EE 8235: Fall 2011 Web Page
Mihailo Jovanovic, University of Minnesota

Modeling, Dynamics, and Control of Distributed Systems

Course description

Instructor and TA

Background material



Course requirements

Course description [top]

Course description: This course deals with modeling, analysis, and control of distributed dynamical systems. These systems are typically described by partial differential equations (PDEs) or interconnected systems of ordinary differential equations (ODEs), and they are of increasing importance in modern science and technology. The course content will be strongly motivated by physical examples ranging from distributed networks of interconnected systems to the problems from hydrodynamic stability and transition to turbulence.

Topics: Examples and motivation. Connections and equivalences between finite and infinite dimensional systems. Abstract evolution equations, regularity, well posedness and semi-groups. Exponential stability. Lyapunov functionals. Spectral conditions for stability. Approximation and numerical methods. Symmetries, arrays and spatial invariance. Transform methods. Spatio-temporal frequency responses. Input-output norms, sensitivity, and robustness of infinite dimensional systems. Pseudospectra. Optimal distributed control. Architectural issues in distributed control design. Optimality of localized distributed controllers. Distributed optimization. Cardinality optimization problems. Alternating direction method of multipliers. Consensus problem in sensor networks. Cooperative control of large-scale vehicle formations. Swarming and flocking. Hydrodynamic stability and transition to turbulence. Pattern formation in reaction-diffusion systems. Parametric resonance in spatio-temporal systems. Spatio-temporal vibrational control.

Audience: This course is aimed at attracting a spectrum of students from across classical engineering disciplines, physics, and applied mathematics. Even though I plan to cover everything from scratch, a solid background in linear systems and linear algebra would be helpful. Those interested should contact the instructor.
Class schedule: TuTh 9:45am - 11:00am, MechE 108, Sept. 6 - Dec. 14

Instructor and TA [top]

Instructor: Mihailo Jovanovic
Office: Keller Hall 5-157
Office hours: Tu 11:00am - noon (or by appointment)

Phone: (612) 625 7870
Web page:

Teaching assistant: TBA

Background material [top]

Linear Systems 1
Stephen Boyd
Introduction to Linear Dynamical Systems
Web page: Stanford Notes (videos, reader, slides, homework, …)
Linear Systems 2
Stephen Boyd
Linear Dynamical Systems
Web page: Stanford Notes (slides, homework, …)
Functional Analysis Erwin Kreyszig
Introductory Functional Analysis with Applications
Wiley, First Edition, ISBN 0-471-50459-9

Texts/notes [top]

Primary text Instructor's notes
Supplementary text 1 Ruth F. Curtain, Hans J. Zwart
An Introduction to Infinite-Dimensional Linear Systems Theory
Springer-Verlag, First Edition, ISBN 0-387-94475-3
Supplementary text 2
Stephen P. Banks
State-Space and Frequency-Domain Methods in the Control of Distributed Parameter Systems
Peter Peregrinus Ltd., First Edition, ISBN 0-863-41000-6
Supplementary text 3
Zheng-Hua Luo, Bao-Zhu Guo, Omer Morgul
Stability and Stabilization of Infinite Dimensional Systems with Applications
Springer-Verlag, First Edition, ISBN 1-852-33124-0
Supplementary text 4 Mehran Mesbahi, Magnus Egerstedt
Graph Theoretic Methods in Multiagent Networks
Princeton University Press, First Edition, ISBN 9780691140612

Software [top]

Matlab/Simulink Homework sets and class project will make use of Matlab and Simulink
Pseudospectral method for solving differential equations J. A. C. Weideman, Satish C. Reddy
A Matlab Differentiation Matrix Suite
Web page: Matlab Functions
Chebfun Lloyd N. Trefethen and others
Chebfun Version 4
Web page: Chebfun V4.1.1864
Pseudospectra Gateway Mark Embree, Lloyd N. Trefethen
Pseudospectra Gateway
Web page: Pseudospectra Gateway
CVX: a package for specifying and solving convex programs Michael Grant, Stephen Boyd
Web page: CVX

Course requirements [top]

Homework: Homework is intended as a vehicle for learning, not as a test. I encourage you to collaborate with your classmates. Please try to invest enough time to understand each homework problem, and independently write the solutions that you turn in.

Exams: We may have one take home exam in the second part of the semester.

Project: A research project is a required portion of this course. Each student will write a report and give a short project presentation at the end of the semester. The project can either be an in depth study of a relevant topic, or an original research idea (ideally something related to your own research). I will suggest a list of potential projects around the middle of the semester.