CS 367: Model-Based Reasoning
Lecture 1 (01/10/2002)
Gautam Biswas
Logistics
Class time: Tu.– Thurs. 1:10-2:25 pm
Location: Room 313, Featheringill Hall
Instructor: Gautam Biswas
Office: Room 250, Featheringill Hall
 Tele: 343-6204
 E-mail: biswas@vuse.vanderbilt.edu
 Office Hours: Tues., Friday: 9:00-10:00
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Lab: EHS Lab, Room 331 Featheringill
Topics
Discrete-Event Systems
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Ref: Introduction to Discrete Event Systems by
Cassandras and Lafortune (1999)
Continuous Systems
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Ref: Systems Dynamics: A Unified Approach
by Karnopp, Rosenberg and Margolis (1990)
Hybrid Systems
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Ref: From lecture notes
Grading Scheme
Home Work Assignments (4): Mathlab, 20Sim, hcc, other packages: 25%
Classroom Presentation(s) – Advanced
topics from basic material+ classroom
participation: 15%
Class Project: 60%
Project Report and Demonstration: 50%
 Presentation of Project: 10%
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Class projects will be individual efforts – it can be a theoretical
and conceptual study, an experimental study, an implementation,
or a combination of the three.
What is Model-based Reasoning?
Methodology for analyzing, understanding, and
predicting behavior of a system, process, or
phenomena using a model.
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System:
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engineering process (continuous) – chemical plants, aircraft,
traffic system,
information process (computer-based or digital) – computer
network, telephone system,
economic process – U.S. economy, world economy, software
industry
Social systems – suburban culture, welfare system
Sometimes hard to categorize systems – notion of
hybrid systems.
What are we going to cover in
this course?
Modeling of systems – look at different
modeling paradigms
Continuous system modeling – quantitative and
qualitative
 Discrete-event modeling
 Hybrid Modeling – modeling multiple
paradigms in an integrated fashion (continuous
+ discrete)
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What are we going to cover in
this course?
Analysis of systems: understanding,
explanation, prediction, and problem
solving
Analytic methods
 Simulation-based methods
 Special purpose methods for achieving
particular tasks, e.g., verification, monitoring,
and fault detection and isolation
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List of Topics
Introductory Lecture (01/16): Modeling of
Systems and its applications
Topic 1(2-3 weeks): Discrete Event Modeling of
Systems (ref: S. Lafortune, et al. – Automata
based models, Petri Net based models(?))
Topic 2(2-3 weeks): Modeling and Analysis of
Physical Systems: The Bond Graph Approach
(Ref: D.C. Karnopp, D.L. Margolis, and R.C. Rosenberg Systems Dynamics: A Unified Approach, 2nd ed., John
Wiley, NY, 1990).
List of Topics (contd. …..)
Topic 3 (2-3 weeks): Methods for analysis of DiscreteEvent and Continuous Dynamic Systems – applications to
control and diagnosis. (Collection of papers).
Topic 4 (2-3 weeks): Modeling and Analysis of Hybrid
Systems. (Lecture Notes and collection of papers).
Topic 5(2 weeks): Fault Detection and Isolation in Hybrid
Systems - (Building Hybrid Observers and Fault Isolation
units).
Topic 6 (rest of semester): Advanced Topics, such as
applications to computational architectures for embedded
systems, embedded control, and fault-adaptive control.
Lecture 1: (Home Work)
Additional reading material: F.E. Cellier, H. Elmqvist, and M. Otter,
“Modeling from Physical Principles,” (pdf file URL:
http://www.vuse.vanderbilt.edu/~biswas/Courses/cs367/papers)
Problems:
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1. The height of water in a reservoir fluctuates with time. If you had to
construct a dynamic system model to help water resource planners predict
variations in the height, what input quantities would you consider? How
many state variables would you need in your model?
2. Suppose you were a heating engineer and you wished to consider your
house as a dynamic system. Without a heater the average temperature of
the house would clearly vary over a 24 hour period. What might you
consider as state variables for a simple dynamic model? How would you
expand your model to predict the temperatures in several rooms in your
house? How does the installation of a thermostat controlled heater change
your model?
Modeling of Dynamic Systems
What exactly is a system? Ambiguous word, but some
characterization:
 Entity that is separable from the rest of the universe
(we call this the environment) by a physical or
conceptual boundary
e.g., human body is a system, coffee maker is a system, air traffic
control is a system, school of fish is a system.
Satisfies the concept of reticulation, i.e., a system can be
looked upon as being made up of interacting parts
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e.g., human body made up of various organs and the nervous
system; coffee maker, container for water, boiler (evaporator),
passages, filter, etc.; air traffic control system – people, machines,
schedules, etc.
What is a Model?
Simplified, abstracted constructs of a system used
to predict the behavior of the system.
Small (finite) description of a very complex reality
Typically constructed to answer particular
questions.
If question changes, does the model change?
Typically modeling involves two tasks: (i) model
building, and (ii) model analysis
Types of Models
Ordinary Differential equations + Algebraic
relations (Quantitative models)
Qualitative Descriptions, especially if our
knowledge of domain and situation is
incomplete.
Other issues – starting point for model
building, causal versus acausal models, etc.
Systems Viewpoint to Modeling
Model to study operation of complete system as
opposed to operation of the individual parts
Method of model building: compositionality
Method of analysis: isolate into parts
Unified approach to modeling, rather than being
domain-specific
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Qualitative reasoning schemes based on (incomplete) analytic
models of system
Energy-based modeling of physical systems
Discrete-event models of systems – change in system directly
linked to the occurrence of events
Combine modeling paradigms – Hybrid Systems approach to
modeling
Modeling of Systems
System
In general, all system models
will be mathematical functions
Subsystems
At times, we will introduce
topological information (e.g.,
for diagnosis)
Components --- primitives
Black box
Interface with other
components
Mathematical or
Logical function
Modeling of Dynamic Systems
State-Determined Systems -- our goal is to start with physical
component descriptions of systems understanding of component
behavior to create mathematical models of the system.
Mathematical model of state-determined system – defined by set
of ordinary differential equations on the so-called state
variables. Algebraic relations define values of other system
variables to state variables.
Dynamic behavior of state-determined system defined by (i)
values of state variables at some initial time, and (ii) future time
history of input quantities to system.
In other words, our system models – satisfy the Markov property
Uses of Dynamic Models
Analysis for prediction, explanation, understanding, and
control. Two types: (a) analytic methods, and (ii)
simulation-based methods. Given S, X at present, and U
for the future, predict future X and Y.
Identification. Given U and Y find S and X consistent with
U and Y. (under normal and faulty conditions)
Synthesis. Given U and a desired Y, find S such that S
acting on U produces Y.
Input Variables
U
Dynamic System, S
State Variables, X
Output Variables
Y