EE291c - ME 236 - CE 291F: Control and Optimization of Distributed Systems and Partial Differential Equations

Disclaimer: This page may be outdated. It is preserved here for informational purposes.

Practical information

Instructor: Professor Alexandre Bayen

Tel: (510) 642-2468
Fax: (510) 643-5264

Lectures: Mon. Tue. 8:00-9:30, 544 Davis Hall

Office Hours: Mon 11-12, Tue. 9:30-10:30 Sutardja Dai Hall (CITRIS) 642

GSI: Qingfang Wu

Office Hours: Thu. 11:30-12:30, Fri. 1-2, Davis Hall 604
e71

Control Number:CE 291F, ME236, EE291. This class is cross listed between EECS, ME and CE so that students can fit it in their respective curricula.

Announcements:

  • 01/17/10: Updated expanded course description is available here.
  • 01/17/10: Lecture slides and notes are now posted here.
  • 02/01/10: Problem set 1 and solutions of problem set 0 are now posted.
  • 02/01/10: First batch of projects is posted.
  • 02/16/10: Problem set 2 emailed to the class, Problem set 2 is due on March 2, in class.
  • 02/21/10: New chapter (chapter 11) of the notes posted here with slides (Ensemble Kalman Filtering)
  • 02/21/10: Project assignment 2 is posted here and due on March 8, in class.
  • 04/05/10: Problem set 4 is posted here and due April 19 in class.

Course description

This is an introductory course to control and optimization of systems driven by partial differential equations (PDEs). The first part of the class will focus on fundamental techniques to solve these equations both analytically (when possible), and numerically. This part of the course will be accessible to students with exposure to control and no (or very little) exposure to partial differential equations. The techniques presented in class will include separation of variables, spectral decomposition, self-similar solutions, characteristics, complex embedding. The second part of the class will address stability, control and optimization of these PDEs. It will be accessible to students without background in control. Stability will be investigated using spectral analysis. Adjoint-based optimization, Hamilton-Jacobi and differential flatness techniques will be applied for open loop trajectory design. Lyapunov techniques will be devised for stabilization and control. 

The class will put emphasis on networks. Applications (in particular course projects) will include networks of one dimensional systems: water distribution channels, electromagnetic waves in transmission cables, towed cable systems for marine oil exploration, highway systems, oil drilling, mine ventilation networks, blood circulation in vessels. Examples in higher dimensions will include 2D or 3D fluid mechanics, in particular propagation of contaminants in water. 

Here is a list of partial differential equations and corresponding applications that will be covered in class:

  1. The wave equation
  2. The Euler-Bernoulli beam equation (materials)
  3. The heat equation (thermosciences)
  4. The LWR equation for highway traffic (transportation)
  5. The Saint-Venant equations, shallow water equations, Hayami'e equation (hydraulics)
  6. The membrane equation (mechanical engineering, MEMS)
  7. The Telegraph equation (communication)
  8. Maxwell’s equations (electromagnetism)
  9. Vibrating string (acoustics)
  10. Vorticity equation (aerodynamics)
  11. Euler’s equations (fluid mechanics)

An expanded description of the class is available here.

General information

  1. Homeworks will count for 40% of the final grade
  2. There will be a midterm, open-book, and open notes, which will count for 20% of the final grade
  3. There will be one class project. Students are encouraged to bring their own research-related projects. Projects will be suggested to students (see sample list of projects for the prevoius years below), if they need. Students are allowed to team up for projects, if the scope of the project is large. The final project will count for 40% of the finla grade.

Sample projects

Here are a few sample projects final presentations (Fall 2007)

  1. Plates Subjected to Moving Loads (Ram Rajagopal, EECS, Branko Kerkez, CEE)
  2. Shock free control of a freeway network, (Ajith Muralidharan, ME, Rene Sanchez, ME)
  3. Reachability Analysis for Hybrid Simulations, (Benjamin Fine, ME)
  4. Analysis of a “Simple” Model of Brain Activity, (Hope Weiss, ME)
  5. 2D implicit surfaces using level set methods, (James Lew, CEE)
  6. Simulation of a Highway using a second order LWR PDE, (Jerry Jariyasunant, CEE)
  7. Option pricing, (Jiangchuan Huang, CEE)
  8. Pricing of Options, (Mathieu Cabannes, CEE)
  9. Using wave propagation properties to identify soil parameters (Moanna Reynau, CEE)

Here are a few sample projects final presentations (Spring 2007)

  1. Safe aerial refueling using Hamilton-Jacobi techniques (Jerry Ding, EECS)
  2. Control of epileptic seizures in the human cortex (Beth Lopour, ME)
  3. Using the viability algorithm to develop a value function for an air traffic control problem (Andrew Tinka, CEE)
  4. Moskowitz surface and fundamental diagram generation (Eric Lew and Shuo Yang, ME)
  5. Parameter identification for soil dynamic systems (Min Chen, CEE)
  6. Active water absorber (Matthiew Carney, ME)
  7. Modeling of single flagellum bacterial motion (Justin Hsia, EECS)
  8. Modeling river dynamics on the Niger river (Emily Kumpel, CEE)
  9. Frequency model in open channel with lateral flow (Qingfang Wu, CEE)

Here are a few sample projects final presentations (Spring 2006)

  1. Modeling and Optimization Analysis of Single Flagellum Bacterial Motion (Edgar Lobaton, EECS)
  2. Liquid Phase Boundary Control for Fabrication of Features in Thermoplastic, Micro-Hair Arrays (Jessica Pannequin, Brian Schubert, EECS)
  3. The Generalization and Application of Particular Solutions to Lamb’s Problem (Greg McLaskey, CEE)
  4. Active Control of Suspension Bridges (Patricia Decker, CEE)
  5. Study on Level Set Approach to Image Segmentation (Xu Guan, CEE)
  6. PDE methods for image processing (Andrew Aquila, EECS)
  7. Reachability Analysis for a Lower Extremity Exoskeleton (Kurt Amundson, ME)
  8. Computing the reachability of the LWR Equation (Ram Rajagopal, EECS)
  9. Planar Cell Polarity in Drosophila melanogaster (Anil Aswani, EECS)

Projects

For the project, you will be expected to conduct significant work on one of the following topics, or a topic of your choice related to the material covered in class:

  1. Modeling systems with PDEs for control purposes
  2. Algorithm design for control and/or optimization of PDE driven systems
  3. Simulation tools for control of PDE driven systems
  4. Hardware implementation of control and/or optimization algorithms on a PDE driven system

You will first review the literature on the subject you have chosen. If you choose your own research topic, you will be responsible for finding the proper set of articles relevant for your problem. If you choose one suggested project, some references will be provided to you as a basis for further reading. Depending on your topic, you will balance your time between algorithm design, simulation, and/or hardware implementation. In the first weeks of the project, you will be expected to set up clear goals with the instructor, and a plan to achieve these goals. You will meet with the instructor several time to assess the progress made on the project. You will give a short presentation of your project to the class at the end of the semester. 

Reporting

You will be expected to write a report, to summarize your work. We suggest that you use these LaTeX files to write up your report, but you are free to use any editing software you like. Remember that your report should be written in a way which is understandable for someone who does not have exposure to the field. Number tables and figures sequentially and refer to them in the text of the results section.  Be sure to label all plot axes and tables and show units of measure.  For calculated quantities, report the appropriate number of significant figures. Here is a rough outline of what a good technical report would look like: 

  1. Introduction:  objectives of your project, background and motivation.
  2. Literature review: describe the state of the art in the field; include all proper references, explain where your project fits. 
  3. Problem investigated. Describe the physical system you are modeling, eventually describe the derivation of the model. Pose the problem of controlling the system.
  4. Control. If you are deriving your own control or optimization algorithm, include all derivations. If the derivations are too long, put them in the appendix, in order to have a clear flow in this section. Summarize your theoretical contributions. 
  5. Simulation. If you are designing a simulation tool for control or optimization purposes, describe which algorithms you have used, and how they address your problem. Describe the software implementation, and the validation of the software (for example on model problems).
  6. Hardware implementation. If you are implementing control algorithms on an experimental testbed, describe which algorithms you have used, and how they address your problem. Describe the hardware implementation.
  7. Results:  present the results of your experiments in tabular and/or graphical form, but include text that organizes and describes the results to guide the reader through them. 
  8. Discussion:  discuss the results, compare with theory, comment on the significance of the results, discuss reasons for disagreement, and suggest how the measurements and the experiment could be improved.
  9. Summarize the main results and findings of the experiment.  Nothing new here; just provide a brief restatement and summary of what is already presented in previous sections.
  10. Bibliography: list all references used in the text.
  11. Appendix: include derivations, raw data, calculations, and spreadsheets if appropriate.


Course material

All course material used for the class can be downloaded from the following URL.