Graduate Courses

FEL3400 - Networked Control Systems

A networked control system consists of a set of dynamical units that interact over a signal exchange network for its coordinated operation and behavior. Such systems have found many applications in diverse areas of science and engineering, including multiple space, air, land, and underwater vehicles, energy and power systems, physiology, and medicine.


Doktorandkurs/graduate course worth 7.5 högskolepoäng (ECTS)
Fall 2007
School of Electrical Engineering, KTH.

This course has ended, but lecture notes and recordings of the lectures are available here.


Magnus Egerstedt

      E-mail: magnus[at]ece[dot]gatech[dot]edu
      Phone: 08 790 6205
      Office: CVAP/CAS, Teknikringen 14, Floor 7, Room 714

Class Room: Himmelriket, Osquldas v. 10, plan 8 (all days except 5/10 when we'll meet in the Seminar Room on plan 5)

Meeting Times: Fridays at 13:15-15:00

Office Hours: By appointment (If this doesn't work, fixed office hours will be set up)

Evaluation: Grades will be based on homework assignments (50%) and a take-home exam (50%). The requirement for passing will be 50% of the total points. The homework assignments will contain theoretical as well as pratical (mainly through matlab-simulations) parts. In order to do well on these assignments, basic knowledge of state-space methods in systems and controls, and some previous experience with matlab programming is desirable.


Currently, significant research efforts are underway in the controls, systems, and communications communities to lay out a foundation for the analysis and control of networked systems. This course will provide an overview of the tools and techniques that have proven instrumental for studying networked control systems as well as outline potential research directions.

The course will be divided into eight parts, corresponding to the following topics:

14/09 - Lecture 1: Networked and Decentralized Control
(limited computational, communications, and controls resources in networked control systems)
21/09 - Lecture 2: Network Models and Graph Theory
(graphs, random graphs, random geometric graphs, state-dependent graphs, switching networks)
28/09 - Lecture 3: The Consensus Equation
(nearest-neighbor rules, agreement protocols, convergence properties)
05/10 - Lecture 4: Formation Control
(shifted consensus, applications in multi-agent robotics)
12/10 - Lecture 5: Hybrid Control Strategies
(collision avoidance, controlled formation changes, switching topologies)
19/10 - Lecture 6: Multi-Agent Robotics: LANdroids
(self-organization, self-optimization, self-healing, tethering, power management)
26/10 - NO CLASS:
02/11 - NO CLASS:
09/11 - Lecture 7: Nonlinear Interaction Laws
(weighted consensus, connectivity, from local rules to global behaviors)
16/11 - Lecture 8: Control of Heterogeneous Networks
(anchor nodes, boundary values, controllability, optimal control)


Homework policy: Collaboration is encouraged when solving the homework problems. However, please produce and hand in your own version of the homework.

There will be around five sets of homework (50% of the grade) in combination with a take-home exam (50% of the grade).

Homework 1
     Due October 5, 2007.
     The Matlab files you will need to solve this homework are:

Homework 2
     Due October 19, 2007.
     The new Matlab files (together with the old ones for HW1) you will need to solve this homework are:

Homework 3
     Due November 9, 2007.
     The new Matlab files (together with the old ones) you will need to solve this homework are:
     You will also need to read the DARPA LANDroids Call For Proposals.

Final Exam
Note: The Final Exam is due on Wednesday, Dec. 5, 2007, at 11:59am!

Handouts and Misc. Extra Material

Lecture 2:
- Read the first four pages of S. Martinez, J. Cortes, and F. Bullo. Motion Coordination with Distributed Information. IEEE Control Systems Magazine, 27(4):75-88, 2007. Available at
- Read chapters 1 and 8 in Algebraic Graph Theory below, by C. Godsil and G. Royle.
- Check out Dan Spielman's excellent MIT lecture notes on spectral graph theory and Cheeger's inequality at

Lecture 3:
- Read the survey paper R. Olfati-Saber and R. M. Murray. "Consensus Problems in Networks of Agents with Switching Topology and Time-Delays," IEEE Trans. on Automatic Control, vol. 49(9), pp. 1520-1533, Sep., 2004. Available at

Lecture 4:
- Read the first couple of pages in T. Eren, P. Belhumer, B.D.O. Anderson, and S. Morse. A framework for maintaining formations based on rigidity. Proceedings of 15th IFAC World Congress on Automatic Control, Barcelona, Spain, July 2002. Available here.