[PPT] - INTRODUCTION TO INTRODUCTION TO HYBRID SYSTEMS: HYBRID SYSTEMS: PowerPoint Presentation

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INTRODUCTION TO INTRODUCTION TO HYBRID SYSTEMS: HYBRID SYSTEMS:

ORIGINS, EXAMPLES, APPLICATIONS ORIGINS, EXAMPLES, APPLICATIONS

C. G. Cassandras
C. G. Cassandras
Dept. of Manufacturing Engineering

and Center for Information and Systems Engineering (CISE) Boston University cgc@bu.edu http://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 → DES ABSTRACTION: DES → HYBRID SYSTEM

EXAMPLES, APPLICATION AREAS

Christos G. Cassandras CODES Lab. - Boston University

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N N E E W W “ M “ M O O D D E E ” ”

x0 x1

) , , (

1 1 1 1

t u z g z = &

TIME

x1 x2

) , , , (

1 1 1 1

t u z x f x = ) , , (

2 2 2 2

t u z g z = & ) , , , (

2 2 1 2 2

t u z x f x =

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-DRIVEN DYNAMICS EVENT-DRIVEN DYNAMICS

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

) , , ( : DRIVEN TIME t u z g z

i i i i =

& ) , , , ( : DRIVEN

EVENT

1

t u z x f x

i i i i i

=

+

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 5

WHAT’S A HYBRID SYSTEM?

CONTINUED

x1 x2

…

Physical State, z Temporal State, x

xi

xi+1 = fi(xi,ui,t)

SWITCHING TIMES HAVE THEIR OWN DYNAMICS! SWITCHING TIMES HAVE THEIR OWN DYNAMICS!

) , , ( t u z g z

i i i i =

& 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 BY REPLACE THE USUAL CONTROL LOOP BY

PLANT PLANT

CONTROLLER

EVENTS

SUPERVISOR

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 7

WHAT’S A HYBRID SYSTEM?

CONTINUED

PLANT

EVENT-DRIVEN DYNAMICS TIME-DRIVEN DYNAMICS

CONTROLLER

Plant: time-driven +

event-driven dynamics

Controller affects both

time-driven + event-driven components

Control may be

continuous signal and/or discrete event

Christos G. Cassandras CODES Lab. - Boston University

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Christos G. Cassandras CODES Lab. - Boston University

TIME-DRIVEN SYSTEMS

HYBRID SYSTEMS

1980 1990 2000

EVENT-DRIVEN SYSTEMS

CONTINUOUS DISCRETE

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DECOMPOSITION DECOMPOSITION

Christos G. Cassandras CODES Lab. - Boston University

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Christos G. Cassandras CODES Lab. - Boston University

MORE COMPLEX LESS COMPLEX

TIME-DRIVEN SYSTEM EVENT-DRIVEN SYSTEM

DECOMPOSITION DECOMPOSITION LESS COMPLEX

What exactly does that mean? What exactly does that mean?

HYBRID SYSTEM

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HIERARCHICAL DECOMPOSITION

PHY PHYSIC ICAL AL PROCESSES PROCESSES DISCRETE-EVENT DISCRETE-EVENT PROCESSES PROCESSES ??? ??? PLANNING PLANNING

AIRCRAFT FLIGHT DYNAMICS COMMANDS, RANDOM EVENTS FLIGHT PLAN

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 12

HIEARARCHICAL DECOMPOSITION

CONTINUED

PHY PHYSIC ICAL AL PROCESSES PROCESSES DISCRETE-EVENT DISCRETE-EVENT PROCESSES PROCESSES ??? ??? PLANNING PLANNING

Diff. Eq’s, Flows, LP

Automata, Petri nets, Queueing, Simulation

Diff. Eq’s,

Detailed Simulation MODEL MODEL Weeks - Months Minutes - Weeks msec - Hours TIME SCALE TIME SCALE

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 13

HYBRID CONTROL SYSTEM

PHYSICAL PHYSICAL PROCESSES PROCESSES DISCRETE-EVENT DISCRETE-EVENT PROCESSES PROCESSES

CONTROL CONTROL CONTROL CONTROL

What exactly does that mean? What exactly does that mean?

Christos G. Cassandras CODES Lab. - Boston University

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ABSTRACTION ABSTRACTION (AGGREGATION) (AGGREGATION)

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 15

TIME-DRIVEN SYSTEM

MORE COMPLEX LESS COMPLEX

HYBRID SYSTEM

ZOOM OUT

EVENT-DRIVEN SYSTEM

ABSTRACTION ABSTRACTION (AGGREGATION) GGREGATION) LESS COMPLEX

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 16

LESS COMPLEX MORECOMPLEX

HYBRID SYSTEM

Christos G. Cassandras CODES Lab. - Boston University

TIME-DRIVEN SYSTEM EVENT-DRIVEN SYSTEM HYBRID SYSTEM

ABSTRACTION ABSTRACTION (AGGREGATION) GGREGATION) DECOMPOSITION DECOMPOSITION

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TOO CLOSE…

too much undesirable detail

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 EXAMPLES

Christos G. Cassandras CODES Lab. - Boston University

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HYBRID SYSTEM EXAMPLES

1. Autonomous Switching, e.g., Hysteresis

u x x + = & u x x + − = & ∆ ≥ x ∆ − ≤ x ∆ − > x ∆ < x

Christos G. Cassandras

CODES Lab. - Boston University

SLIDE 20

HYBRID SYSTEM EXAMPLES

CONTINUED

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

mg v v y v v x

y y x x

− = = = = & & & & , ,

Switching Events

Christos G. Cassandras

CODES Lab. - Boston University

SLIDE 21

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

SLIDE 24

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)

OPERATION OPERATION

NEW TEMPORAL STATE TEMPORAL STATE PHYSICAL STATE NEW PHYSICAL STATE

Time-driven Dynamics Event-driven Dynamics

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 25

HYBRID SYSTEMS IN MANUFACTURING

CONTINUED

EVENT-DRIVEN COMPONENT TIME-DRIVEN COMPONENT

Part Arrivals Part Departures

ui

( )

t u z g t z

i i i

, , ) ( = &

ai, zi(ai) xi, zi(xi)

{ }

) ( , max

1 i i i i i

u s a x x + =

−

Christos G. Cassandras CODES Lab. - Boston University

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EXAMPLE

PROCESS TIME PROCESS TIME STATE STATE

ust be processed this state (e.g., desired temperature)

zi(ui) si(ui)

Every part starts at this state …and m to

Christos G. Cassandras CODES Lab. - Boston University

SLIDE 27

HYBRID SYSTEMS IN COOPERATIVE CONTROL

Christos G. Cassandras CODES Lab. - Boston University

BASE TARGET THREATS

TIME-DRIVEN DYNAMICS 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 heading Over Event-Driven Receding Horizon V6 Current Control Horizon

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ABSTRACTION OF A DISCRETE-EVENT SYSTEM

Christos G. Cassandras CODES Lab. - Boston University

DISCRETE-EVENT SYSTEM

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ABSTRACTION OF A DISCRETE-EVENT SYSTEM

DISCRETE-EVENT SYSTEM HYBRID SYSTEM

Christos G. Cassandras CODES Lab. - Boston University

EVENTS TIME-DRIVEN FLOW RATE DYNAMICS

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

Christos G. Cassandras CODES Lab. - Boston University

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DESIGN, ANALYSIS, SYNTHESIS ISSUES

Differential equations with jumps/switches: Stability, Robustness Optimal Control, etc. TIME-DRIVEN WORLD EVENT-DRIVEN WORLD Automata with state transitions dependent on diff. equations: Supervisory Control, Reachability Perturbation 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