EECE 396-1
Hybrid and Embedded Systems: Computation
T. John Koo
Institute for Software Integrated Systems
Department of Electrical Engineering and Computer Science
Vanderbilt University
300 Featheringill Hall
January 14, 2004
john.koo@vanderbilt.edu
http://www.vuse.vanderbilt.edu/~kootj
Hybrid Systems

UC Berkeley






Stanford University


Spring 2002 by T. John Koo, S. Shankar Sastry
http://robotics.eecs.berkeley.edu/~koo/Sp02/
Spring 2001 by T. John Koo, S. Shankar Sastry
http://robotics.eecs.berkeley.edu/~koo/Sp01/
Spring 2000 by Karl. H. Johansson, Luca de Alfaro, Thomas A. Henzinger
http://www.s3.kth.se/~kallej/eecs291e/
Spring 1999 by John Lygeros, S. Shankar Sastry
http://robotics.eecs.berkeley.edu/~lygeros/Teaching/ee291E.html
Spring 1998 by Thomas A. Henzinger, S. Shankar Sastry
Spring 2002 by Claire Tomlin
http://www.stanford.edu/class/aa278a/
University of Pennsylvania

Fall 2000 by Rajeev Alur, George J. Pappas
http://www.seas.upenn.edu/~pappasg/EE601/
2
Hybrid System
 A system built from atomic discrete
components and continuous
components by parallel and serial
composition, arbitrarily nested.
q1
 The behaviors and interactions of
components are governed by models
of computation (MOCs).
 Discrete Components
u
q2
q3
x
xç = f (x) + g(x)u

Finite State Machine (FSM)
 Discrete Event (DE)
 Synchronous Data Flow (SDF)
 Continuous Components

Ordinary Differential Equation (ODE)
 Partial Differential Equation (PDE)
3
Hybrid System
 Continuous systems with phased
operations

Bouncing ball
 Circuits with diodes
 Switching circuits
 Continuous systems controlled by
discrete inputs





Thermostat
Water tank
Engine control systems
Multi-modal systems
Embedded control systems
q1
u
q2
q3
x
xç = f (x) + g(x)u
4
The Heterogeneity of Systems
engine
E State
H
Finite
Machine
C
power train
I
Continuous Time
fuel
air
Discrete Event
embedded controller
sensors
An Engine Control System
5
Models of Computation
Finite State Machine
• states
engine
• transitions
E
H
C
I
fuel
air
power train
Continuous Time
• continuous functions
• continuous time
• continuous signals
Discrete Event
• operations on events
embedded controller
• continuous time
• discrete events
sensors
6
The Hierarchical View of
Systems
controller
car model
engine
power
train
7
Embedded Systems
 Embedded systems
composed of hardware and
software components are
designed to interact with a
physical environment in
real-time in order to fulfill
control objectives and
design specifications.
Embedded Software
Operating System
Board Support Packages
Embedded Hardware
Environment
8
Embedded Systems
 Embedded software refers
to application software to
process information to and
fro between the information
and physical worlds.
q1
D/A
u
q2
Embedded Software
Operating System
q3
Board Support Packages
Embedded Hardware
A/D
x
Environment
xç = f (x) + g(x)u
9
High-Confidence
Embedded Software
Embedded Computer
Embedded
Software
 From Design to
Implementation
u [k ]
q1
u( t )
q2
q3
x (t )
Servos
q1
q2
q3
x [k ]
GPS Card
INS
How?
xç = f (x) + g(x)u
u( t )
x (t )
1. Guaranteed closed-loop performance
2. Interaction between asynchronous and
synchronous components
10
High-Confidence
Embedded Software
10Hz
Nav Data to
Vision computer
@10Hz
PERIODIC
VCOMM
ULREAD
4±1Hz
Ultrasonic
sensors@4±1Hz
APERIODIC
Nav data
Control output
at 50Hz
Relative Altitude
PERIODIC
100Hz
DQICONT
INS Update Boeing DQI-NP
RX values
Yamaha Receiver
(using HW INT & proxy)
DGPS measurement
Ground
Station
ANYTIME
Ground computer
Win 98
Processes
running on QNX
PRTK@ 5Hz
PXY@1Hz
PERIODIC
DQIGPS
GPS Update
RS-232
Shared Memory
Radio link
NovAtel GPS RT-2
11
Why Hybrid Systems?
 Modeling abstraction of

Continuous systems with phased operation (e.g. walking robots,
mechanical systems with collisions, circuits with diodes)
 Continuous systems controlled by discrete inputs (e.g. switches, valves,
digital computers)
 Coordinating processes (multi-agent systems)
 Important in applications

Hardware verification/CAD, real time software
 Manufacturing, communication networks, multimedia
 Large scale, multi-agent systems




Automated Highway Systems (AHS)
Air Traffic Management Systems (ATM)
Uninhabited Aerial Vehicles (UAV)
Power Networks
12
Different Approaches
13
Research Directions
14
What Are Hybrid Systems?
 Dynamical systems with interacting continuous and
discrete dynamics
15
Proposed Framework
Control Theory
Computer Science
Models of computation
Communication models
Discrete event systems
Control of individual agents
Continuous models
Differential equations
Hybrid Systems
16
Power Electronics
 Power electronics found in:



DC-DC converters
Power supplies
Electric machine drives
 Circuits can be defined as networks of:

Voltage and current sources (DC or AC)
 Linear elements (R, L, C)
 Semiconductors used as switches (diodes, transistors)
ENNA GmbH
17
Power Electronics
 Discrete dynamics


N switches, (up to) 2N discrete states
Only discrete inputs (switching): some
discrete transitions under control, others
not
 Continuous dynamics

Linear or affine dynamics at each discrete
state
+
ENNA GmbH
+
23=8 possible configurations
18
Power Electronics : DC-DC
Converters
iL
+
Vin
-
L
sw1
2
sw2
C
R
1
2
+
Vout
-
Vout
 Have a DC supply (e.g. battery), but need
a different DC voltage
 Different configurations depending on
whether Vin<Vout or Vin>Vout
 Control switching to maintain Vout with
changes in load (R), and Vin
iL
19
Two Output DC-DC Converter
sw3
iL
C3
+
Vin
sw1
1
iL
VoutA
2
sw2
L
3 1
2
C2
R2
R3
+
+
VoutB
VoutA
-
-
3
 Want two DC output voltages
 Inductors are big and heavy, so
only want to use one
 Similar to “two tank” problem
VoutB
20
Circuit Operation
 One and only one switch
closed at any time
 Each switch state has a
continuous dynamics
sw1: iL, VoutA, VoutB
sw2: iL , VoutA , VoutB
sw3: iL , VoutA, VoutB 
21
Design Objective
iL , VoutA, VoutB 
iL, VoutA, VoutB
iL , VoutA , VoutB
Objective: Regulate two output voltages and limit current by
switching between three discrete states with continuous dynamics.
22
Typical Circuit
Analysis/Control
T
 Governing equations
T

Time domain, steady state
 Energy balance
 System dynamics

i1
Discretization in time



(1- )T
Switched quantity only sampled at
discrete instants
Assumes a fixed clock
i0
match!
Averaging


Switched quantity approximated
by a moving average
Assumes switching is much faster
than system time constants
i2
iL(t)
iL(t)
 Control

Linearize with duty () as input
 Use classical control techniques
iL[k]
23
Outline
 Background on Power Electronics
 Hybrid Modeling of DC-DC Converters
 Controlled Invariant Balls
 Conclusions
iL
+
Vin
-
L
sw1
sw2
C
R
+
Vout
-
24
Problem Formulation
25
Problem Formulation
 Parallel Composition of Hybrid
H1
Automata
q1
û = û1
x 2 G12
x 2 G21
x2X
q2
 Given a collection of Modes
û = û2
and Edges, design Guards
H2
q1
xç(t ) = f q1(x(t ))
x(t ) 2 I q1
û2 Î
û = û2
û = û1
q2
xç(t ) = f q2(x(t ))
x(t ) 2 I q2
26
Research Issues
 Modeling & Simulation


Control: classify discrete phenomena, existence and uniqueness of
execution, Zeno [Branicky, Brockett, van der Schaft, Astrom]
Computer Science: composition and abstraction operations [AlurHenzinger, Lynch, Sifakis, Varaiya]
 Analysis & Verification

Control: stability, Lyapunov techniques [Branicky, Michel], LMI
techniques [Johansson-Rantzer]
 Computer Science: Algorithmic [Alur-Henzinger, Sifakis, PappasLafferrier-Sastry] or deductive methods [Lynch, Manna, Pnuelli],
Abstraction [Pappas-Tabuada, Koo-Sastry]
 Controller Synthesis


Control: optimal control [Branicky-Mitter, Bensoussan-Menaldi],
hierarchical control [Caines, Pappas-Sastry], supervisory control
[Lemmon-Antsaklis], safety specifications [Lygeros-Sastry, TomlinLygeros-Sastry], control mode switching [Koo-Pappas-Sastry]
Computer Science: algorithmic synthesis [Maler et.al., Wong-Toi],
synthesis based on HJB [Mitchell-Tomlin]
27
Hybrid Systems
28
Hybrid Systems
 Hybrid Automata (Lygeros-Tomlin-Sastry, 2001)
Ref: J. Lygeros, C. Tomlin, and S. Sastry,
The Art of Hybrid Systems, July 2001.
29
Hybrid Systems
Enabled Discrete Evolution
Guard AB
Q
Reset AB
Invariant set A
X
Invariant set B
30
Hybrid Systems
Forced Discrete Evolution
Guard AB
Q
Reset AB
Invariant set A
X
Invariant set B
31
Hybrid Systems
32
Thermostat
Non-deterministic Hybrid
Automaton
t
33
Motivating Examples:Two
Tanks
34
Zeno—infinitely many jumps
in finite time
If
Water Tank Automaton
35
Motivating Examples:
Bouncing Ball
Zeno Hybrid Autamaton
36
Computational Tools
 Simulation
 Ptolemy II: ptolemy.eecs.berkeley.edu
 Modelica: www.modelica.org
 SHIFT: www.path.berkeley.edu/shift
 Dymola: www.dynasim.se
 OmSim: www.control.lth.se/~cace/omsim.html
 ABACUSS: yoric.mit.edu/abacuss/abacuss.html
 Stateflow: www.mathworks.com/products/stateflow
 CHARON: http://www.cis.upenn.edu/mobies/charon/
 Masaccio:
http://www-cad.eecs.berkeley.edu/~tah/Publications/masaccio.html
37
Computational Tools
 Simulation
Masaccio
CHARON
Ptolemy II
Dymola
Modelica
StateFlow/Simulink
System
Complexity
ABACUSS
SHIFT
OmSim
Models of Computation
38
Verification
 Deductive Methods

Theorem-Proving techniques [Lynch, Manna, Pnuelli]
 Model Checking

State-space exploration [Alur-Henzinger, Sifakis, Pappas-LafferrierSastry]
Reachability Problem
Check if Post ( X S) \ X F = ; ?
XF
XS
Post ( X S)
Forward Reachable Set
Post ( P) = f x 2 X j 9x 0 2 P 9t õ 0 s:t: x = þ( t; r i ; x 0)g
39
Computational Tools – Hybrid
Systems
 Reach Sets Computation
Finite
Automata
COSPAN
SMV
VIS
…
Timed
Automata
Linear
Automata
xç = 1
Axç ô b
xç = Ax
HYTECH
Requiem
Timed COSPAN
KRONOS
Timed HSIS
VERITI
UPPAAL
Linear
Hybrid Systems
Si (r i )
Nonlinear
Hybrid Systems
xç = f ( x )
d/dt
CheckMate
Sj (r j )
Pr ei (Sj (r j ); r i )
40
Research Directions
Development of formal methods for the design of
high-confidence embedded software based on
hybrid system theory with applications to
distributed, network-centric, embedded systems
such as sensor networks, power electronics
circuits, and cooperative UAV systems
 Hybrid Systems
 Embedded Software
 High-Confidence Embedded Systems
 Network-Centric Distributed Systems
41
Research Collaboration
 Institutions








Center for Hybrid and Embedded Systems and Software (CHESS),
University of California at Berkeley
GRASP Laboratory, University of Pennsylvania
Hybrid Systems Laboratory, Stanford University
Control Group, Cambridge University
INRIA, France
KTH, Sweden
Honeywell Laboratories
Cadence Berkeley Laboratory
 Conferences





Workshop on Hybrid Systems: Computation and Control (HSCC)
Workshop on Embedded Software (EMSOFT)
IEEE Conference on Decision and Control (CDC)
IEEE Conference on Robotics and Automation (ICRA)
…
42
International Workshop on
Hybrid Systems: Computation and Control
University of Pennsylvania
March, 2004
http://www.seas.upenn.edu/hybrid/HSCC04/
End
44