INTRODUCTION TO HYBRID SYSTEMS · N E W “M O D E ” x0 x1 z&1 =g1(z1,u1,t) TIME x1 x2 x1...

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


NEW “MODE”

x0

x1

),,( 1111 tuzgz =&

TIME

x1

x2

),,,( 11011 tuzxfx =

),,( 2222 tuzgz =&

),,,( 22122 tuzxfx =


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 =+



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



PLANT

CONTROLLER

REPLACE THE USUAL CONTROL LOOP BYREPLACE THE USUAL CONTROL LOOP BY

PLANTPLANT

CONTROLLER

EVENTS

SUPERVISOR



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



TIME-DRIVENSYSTEMS

HYBRIDSYSTEMS

1980

1990

2000

EVENT-DRIVENSYSTEMS

CONTINUOUS DISCRETE

DECOMPOSITION



MORE COMPLEXLESS COMPLEX

TIME-DRIVENSYSTEM

EVENT-DRIVENSYSTEM

DECOMPOSITIONLESS COMPLEX

What exactlydoes that mean?

What exactlydoes that mean? HYBRID

SYSTEM

HIERARCHICAL DECOMPOSITION

PHYSICALPROCESSES

DISCRETE-EVENTPROCESSES

???

PLANNING

AIRCRAFTFLIGHTDYNAMICS

COMMANDS,RANDOMEVENTS

FLIGHT PLAN


HIEARARCHICAL DECOMPOSITION CONTINUED

PHYSICALPROCESSES


???

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


HYBRID CONTROL SYSTEM

PHYSICALPROCESSES


CONTROLCONTROL




ABSTRACTION(AGGREGATION)


TIME-DRIVENSYSTEM

MORE COMPLEXLESS COMPLEX

HYBRIDSYSTEM

ZOOM OUT

EVENT-DRIVENSYSTEM

ABSTRACTION(AGGREGATION)LESS COMPLEX


LESS COMPLEX MORECOMPLEX

HYBRIDSYSTEM


TIME-DRIVENSYSTEM

EVENT-DRIVENSYSTEM

HYBRIDSYSTEM

ABSTRACTION(AGGREGATION) DECOMPOSITION

TOO CLOSE…too much

undesirabledetail

TOO FAR…model not

detailed enough


JUST RIGHT…good model CREDIT: W.B. Gong

WHAT IS THE RIGHT ABSTRACTION LEVEL ?

EXAMPLES


HYBRID SYSTEM EXAMPLES

1. Autonomous Switching, e.g., Hysteresis

uxx +=& uxx +−=&∆≥x

∆−≤x

∆−>x∆<x


HYBRID SYSTEM EXAMPLES CONTINUED

2. External Switching, e.g., Zeno’s bouncing ball

mgvvyvvx

yy

xx

−====

&&

&&

,0 ,

SwitchingEvents



3. Controlled Switching, e.g., Interconnected tanks


u1(t)

u3(t)

HIGH

LOW

HIGH

LOW

HIGH

LOW

u2(t)


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


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• ...


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


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 += −


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


HYBRID SYSTEMS IN COOPERATIVE CONTROL


BASE

TARGET

THREATS

TIME-DRIVENDYNAMICS

EVENT: threat sensed

EVENT: info. communicated by team member

HYBRID SYSTEMS IN COOP. CONTROL CONTINUED


V1

V2

V3

V4

V5

HYBRID SYSTEMS IN COOP. CONTROL CONTINUED


V1

V2

V3

V4

V5

Optimal headingOver

Event-DrivenReceding Horizon

V6

Current Control Horizon

ABSTRACTION OF A DISCRETE-EVENT SYSTEM


DISCRETE-EVENTSYSTEM

ABSTRACTION OF A DISCRETE-EVENT SYSTEM

DISCRETE-EVENTSYSTEM

HYBRIDSYSTEM


EVENTSTIME-DRIVENFLOW RATE DYNAMICS

http://vita.bu.edu/cgc/hybrid


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]


INTRODUCTION TO HYBRID SYSTEMS · N E W “M O D E ” x0 x1 z&1 =g1(z1,u1,t) TIME x1 x2 x1...

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