INTRODUCTION TO HYBRID SYSTEMS: ORIGINS, EXAMPLES, APPLICATIONS C. G. Cassandras Dept. of Manufacturing Engineering and Center for Information and Systems Engineering (CISE) Boston University [email protected]http://vita.bu.edu/cgc Christos G. Cassandras CODES Lab. - Boston University
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INTRODUCTION TO HYBRID SYSTEMS · N E W “M O D E ” x0 x1 z&1 =g1(z1,u1,t) TIME x1 x2 x1 =f1(x0,z1,u1,t) z&2 =g2(z2,u2,t) x2 =f2(x1,z2,u2,t) Christos G. Cassandras CODES Lab. -
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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
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
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?
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
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
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
Christos G. Cassandras CODES Lab. - Boston University
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
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
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
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
HYBRID SYSTEMS IN COOP. CONTROL CONTINUED
Christos G. Cassandras CODES Lab. - Boston University
V1
V2
V3
V4
V5
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
ABSTRACTION OF A DISCRETE-EVENT SYSTEM
Christos G. Cassandras CODES Lab. - Boston University
DISCRETE-EVENTSYSTEM
ABSTRACTION OF A DISCRETE-EVENT SYSTEM
DISCRETE-EVENTSYSTEM
HYBRIDSYSTEM
Christos G. Cassandras CODES Lab. - Boston University
EVENTSTIME-DRIVENFLOW RATE DYNAMICS
http://vita.bu.edu/cgc/hybrid
Christos G. Cassandras CODES Lab. - Boston University
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