Download Control of Dynamic Discrete-Event Systems

Control of Dynamic
Discrete-Event Systems
Lenko Grigorov
Master’s Thesis, QU
supervisor: Dr. Karen Rudie
Discrete-Event Systems
(background)
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Discrete-Event Systems are systems where
events (changes of state) occur:
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spontaneously
logically ordered relative to each other
not tied to a continuous global time
Common representation of DESs:
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Finite-state machines
G=(,Q,,q0,Qf)
(Cassandras and Lafortune, Introduction to Discrete Event Systems, 1999)
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Motivation
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Control of a specific class of DESs
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dynamic (change with time)
relatively large
with continuous lifecycle
with requirements with different levels of
stringency
Such systems are common in real life
Classical DES control methods are not
suitable
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Outline
1.
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Definition of Dynamic Discrete-Event
Systems
Redundancy for Modular Architecture
Optimal DDES control
Experiment
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DES Modular
Architecture
(background)
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Separate small DES
modules
Combined using a
synchronous composition
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an event can happen in a
module  it can happen in
the system
if modules have common
events, these events
happen simultaneously
(Cassandras and Lafortune, Introduction to Discrete Event Systems, 1999)
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Dynamic DES Model
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Time
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Sets of modules
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Mi = {M1i, M2i, …, Mni}, i{0, 1, 2, …}
||Mi = M1i || M2i || … || Mni
DDES G={(||Mi, i) | i{0, 1, 2, …})
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discrete
increases by one after every event
at time i, Gi = ||Mi
No restrictions on the sets Mi
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Redundancy for
Modular Architecture
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Mi  Mi+1  
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Given operation 
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thus some part of ||Mi may be reused to compute
||Mi+1
commutative
associative
How to compute A = A1  A2  …  An so
that recomputing A after a structure change
is least expensive?
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redundant storage of intermediate results
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Redundancy Structures
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Stack structure – simple
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Tree structure – robust to random changes
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use when: the result of the operation does not
increase exponentially, older modules are stable
disadvantages: large size when used with
synchronous composition
use when: the oldest elements have highest
chance to change
Hybrid structure – small footprint
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use when: there is small storage space
disadvantages: may demand more computations,
while savings in space are insignificant
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Complexity of
Redundancy Structures
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Standard Online Control
(background)
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Construct a limited-depth tree of the possible
future behavior of the system
For each node, determine if the string leading
to it is acceptable
Propagate the information back to the root
Disable events leading to “unsafe” states
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where we cannot prevent the execution of an
unacceptable string
Repeat this after each execution of an event
(Chung, Lafortune, and Lin, “Limited lookahead policies in supervisory
control of discrete event systems”, 1992)
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Valuation of Event Strings
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Two functions are defined by the user
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The value function gives the “value” of event
strings, according to some criteria
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The goal function indicates which strings
accomplish a task
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v(s)  R, s  L(G)
greater v(s)  string is more desirable
v(s) = -  string is unacceptable
g(s)  {0,1}, s  L(G)
no need to investigate the look-ahead tree further
similar to final (marked) states, but works on strings
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Optimal DDES Control
Algorithm
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Online control using the value and goal
functions
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exploration of a branch in the tree is carried until
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a goal is generated,
an unacceptable string is generated, or
the depth limit is reached
the value function is used to obtain the benefit of
the different paths (event strings)
the controller selects the path which may yield the
greatest benefit
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Advantages (1)
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Attempts to guide the system to the
maximal benefit for the user
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quality depends on the way the system
evolves
The use of the value function renders
the control process more robust to
failures
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it does the best possible with the available
resources
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Advantages (2)
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The algorithm adapts automatically to
different types of dynamics in the system
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structural changes
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changes of goals
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the constituent modules change
changes in the requirements for the system behavior
changes in the evaluation of events
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events have varying costs
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depending on the event string
depending on time
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Advantages (3)
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Requirements on the system behavior
can have many levels of stringency
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The method does not need access to
the complete system model
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not only acceptable/unacceptable
can work with large systems
The algorithm can be implemented as
modular software
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Issues in
Optimal DDES Control
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The control may not be optimal
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if the tree depth is too limited
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if the tree depth is too big
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the controller cannot observe far enough along the event
strings to compute relevant costs and payoffs
the controller bases its decisions on the current system,
while the system may change in the future
The complexity of the algorithm is affected by
the particular value and goal functions used
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may be significantly greater than the complexity of
standard online control
O(kNv(s)g(s))
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Experiment
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Different number of trains enter or leave a
system of railroads
A set of requirements on the system behavior
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no trains can be at the same section of a track,
etc.
Comparison between optimal DDES control
and simple online control
(Experiment based on: Chung, Lafortune, and Lin, “Supervisory control
using variable lookahead policies”, 1994)
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Experiment Results
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The overall system behavior is much closer to
the requirements
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strings have higher value
more trains arrive at train stations per unit time
more balanced use of the resources
Disadvantages
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significant increase in the time to make a decision
can work only with a much smaller tree-depth
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Conclusion and Contributions
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The use of redundancy structures can
reduce the number of computations
needed to rebuild the model of a
system after it changes
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different types of redundancy structures
available for different applications
can be used in other areas
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not limited to the synchronous composition of
modules
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Conclusion and Contributions
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The proposed control method can be used
successfully to supervise dynamic discreteevent systems
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achieves near-optimal control
adapts automatically to dynamics in the system
allows a very flexible definition of requirements
is more robust to system failures
is easily implementable as modular software
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Selected References
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C. G. Cassandras and S. Lafortune. Introduction to
Discrete Event Systems. Kluwer Academic Publishers,
Norwell, Massachusetts, USA, 1999,
Sheng-Luen Chung, Stéphane Lafortune, and Feng
Lin. Limited lookahead policies in supervisory control
of discrete event systems. IEEE Transactions on
Automatic Control, 37(12):1921–1935, 1992,
Sheng-Luen Chung, Stéphane Lafortune, and Feng
Lin. Supervisory control using variable lookahead
policies. Discrete Event Dynamic Systems: Theory
and Applications, 4:237–268, 1994.
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