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INTRODUCTION TOHYBRID SYSTEMS:
ORIGINS, EXAMPLES, APPLICATIONS
C. G. CassandrasDept. of Manufacturing EngineeringandCenter for Information and Systems Engineering (CISE)Boston [email protected]://vita.bu.edu/cgc
Christos G. Cassandras CODES Lab. - Boston University
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OUTLINE
WHAT’S A HYBRID SYSTEM…
HYBRID SYSTEMS AND COMPLEXITY:DECOMPOSITION: HYBRID SYSTEM → DESABSTRACTION: DES → HYBRID SYSTEM
EXAMPLES, APPLICATION AREAS
Christos G. Cassandras CODES Lab. - Boston University
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NEW “MODE”
x0
x1
),,( 1111 tuzgz =&
TIME
x1
x2
),,,( 11011 tuzxfx =
),,( 2222 tuzgz =&
),,,( 22122 tuzxfx =
Christos G. Cassandras CODES Lab. - Boston University
More on modeling frameworks, open problems, etc: [Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000]More on modeling frameworks, open problems, etc: [Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000]
TIME-DRIVENDYNAMICS
EVENT-DRIVENDYNAMICS
WHAT’S A HYBRID SYSTEM?
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WHAT’S A HYBRID SYSTEM? CONTINUED
TIME
x0
x1
TIME
x1
x2
TIME
x2
x3
TIME
x3
x4
TIME
xi
xi+1
xi
xi+1
),,(:DRIVENTIME
tuzgz iiii =&
),,,(:DRIVEN-EVENT
1 tuzxfx iiiii =+
Christos G. Cassandras CODES Lab. - Boston University
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WHAT’S A HYBRID SYSTEM? CONTINUED
x1 x2
…
Physical State, z
Temporal State, xxi
xi+1 = fi(xi,ui,t)SWITCHING TIMESHAVE THEIR OWN
DYNAMICS!
SWITCHING TIMESHAVE THEIR OWN
DYNAMICS!
),,( tuzgz iiii =&
hybrid
Switching Times
Christos G. Cassandras CODES Lab. - Boston University
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WHAT’S A HYBRID SYSTEM? CONTINUED
PLANT
CONTROLLER
REPLACE THE USUAL CONTROL LOOP BYREPLACE THE USUAL CONTROL LOOP BY
PLANTPLANT
CONTROLLER
EVENTS
SUPERVISOR
Christos G. Cassandras CODES Lab. - Boston University
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WHAT’S A HYBRID SYSTEM? CONTINUED
PLANT
EVENT-DRIVENDYNAMICS
TIME-DRIVENDYNAMICS
CONTROLLER
• Plant: time-driven + event-driven dynamics
• Controller affects bothtime-driven + event-driven components
• Control may becontinuous signal and/or discrete event
Christos G. Cassandras CODES Lab. - Boston University
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Christos G. Cassandras CODES Lab. - Boston University
TIME-DRIVENSYSTEMS
HYBRIDSYSTEMS
1980
1990
2000
EVENT-DRIVENSYSTEMS
CONTINUOUS DISCRETE
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DECOMPOSITION
Christos G. Cassandras CODES Lab. - Boston University
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Christos G. Cassandras CODES Lab. - Boston University
MORE COMPLEXLESS COMPLEX
TIME-DRIVENSYSTEM
EVENT-DRIVENSYSTEM
DECOMPOSITIONLESS COMPLEX
What exactlydoes that mean?
What exactlydoes that mean? HYBRID
SYSTEM
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HIERARCHICAL DECOMPOSITION
PHYSICALPROCESSES
DISCRETE-EVENTPROCESSES
???
PLANNING
AIRCRAFTFLIGHTDYNAMICS
COMMANDS,RANDOMEVENTS
FLIGHT PLAN
Christos G. Cassandras CODES Lab. - Boston University
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HIEARARCHICAL DECOMPOSITION CONTINUED
PHYSICALPROCESSES
DISCRETE-EVENTPROCESSES
???
PLANNINGDiff. Eq’s, Flows, LP
Automata, Petri nets,Queueing, Simulation
Diff. Eq’s, Detailed Simulation
MODELMODEL
Weeks - Months
Minutes - Weeks
msec - Hours
TIME SCALETIME SCALE
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID CONTROL SYSTEM
PHYSICALPROCESSES
DISCRETE-EVENTPROCESSES
CONTROLCONTROL
What exactlydoes that mean?
What exactlydoes that mean?
Christos G. Cassandras CODES Lab. - Boston University
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ABSTRACTION(AGGREGATION)
Christos G. Cassandras CODES Lab. - Boston University
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TIME-DRIVENSYSTEM
MORE COMPLEXLESS COMPLEX
HYBRIDSYSTEM
ZOOM OUT
EVENT-DRIVENSYSTEM
ABSTRACTION(AGGREGATION)LESS COMPLEX
Christos G. Cassandras CODES Lab. - Boston University
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LESS COMPLEX MORECOMPLEX
HYBRIDSYSTEM
Christos G. Cassandras CODES Lab. - Boston University
TIME-DRIVENSYSTEM
EVENT-DRIVENSYSTEM
HYBRIDSYSTEM
ABSTRACTION(AGGREGATION) DECOMPOSITION
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TOO CLOSE…too much
undesirabledetail
TOO FAR…model not
detailed enough
Christos G. Cassandras CODES Lab. - Boston University
JUST RIGHT…good model CREDIT: W.B. Gong
WHAT IS THE RIGHT ABSTRACTION LEVEL ?
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EXAMPLES
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEM EXAMPLES
1. Autonomous Switching, e.g., Hysteresis
uxx +=& uxx +−=&∆≥x
∆−≤x
∆−>x∆<x
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEM EXAMPLES CONTINUED
2. External Switching, e.g., Zeno’s bouncing ball
mgvvyvvx
yy
xx
−====
&&
&&
,0 ,
SwitchingEvents
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEM EXAMPLES CONTINUED
3. Controlled Switching, e.g., Interconnected tanks
Christos G. Cassandras CODES Lab. - Boston University
u1(t)
u3(t)
HIGH
LOW
HIGH
LOW
HIGH
LOW
u2(t)
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HYBRID SYSTEM EXAMPLES CONTINUED
4. Other cases of controlled switching:
- Diving: control depths for decompression
TRADEOFF: Safety vs. Time
- Vehicle transmission: control gear switching
TRADEOFF: Efficiency vs. Time
- Low-power electronics: power control
TRADEOFF: Power conservation vs. Time
- Manufacturing: process control + operational control
TRADEOFF: Product quality vs. Time
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEMS IN MANUFACTURING
Key questions facing manufacturing system integrators:
• How to integrate ‘process control’ with ‘operations control’ ?
• How to improve product QUALITY within reasonable TIME ?
PROCESS CONTROL• Physicists• Material Scientists• Chemical Engineers• ...
OPERATIONS CONTROL• Industrial Engineers, OR• Schedulers• Inventory Control• ...
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEMS IN MANUFACTURING CONTINUED
Throughout a manuf. process, each part is characterized by
• A PHYSICAL state (e.g., size, temperature, strain)
• A TEMPORAL state (e.g., total time in system, total time to due-date)
OPERATIONOPERATION
NEW TEMPORAL
STATE
TEMPORALSTATE
PHYSICALSTATE
NEW PHYSICAL
STATE
Time-drivenDynamics
Event-drivenDynamics
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEMS IN MANUFACTURING CONTINUED
EVENT-DRIVENCOMPONENT
TIME-DRIVENCOMPONENT
PartArrivals Part
Departures
ui ( )tuzgtz iii ,,)( =&
ai, zi(ai) xi, zi(xi)
{ } )(,max 1 iiiii usaxx += −
Christos G. Cassandras CODES Lab. - Boston University
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EXAMPLE
PROCESS TIMEPROCESS TIME
STATESTATE
ust be processed
this state(e.g., desired temperature)
zi(ui)
si(ui)
Every part starts
at this state
…and mto
Christos G. Cassandras CODES Lab. - Boston University
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HYBRID SYSTEMS IN COOPERATIVE CONTROL
Christos G. Cassandras CODES Lab. - Boston University
BASE
TARGET
THREATS
TIME-DRIVENDYNAMICS
EVENT: threat sensed
EVENT: info. communicated by team member
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HYBRID SYSTEMS IN COOP. CONTROL CONTINUED
Christos G. Cassandras CODES Lab. - Boston University
V1
V2
V3
V4
V5
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HYBRID SYSTEMS IN COOP. CONTROL CONTINUED
Christos G. Cassandras CODES Lab. - Boston University
V1
V2
V3
V4
V5
Optimal headingOver
Event-DrivenReceding Horizon
V6
Current Control Horizon
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ABSTRACTION OF A DISCRETE-EVENT SYSTEM
Christos G. Cassandras CODES Lab. - Boston University
DISCRETE-EVENTSYSTEM
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ABSTRACTION OF A DISCRETE-EVENT SYSTEM
DISCRETE-EVENTSYSTEM
HYBRIDSYSTEM
Christos G. Cassandras CODES Lab. - Boston University
EVENTSTIME-DRIVENFLOW RATE DYNAMICS
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http://vita.bu.edu/cgc/hybrid
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DESIGN, ANALYSIS, SYNTHESIS ISSUES
Differential equationswith jumps/switches:Stability, RobustnessOptimal Control, etc.
TIME-DRIVENWORLD
EVENT-DRIVENWORLD
Automata with state transitions dependent on diff. equations:Supervisory Control, ReachabilityPerturbation Analysis, etc.
DECIDABILITY, VERIFICATION, QUANTIZATION, SIMULATION, …[Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000][Proc. of IEEE Special Issue (Antsaklis, Ed.), 2000]
Christos G. Cassandras CODES Lab. - Boston University