Strong programming skills are a `must’ for this project.
Interested students should contact leila.bridgeman@duke.edu. Please provide a brief (<0.5 page) introduction detailing
- what project(s) you are interested in,
- your motivations,
- any relevant experience you have,
- any relevant coursework you have completed, and
- what time commitment you are interested in.