EECE 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,

2 Hybrid Systems UC Berkeley 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

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 The Heterogeneity of Systems power train embedded controller sensors fuelair EH CI engine Continuous Time Finite State Machine Discrete Event An Engine Control System

6 Models of Computation power train embedded controller sensors fuelair EH CI engine Continuous Time continuous functions continuous time continuous signals Finite State Machine states transitions Discrete Event operations on events continuous time discrete events

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

8 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

9 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/AA/D

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

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

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

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 Power Electronics Discrete dynamics N switches, (up to) 2 N discrete states Only discrete inputs (switching): some discrete transitions under control, others not Continuous dynamics Linear or affine dynamics at each discrete state =8 possible configurations

19 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 Control switching to maintain Vout with changes in load (R), and Vin V in L CR sw1 sw V out iLiL iLiL 212

20 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 V in L C2C2 R2R2 sw1 sw V outA iLiL + - V outB sw3 C3C3 R3R3 iLiL V outA V outB

21 Circuit Operation One and only one switch closed at any time Each switch state has a continuous dynamics sw1: i L , V outA , V outB  sw2: i L , V outA , V outB  sw3: i L , V outA , V outB 

22 Design Objective Objective: Regulate two output voltages and limit current by switching between three discrete states with continuous dynamics. i L , V outA , V outB  i L , V outA , V outB  i L , V outA , V outB 

23 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 T  T(1-  )T i0i0 i1i1 i2i2 match! i L (t) i L [k]

24 Outline Background on Power Electronics Hybrid Modeling of DC-DC Converters Controlled Invariant Balls Conclusions V in L CR sw1 sw V out iLiL

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

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

32 Hybrid Systems

33 Motivating Examples: Thermostat Non-deterministic Hybrid Automaton

34 Motivating Examples:Two Tanks

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

36 Motivating Examples: Bouncing Ball Zeno Hybrid Autamaton

37 Computational Tools Simulation Ptolemy II: ptolemy.eecs.berkeley.eduptolemy.eecs.berkeley.edu Modelica: SHIFT: Dymola: OmSim: ABACUSS: yoric.mit.edu/abacuss/abacuss.htmlyoric.mit.edu/abacuss/abacuss.html Stateflow: CHARON: Masaccio:

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

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

40 Computational Tools – Hybrid Systems Reach Sets Computation Finite Automata Timed Automata Linear Automata Linear Hybrid Systems Nonlinear Hybrid Systems d/dt CheckMate Timed COSPAN KRONOS Timed HSIS VERITI UPPAAL HYTECHCOSPAN SMV VIS … Requiem

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) …

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

44 End