ESE 601: Hybrid Systems. Instructor: Agung Julius Teaching assistant: Ali Ahmadzadeh

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1 ESE 601: Hybrid Systems Instructor: Agung Julius Teaching assistant: Ali Ahmadzadeh

2 Schedule Class schedule : Monday & Wednesday Towne 305 Office hours : to be discussed (3 hrs/week) s: agung@seasupennedu aliahmad@graspupennedu

3 Course website Visit the course website: wwwseasupennedu/~agung/ese601htm I will post course plan, announcements, downloadable course materials, homework sets Join the course mailing list in the website Q&A and announcements outside of the class can be done through the mailing list Important: Following the university regulation, some course materials on the website will be password protected

4 Grading There will be three homework sets (15 points each), due after 2 weeks You can discuss the homework, but do not copy, ie work independently Tentative homework schedule is on the website There will be no exam, but final project (55 points) If time permits, there will be project presentation

5 Final project You have to submit a project proposal (1-2 pages) that describes: What you want to do in the project How the project is related with the course References (if any) A project can be, for example: A summary of a few coherent papers Modeling and/or analysis of hybrid systems Controller design You have to submit a project report (>6 pages)

6 Course contents Review on background materials (continuous and discrete event systems) Introduction to hybrid systems, modeling formalisms Modeling and analysis tool CHARON Verification of hybrid systems and software tools Stability analysis of hybrid systems

7 Course contents Controller design Stochastic hybrid systems Guest lectures on HS in biology and robotics

8 Hybrid systems Hybrid systems: systems that have both continuous and discrete aspects in the dynamics Continuous: continuous time, differential equations, smooth evolution, infinite/noncountable states Discrete: discontinuities, finite/countable states, discrete time

9 Discrete and Continuous Control Theory Continuous systems Stability, control Feedback, robustness Computer Science Transition systems Composition, abstraction Concurrency models Hybrid Systems Software controlled systems Multi-modal systems Embedded real-time systems Multi-agent systems

10 Emerging applications Latest BMW : 72 networked microprocessors Boeing 777 : 1280 networked microprocessors

11 Networked embedded systems Network Controller SW/HW Controller SW/HW Actuator Sensor Actuator Sensor Physical System Physical System

12 Networked embedded systems Network Controller SW/HW Controller SW/HW Actuator Sensor Actuator Sensor Physical System Physical System Physical system is continuous, software is discrete

millions Post-explosion analysis singled out a software program as the cause of the accident Interestingly, the same program

13 Lesson from Ariane 5 Ariane 5, an unmanned rocket, was launched on 4 th June 1996 The rocket exploded 37s after launching, due to software error The program had been running for 10 years, costing $7 billions The rocket and its cargo itself cost $500 millions Post-explosion analysis singled out a software program as the cause of the accident Interestingly, the same program functioned perfectly on Ariane 4, and was copied to Ariane 5 for that reason What had changed, was the physical system around the software

14 Exporting Science Control Theory Continuous systems Stability, control Feedback, robustness Computer Science Transition systems Composition, abstraction Concurrency models Composition Abstraction Concurrency Robustness Feedback Stability

15 Different views Computer science perspective View the physics from the eyes of the software Modeling result : Hybrid automaton Control theory perspective View the software from the eyes of the physics Modeling result : Switched control systems

16 Hybrid behavior arises in Hybrid dynamics Hybrid model is a simplification of a larger nonlinear model Quantized control of continuous systems Input and observation sets are finite Logic based switching Software is designed to supervise various dynamics/controllers Partial synchronization of many continuous systems Resource allocation for competing multi-agent systems Hybrid specifications of continuous systems Plant is continuous, but specification is discrete or hybrid

17 Nuclear reactor example Without rods With rod 1 With rod 2 T = 01 T T = 01 T T = 01 T Rod 1 and 2 cannot be used simultaneously Once a rod is removed, you cannot use it for 10 minutes Specification : Keep temperature between 510 and 550 degrees If T=550 then either a rod is available or we shutdown the plant

18 Software model of nuclear reactor Rod1 NoRod Rod2 Shutdown

19 Hybrid model of nuclear reactor T = 510 y = 10 y2 1 = 10 Rod1 NoRod T Rod2 550 y = T = 01 T 56 T = 01 T 50 T = 01 T 60 y 1 = 1 y 2 = 1 y 1 = 1 y 2 = 1 y 1 = 1 y 2 = 1 T 510 T = 510 y : = 1 0 T 550 T = 510 y : = 0 2 T 510 T = 550 y < 10 y2 1 < 10 Analysis : Is shutdown reachable? Algorithmic verification : NO Shutdown T = 01 T 50 y 1 = 1 y 2 = 1 true

20 The train gate example x θ approach raise lower exit Controller System = Train Gate Controller Safety specification : If train is within 10 meters of the crossing, then gate should completely closed Liveness specification : Keep gate open as much as possible

21 Train model x 2000 far near past - 50 x 40 x = 1000 approach x = 0-50 x x 30 x 1000 exit x = 100 x' [2000, ) x 0 x -100

22 Gate model θ = 90 raise raising θ = 9 θ = 90 open θ = 0 raise θ 90 lower θ = 90 raise lower raise lowering θ = 9 θ = 0 closed θ = 0 θ 0 θ = 0 lower lower

23 Controller model y : = 0 exit true Goingtolower y : = 0 idle y : = 0 Goingto raise ẏ = 1 approach ẏ = 1 exit ẏ = 1 y d lower true raise y d y : = 0 approach

24 Synchronized transitions x 2000 far - 50 x 40 x = 1000 approach near past x = 0-50 x x 30 x 1000 exit x = 100 x' [2000, ) x 0 x -100 y : = 0 exit true Going tolower y : = 0 idle y : = 0 Going to raise ẏ = 1 approach ẏ = 1 exit ẏ = 1 y d lower true raise y d y : = 0 approach

25 Verifying the controller x θ approach raise lower exit Controller System = Train Gate Controller Safety specification : Can we avoid the set θ > 0 (-10 x 10)? Parametric verification : 49 YES if d 5

An introduction to hybrid systems theory and applications. Thanks to. Goals for this mini-course. Acknowledgments. Some references

An introduction to hybrid systems theory and applications Thanks to School Organizers Maurice Heemels Bart De Schutter George J Pappas Departments of ESE and CIS University of Pennsylvania pappasg@eeupennedu