UROPs in EAPS

Period: IAP, Spring, Summer, Fall
Department: EAPS
Faculty Supervisor: Sai Ravela | Direct Supervisor: Samiya Alkhairy

Opportunity: The UROP will be supported by the research mentor and have regular meetings with her. The UROP will grow as a researcher and be supported in their growth by being given increasing creative liberties as the project goes on. Over the course of this exciting new project, the student will learn about analytic modeling, symbolic coding, systems of differential equations, dynamics and control, as well as how to document code, communicate their work, and overcome bottlenecks. Depending on the duration of the project, the student may also learn about optimal control, aircraft autopilots, and climate and environmental aspects that this work will ultimately be used for.

Background: We have been developing analytic – and consequently interpretable and computationally efficient, methods for dynamics and control. The mathematical formulation of the plant and controller is direct and native to the problem’s variables and does not require defining state variables unlike the state space formulation and associated methods. The novel formulation admits systems of equations that may include algebraic equations and differential of various orders. The associated analytic methods are: a solution method that results in an expression for a solver that does not need to be computed at each time step, a state estimator that is an analytic counterpart to Kalman filters, and a controller which solves for inputs simultaneous with the dynamic variables. The methods are for linear continuous time systems and are easily reformulated for discrete time.

Project scope: In this project, the student will work on developing a symbolic toolbox and associated test set for the novel analytic methods for dynamics, estimations, and control developed by the mentor who will supervise the student directly. This project involves developing annotated code and providing short write-ups for the following based on classical methods and the new methods: numerical and analytic methods for solving polynomials; state space formulation and methods for solution (analytic and numerical), state estimation (numerical), and control (numerical); novel DAE system formulation and analytic methods for solution, state estimation, and controls.

Significance: The symbolic toolkit developed in this project will be used for an aircraft autopilot. It will be coupled with a novel ensemble nonlinear method for controls. In the future, these coupled methods will be implemented synergistically to develop fast, resilient, adaptive, energy efficient, autopilots that follow a set path accurately. Our goal is to later develop this coupled autopilot for an atmospheric observatory. The observatory will take measurements from desired locations in the stratosphere (e.g. over hurricanes, volcanoes) which is useful for assessing environmental hazards and for atmospheric modeling. The symbolic toolbox will also broader significance as it will later be open source and will enable researchers and engineers to not only benefit from its properties but also to use it directly for a variety of problems without requiring them to formulate and develop code specific to their system. 

Required Skills or Prerequisites: We are looking for students who are motivated, methodical, organized, and have good communication skills and sufficient time during the semester. The ability to read papers and implement algorithms from those papers is very advantageous but not necessary.

The UROP student should also:
1) Be comfortable with programing and documentation is able to learn symbolic coding quickly
2) Be familiar with ordinary differential equations and has an interest in dynamics and control

Number of openings: 1

Contact: Samiya Alkhairy | samiya@mit.edu 
URL: UROP Site Listing Page  |  Earth Signals and Systems Group Site