1. CSCI1600: Embedded and Real Time Software Lecture 8: Modeling III: Hybrid Systems Steven Reiss, Fall 2015

2. Time and Finite State Automata  We’ve added timing to our automata in an ad-hoc fashion  Added timer events  Indicated length of time in a state (min/max)  No notion of absolute time, clocks, etc.  In order to prove properties of the system  With respect to time  We need a cleaner, more formal representation

3. Timed Automata  Basic idea  Extended finite state machine  Add the notion of timer variables (bounded)  Timer variables can be set explicitly  All timer variables are periodically incremented  Can think of this as every k milliseconds  But in general it is considered a tick  Timer variables can be used in conditions  No ad-hoc time constraints

4. Timed Automata

5. Another example

6. Extended timed automata

7. Modeling and the Real World  Often we want to model both the system and the world  The system is a finite automata  The real world is continuous & not just clocks  Problems  How to combine the two  What can we do with the combination  Understanding  Proving properties

8. Modeling in the Real World

9. Hybrid Automata  State variables reflect the real world  Updates done over time automatically  Updates can use continuous modeling  Can specify velocity, acceleration rather than position  Can specify rules for doing the update

10. Bouncing Ball Example

11. RC Car

12. Hybrid Timed Automata  The external (timed) portion is set outside the automata  Rules for continuous update  Model the physics of the real world

13. Why Model the World?  Does the code need to know the state of the real world  Either precisely or approximately  Does it need to compute that state  Or retrieve it via sensors  How accurate can you model the world?  Consider speed control on a car  Proving properties of the program wrt the model  Does this prove the system correct

14. Implementation Approach  Get information from the real world  What the actual speed is, change of speed  Actual temperature (and change rate)  Compute the difference between actual and desired  This is called the error  Use this to determine the action  This is considered feedback

15. Control Theory  Why are computers called “digital computers”  What is the alternative  What is an analog computer  It turns out that analog computers are easy to build  Either mechanically or electronically  Predate digital computers

16. Analog Computers

17. Analog Computer  Can do simple math operations  Some complex math operations are easy  Integration, differentiation

18. Controlling Physical Systems  Analog computers are designed for this  If you want a car to go in a straight line  Use feedback from left/right to update steering  Use intergrator to determine how much off and to control system  Analog control is all about feedback  We can do the same in digital systems  Covered a week from Monday  First we need to cover details for the assignment  And some additional modeling concepts

19. Homework  Read Chapter 7.1