CSE 510: Hybrid Systems

[Announcements][Projects]


Instructor: Radu Grosu ( grosu@cs.sunysb.edu),
Class: Tue/Thu 12:50pm - 2:10pm, room Ch123 (Chemistry)
Office hours: TueThu 11:30pm-12:30pm, CS Building room 1425, and by appointment

Contents

Motivation

Hybrid systems are becoming an integral part of nearly every engineered product: they control consumer products, commercial aircraft, nuclear power plants, medical devices, weapon systems, aerospace systems, automobiles, public transportation systems, and so on. At the same time quality and confidence issues are increasing in importance. Errors may result in loss of life, destruction of property, failure of businesses, and environmental harm. Today, designers check that a hybrid system works properly by using simulation and testing. However, as hybrid systems become more complex and pervasive, these traditional techniques are not sufficient to assure desired reliability. Model checking and related computer-aided verification techniques are emerging as practical alternatives. They allow the designer to verify that a mathematical model of a system satisfies its abstract logical specification. This approach has been most effective for control-intensive components, and is rapidly becoming an integral part of the design cycle in many companies.

Objectives

By the end of this course the students will be provided with detailed knowledge and substantial experience in:

  • The mathematical modeling and analysis of signals and systems, relating their declarative, what is, with their imperative, how to, views, respectively.
  • The application and unified treatment of finite automata and difference equations, as linear systems over semimodules and vector spaces, respectively.

    • Prerequisites

    CSE 214, CSE 220, and CSE 303 are relevant but not required. Experience with MathLab is also helpful.

    Overview

    In the class, we will discuss the theoretical aspects of designing, simulating and verifying a hybrid system. In the projects, you will then apply the theory you have learned in the class. The design and analysis of hybrid systems typically involves the following concepts:

    Reading

    The course will use the following textbooks:
    1. Structure and Interpretation of Signals and Systems by E.A. Lee and P. Varaiya, Addison-Wesley, 2003, 647pp, ISBN 0-201-74551-8.
    2. Linear Systems Theory, Second Edition by Ferenc Szidarovszky and A. Terry Bahill, CRC Press, 1998, ISBN 0-8493-1687-1.
    3. Graphs, Dioids and Semirings: New Models and Algorithms by M. Gondran and M. Minoux, Springer, 2008, 383pp, ISBN 978-0-387-75449-9.
    Slides will be posted as links in the tentative schedule below.

    Software

    Most of the homeworks are going to use MATLAB. You can run MATLAB on the compservs by typing /usr/local/bin/matlab. You can find various information about MATLAB and a tutorial here.
     

    Communication

    In order to exchange ideas and experience with each other, you may want to use the news group created specially for cse510. To subscribe to this group, proceed as follows (e.g. with  the netscape browser): (1) right click the news.sunysb.edu, (2) select subscribe to Newsgroups, (3) choose the search panel and search for sbcs.cse510, (4) select the sbcs.cse510 newsgroup and click on the subscribe button. Now you are ready to send and retrieve messages.

    Grading

    Your performance on the projects and homework assignments will determine your final grade.

    Your Rights and Responsibilities


    Special Needs

    If you have a physical, psychological, medical or learning disability that may impact on your ability to carry out assigned course work, you are urged to contact the staff in the Disabled

    Student Services office (DSS), Room 133 Humanities, 632-6748/TDD. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate.

    All information and documentation of disability is confidential.

    The Importance of Being Earnest

    Because a primary goal of the course is to teach professionalism, any academic dishonesty will be viewed as evidence that this goal has not been achieved. Any act of cheating will be treated with utmost seriousness.

    You can discuss the course material with other students, but not the homework assignments themselves. In effect, you can discuss the problems but not the solutions. If you help another student with a homework, use examples that do not resemble those in the homework. Remember that there are many different ways to solve the same problem; even solutions with the same central idea can be formulated in many different ways. Therefore, suspiciously similar homework solutions will be considered as evidence of disallowed collaboration or copying.

    In case you have any questions about whether an act of collaboration may constitute "cheating", please come and talk to the instructor beforehand to clarify the issue.

    Copying an assignment from another student in this class or obtaining a solution from some other source will lead to an automatic F for this course and to a disciplinary action. Allowing another student to copy one's work will be treated as an act of academic dishonesty, leading to the same penalty as copying. You should learn how to protect your data. Failure to do so is also unprofessional and it may expose you to the danger that someone will copy your homework and will submit it as his or her own (see above). In this case, you may be given a score of 0 for the assignment in question (and the other party will get an F).

     All cases of academic dishonesty will be reviewed by the Engineeing College's committee (CASA).

    Survival Tips

    Do not postpone working on assignments. Start working on programming assignments as soon as they are handed out. Do not wait till the day before the deadline. You will see that assignments take much more time when you work on them under pressure, than when you are more relaxed. Remember that no late submissions are allowed.

    Do not postpone working on assignments! This cannot be understated. Despite the above warning, most students will end up working only around the deadline. Remember, the homeworks usually take more time that it initially appears. Furthermore, I expect both the TA and me to be swamped on the office hours before projects are due. So, you, being wiser than the rest, should start earlier and beat the rush!

    Tentative Schedule

     
       Date   Topic   Chapter   Homeworks 
     1.   Jan 27   Overview of finite automata as linear systems.   Overview   
     2.   Jan 29   Signals and their definition.   [1]:1.1   [1]:A   
     3.   Feb 03   Systems and their definition.   [1]:1.2   [1]:A   
     4.   Feb 05   Systems composition.   [1]:2      [1]:A   
     5.   Feb 10   Linear systems over vector spaces..   [3]:1   H1 out 
     6.   Feb 12   Discrete time-invariant linear systems. State space representation   [1]:5, [2]:2.2   
     7.   Feb 17   Solution of discrete time-invariant systems.  [1]:5, [2]:2.2   
     8.   Feb 19   Linear systems and the division ring of matrices.   [2]:1.3, [3]:1   
     9.   Feb 24   Determinants and matrix inversion.   [2]:1.3, [3]:1   H1 due. H2 out 
     10.   Feb 26   Matrix diagonalization and matrix functions.   [2]:1.3, [3]:1   
     11.   Mar 03   Generalized eigenvectors and the Jordan canonical form.   [2]:1.3, [3]:1   
     12.   Mar 05   The Z-Tranform of discrete linear systems.   [1]:9, [2]:2.2.3   
     13.   Mar 10   The Z-Tranform of discrete linear systems.   [1]:9, [2]:2.2.3   H2 due. H3 Out 
     14.   Mar 12   Observability and reachability: observability.   [2].6   
     15.   Mar 17   Observability and reachability: reachability.   [2].5   
     16.   Mar 19   Canonically ordered monoids, semirings and dioids.   [3]:1   
     17.   Mar 24   Semimodules.   [3]:5   H3 due. H4 Out 
     18.   Mar 26   Observability and reachability of automata.   HSCC'09 paper   
     19.   Mar 31  Observability and reachability of automata.   HSCC'09 paper   
     20.   Apr 02   The S-Transform and Gaussian elimination.      H4 due, H5 Out 
    ***  Apr 07   Spring recess (no class)     
    ***  Apr 09   Spring recess (no class)     
     21.   Apr 14   The S-Transform and Gaussian elimination.      
     22.   Apr 16   Stability. Laplace transform.      H5 due. H6 Out 
     23.   Apr 21   Laplace and Z transforms. Prop of Z. FR and poles.   [1]:13   
     24.   Apr 23   Laplace and Z transforms. Prop of L. FR and poles. Steady state.   [1]:13   
     25.   Apr 28   Composition and feedback control. Cascade and parallel composition.   [1]:14   
     26.   May 30   Composition and feedback control. Feedback composition.   [1]:14   H5 due. H6 Out 
     27.   May 05   Nonlinear systems and linearization. Phase plane.     
     28.   May 07   Nonlinear systems and linearization.     

    Last updated on Mar 19, 2009 by Radu Grosu