1. 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

2. Hybrid Systems UC Berkeley Stanford University
Spring 2002 by T. John Koo, S. Shankar Sastry
Spring 2001 by T. John Koo, S. Shankar Sastry
Spring 2000 by Karl. H. Johansson, Luca de Alfaro, Thomas A. Henzinger
Spring 1999 by John Lygeros, S. Shankar Sastry
Spring 1998 by Thomas A. Henzinger, S. Shankar Sastry
Stanford University
Spring 2002 by Claire Tomlin
University of Pennsylvania
Fall 2000 by Rajeev Alur, George J. Pappas 2

3. Hybrid System
A system built from atomic discrete components and continuous components by parallel and serial composition, arbitrarily nested.
The behaviors and interactions of components are governed by models of computation (MOCs).
Discrete Components
Finite State Machine (FSM)
Discrete Event (DE)
Synchronous Data Flow (SDF)
Continuous Components
Ordinary Differential Equation (ODE)
Partial Differential Equation (PDE) 3

4. 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 4

5. The Heterogeneity of Systems
power train
Discrete Event
Continuous Time
Finite State
Machine
engine E H C I
(I)Intake - (C) Compression – (E) Ignition – (H) Exhaust
fuel
air
embedded controller
sensors
An Engine Control System 5

6. Models of Computation power train E H C I fuel air embedded controller
Finite State Machine
states
transitions
engine E H C I
Continuous Time
continuous functions
continuous time
continuous signals
fuel
air
Discrete Event
operations on events
continuous time
discrete events
embedded controller
sensors 6

7. The Hierarchical View of Systems
controller
car model
engine
power
train I C H E 7

8. Board Support Packages
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.
Environment
Embedded Hardware
Board Support Packages
Operating System
Embedded Software
This is the kind of embedded system we are interested.
(You may want to close the loop, according to Shankar)
Environment refers to the collection of objects which cannot be designed
Platform refers to Embedded hardware, board support packages and operating system which can be selected for constructing the system. Commercial off-the-shelf are commonly used.
Use of the middleware helps isolate application software components from the underlying hardware and operating systems in the embedded computing platform 8

9. Board Support Packages
Embedded Systems
Embedded software refers to application software to process information to and fro between the information and physical worlds.
Environment
Embedded Hardware
Board Support Packages
Operating System
Embedded Software
D/A
A/D
(You may want to close the LOOP, according to Shankar)
Environment refers to the collection of objects which cannot be designed
Platform refers to Embedded hardware, board support packages and operating system which can be selected for constructing the system. Commercial off-the-shelf are commonly used.
Use of the middleware helps isolate application software components from the underlying hardware and operating systems in the embedded computing platform 9

10. High-Confidence Embedded Software
Embedded Computer
From Design to Implementation
Embedded
Software
How?
Servos
GPS Card
INS
1. Guaranteed closed-loop performance
2. Interaction between asynchronous and synchronous components 10

11. High-Confidence Embedded Software
4±1Hz
10Hz
Nav Data to
Vision computer
@10Hz
PERIODIC
VCOMM
ULREAD
Ultrasonic
APERIODIC
Relative Altitude
Nav data
Processes
running on QNX
Control output
at 50Hz
DQICONT
PERIODIC
100Hz
INS Update
Boeing DQI-NP
Flight Status
Command
RX values
Yamaha Receiver
(using HW INT & proxy)
Ground
Station
Concurrent processes
Explain: current configuration
We would like to show the case of integrating different legancy system componensts
Rather than synthesizing them all at once. Is all about integration!!
DGPS measurement
RS-232
5Hz
DQIGPS
Shared Memory
ANYTIME
PERIODIC
Radio link
GPS Update
Ground computer
Win 98
NovAtel GPS RT-2 11

12. Why Hybrid Systems? Modeling abstraction of Important in applications
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

13. Different Approaches 13

14. Research Directions 14

15. What Are Hybrid Systems?
Dynamical systems with interacting continuous and discrete dynamics 15

16. Proposed Framework Control Theory Computer Science Hybrid Systems
Control of individual agents
Continuous models
Differential equations
Computer Science
Models of computation
Communication models
Discrete event systems
Hybrid Systems 16

17. 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

18. Power Electronics Discrete dynamics Continuous 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

19. Power Electronics : DC-DC Converters
Vin L C R
sw1
sw2 + -
Vout iL iL
Vout 2 1
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 19

20. Two Output DC-DC Converter
Vin L C2 R2
sw1
sw2 + -
VoutA iL
VoutB
sw3 C3 R3 iL
VoutA
VoutB 1 2 3
US Patent since it can reduce the number of inductors used by having extra switches!!
Want two DC output voltages
Inductors are big and heavy, so only want to use one
Similar to “two tank” problem 20

21. Circuit Operation sw1: iL, VoutA, VoutB sw2: iL , VoutA , VoutB
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

22. Design Objective iL , VoutA, VoutB  iL, VoutA, VoutB
Objective: Regulate two output voltages and limit current by switching between three discrete states with continuous dynamics. 22

23. Typical Circuit Analysis/Control
match!
Governing equations
Time domain, steady state
Energy balance
System dynamics
Discretization in time
Switched quantity only sampled at discrete instants
Assumes a fixed clock
Averaging
Switched quantity approximated by a moving average
Assumes switching is much faster than system time constants
Control
Linearize with duty () as input
Use classical control techniques
iL(t)
iL(t)
iL[k] 23

24. Outline Background on Power Electronics
Hybrid Modeling of DC-DC Converters
Controlled Invariant Balls
Conclusions
Vin L C R
sw1
sw2 + -
Vout iL 24

25. Problem Formulation
Connectivity between each pair of modes defines an edge 25

26. Problem Formulation Parallel Composition of Hybrid Automata
Given a collection of Modes and Edges, design Guards
Given a design of DC-DC converter, one can model it as a hybrid automaton. State-feedback is used. But the control is a discrete symbol which corresponds to a specific switch configuration.
Notice that the design is event-triggered and exact. While using duty cycle, the controller is based on time domain analysis on a discrete-time averaged system model. 26

27. Research Issues Modeling & Simulation Analysis & Verification
Control: classify discrete phenomena, existence and uniqueness of execution, Zeno [Branicky, Brockett, van der Schaft, Astrom]
Computer Science: composition and abstraction operations [Alur-Henzinger, Lynch, Sifakis, Varaiya]
Analysis & Verification
Control: stability, Lyapunov techniques [Branicky, Michel], LMI techniques [Johansson-Rantzer]
Computer Science: Algorithmic [Alur-Henzinger, Sifakis, Pappas-Lafferrier-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, Tomlin-Lygeros-Sastry], control mode switching [Koo-Pappas-Sastry]
Computer Science: algorithmic synthesis [Maler et.al., Wong-Toi], synthesis based on HJB [Mitchell-Tomlin] 27

28. Hybrid Systems 28

29. Hybrid Systems Hybrid Automata (Lygeros-Tomlin-Sastry, 2001)
Ref: J. Lygeros, C. Tomlin, and S. Sastry,
The Art of Hybrid Systems, July 2001. 29

30. Hybrid Systems Q X Enabled Discrete Evolution Guard AB Reset AB
Invariant set A X
Invariant set B 30

31. Hybrid Systems Q X Forced Discrete Evolution Guard AB Reset AB
Invariant set A X
Invariant set B 31

32. Hybrid Systems 32

33. Motivating Examples: Thermostat Non-deterministic Hybrid Automaton33

34. Motivating Examples:Two Tanks34

35. Zeno—infinitely many jumps in finite timeIf
Water Tank Automaton 35

36. Motivating Examples: Bouncing Ball Zeno Hybrid Autamaton36

37. Computational Tools Simulation Ptolemy II: ptolemy.eecs.berkeley.edu
Modelica:
SHIFT:
Dymola:
OmSim:
ABACUSS: yoric.mit.edu/abacuss/abacuss.html
Stateflow:
CHARON:
Masaccio:
Omola is an object-oriented language for modelling of continuous time and discrete event dynamical systems.
OmSim is an environment for modelling and simulation based on Omola.
The object-oriented modeling language Modelica is designed to allow convenient, component-oriented modeling of complex physical systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-oriented subcomponents.
ABACUSS II is the next generation open modeling environment and simulator.
Dynasim has developed Dymola with a new technology for multi-enginering modeling and simulation for use within automotive, aerospace, robotics, process and other applications. Dymola allows simulation of the dynamic behavior and complex interactions between, for example, mechanical, electrical, thermodynamic, hydraulic and control systems. 37

38. Computational Tools Simulation Masaccio CHARON Ptolemy II Dymola
Modelica
StateFlow/Simulink
System
Complexity
Omola is an object-oriented language for modelling of continuous time and discrete event dynamical systems.
OmSim is an environment for modelling and simulation based on Omola.
The object-oriented modeling language Modelica is designed to allow convenient, component-oriented modeling of complex physical systems, e.g., systems containing mechanical, electrical, electronic, hydraulic, thermal, control, electric power or process-oriented subcomponents.
ABACUSS II is the next generation open modeling environment and simulator.
Dynasim has developed Dymola with a new technology for multi-enginering modeling and simulation for use within automotive, aerospace, robotics, process and other applications. Dymola allows simulation of the dynamic behavior and complex interactions between, for example, mechanical, electrical, thermodynamic, hydraulic and control systems.
ABACUSS
SHIFT
OmSim
Models of Computation 38

39. Verification Deductive Methods Model Checking
Theorem-Proving techniques [Lynch, Manna, Pnuelli]
Model Checking
State-space exploration [Alur-Henzinger, Sifakis, Pappas-Lafferrier-Sastry]
Reachability Problem
Forward Reachable Set 39

40. Computational Tools – Hybrid Systems
Reach Sets Computation
Finite
Automata
Timed
Automata
Linear
Automata
Linear
Hybrid Systems
Nonlinear
Hybrid Systems
COSPAN
SMV
VIS …
Timed COSPAN
KRONOS
Timed HSIS
VERITI
UPPAAL
HYTECH
Requiem
d/dt
CheckMate
Verification tools
One thing that I would like to do here is to develop reachability tools for Nonlinear Hybrid Systems 40

41. 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
the 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, and cooperative UAV systems.
Hybrid Systems
Embedded Software
High-Confidence Embedded Systems
Network-Centric Distributed Systems 41

42. 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

43. International Workshop on Hybrid Systems: Computation and Control University of Pennsylvania March, 2004

44. End 44