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Note for Embedded System - ES by Abhishek Apoorv

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c Copyright 2010 Edward Ashford Lee & Sanjit Arunkumar Seshia All rights reserved Version 0.5 August 14, 2010 ISBN xxx-xxx-xxx-x

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Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii What this Book is About . . . . . . . . . . . . . . . . . . . . . . . xiii Why We Wrote this Book . . . . . . . . . . . . . . . . . . . . . . . xiv What is Missing . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii How to Use this Book . . . . . . . . . . . . . . . . . . . . . . . . . xvii Sidebar: Reporting Errors . . . . . . . . . . . . . . . . . . . . . . xix Intended Audience . . . . . . . . . . . . . . . . . . . . . . . . . . xx Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . xx Sidebar: Notes for Instructors . . . . . . . . . . . . . . . . . . . . xx Sidebar: Further Reading . . . . . . . . . . . . . . . . . . . . . . . xxi 1 Introduction 1 1.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Sidebar: About the Term “Cyber-Physical Systems” . . . . . . . . . 2 1.2 Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 The Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 1.3.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 iii

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CONTENTS I Modeling Dynamic Behaviors 17 2 Continuous Dynamics 19 2.1 2.2 2.3 Newtonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . Actor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Systems . . . . . . . . . . . . . . . . . . . . . . . . . 20 25 29 2.3.1 Causal Systems . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.2 Memoryless Systems . . . . . . . . . . . . . . . . . . . . . 30 2.3.3 Linearity and Time Invariance . . . . . . . . . . . . . . . . 30 2.3.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 38 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Discrete Dynamics 43 3.1 Discrete Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Sidebar: Probing Further: Discrete Signals . . . . . . . . . . . . . 46 Sidebar: Probing Further: Modeling Actors as Functions . . . . . . 47 The Notion of State . . . . . . . . . . Finite-State Machines . . . . . . . . . 3.3.1 Transitions . . . . . . . . . . 3.3.2 When a Reaction Occurs . . . Sidebar: Probing Further: Hysteresis . . . . . 49 50 50 54 54 Update Functions . . . . . . . . . . . . . . . . . . . . . . . 56 Sidebar: Software Tools Supporting FSMs . . . . . . . . . . . . . . 57 3.3.4 Determinacy and Receptiveness . . . . . . . . . . . . . . . 59 3.4 Extended State Machines . . . . . . . . . . . . . . . . . . . . . . . Sidebar: Moore Machines and Mealy Machines . . . . . . . . . . . 59 60 3.5 Nondeterminism . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Formal Model . . . . . . . . . . . . . . . . . . . . . . . . . 65 67 2.4 2.5 3 3.2 3.3 3.3.3 iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lee & Seshia, Introduction to Embedded Systems, version 0.5

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