EECE 396-1 Hybrid and Embedded Systems: Computation

1. EECE 396-1Hybrid 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

2. Hybrid Systems • UC Berkeley • 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 • Stanford University • 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/

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)

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

5. Finite State Machine E H C I Continuous Time Discrete Event The Heterogeneity of Systems power train engine fuel air embedded controller sensors An Engine Control System

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

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

8. Embedded Software Operating System Board Support Packages Embedded Hardware Environment 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.

9. Embedded Software Operating System Board Support Packages D/A A/D Embedded Hardware Environment Embedded Systems • Embedded software refers to application software to process information to and fro between the information and physical worlds.

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

11. High-Confidence Embedded Software 10Hz 4±1Hz Nav Data to Vision computer @10Hz Ultrasonic sensors@4±1Hz Nav data Relative Altitude Control output at 50Hz Flight Status Boeing DQI-NP INS Update Command Yamaha Receiver (using HW INT & proxy) RX values VCOMM ULREAD PERIODIC APERIODIC Processes running on QNX DQICONT PERIODIC 100Hz Ground Station DGPS measurement RS-232 PRTK@ 5Hz PXY@1Hz Shared Memory DQIGPS PERIODIC ANYTIME Radio link GPS Update Ground computer Win 98 NovAtel GPS RT-2

12. 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

13. Different Approaches

14. Research Directions

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

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

17. ENNA GmbH 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)

18. ENNA GmbH + + 23=8 possible configurations 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

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

20. iL sw3 1 2 3 1 2 3 + C3 R3 sw2 + iL VoutB + L VoutA - Vin sw1 C2 R2 - - VoutA VoutB Two Output DC-DC Converter • Want two DC output voltages • Inductors are big and heavy, so only want to use one • Similar to “two tank” problem

21. sw1: iL, VoutA, VoutB sw2: iL , VoutA , VoutB sw3: iL , VoutA, VoutB  Circuit Operation • One and only one switch closed at any time • Each switch state has a continuous dynamics

22. 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.

23. T  T (1- )T i1 i0 i2 match! Typical Circuit Analysis/Control • 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]

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

25. Problem Formulation

26. Problem Formulation • Parallel Composition of Hybrid Automata • Given a collection of Modes and Edges, design Guards

27. 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 [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]

28. Hybrid Systems

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

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

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

32. Hybrid Systems

33. Motivating Examples: ThermostatNon-deterministic Hybrid Automaton

34. Motivating Examples:Two Tanks

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

36. Motivating Examples: Bouncing BallZeno Hybrid Autamaton

37. 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

38. Computational Tools • Simulation Masaccio CHARON Ptolemy II Dymola Modelica StateFlow/Simulink System Complexity ABACUSS SHIFT OmSim Models of Computation

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

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

41. Research Directions • Hybrid Systems • Embedded Software • High-Confidence Embedded Systems • Network-Centric Distributed Systems 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

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) • …

43. International Workshop on Hybrid Systems: Computation and ControlUniversity of PennsylvaniaMarch, 2004 http://www.seas.upenn.edu/hybrid/HSCC04/

44. End