Embedded systems ecec 356 fall 2014 cat 268
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Embedded Systems ECEC 356 –Fall 2014 CAT 268. Chapter 3 – model based design Chapter 4 – extended state machines and hybrid automata. Eric Wait 10/7-9/2014. Last Week – Chapter 2 This Week – Chapter 3,4 Next Week – Chapter 4, exam 1. Eric Wait. LEVER 3-D. Credentials

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Embedded Systems ECEC 356 –Fall 2014 CAT 268

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Embedded systems ecec 356 fall 2014 cat 268

Embedded SystemsECEC 356 –Fall 2014 CAT 268

  • Chapter 3 – model based design

  • Chapter 4 – extended state machines and hybrid automata

Eric Wait

10/7-9/2014


Embedded systems ecec 356 fall 2014 cat 268

  • Last Week – Chapter 2

  • This Week – Chapter 3,4

  • Next Week – Chapter 4, exam 1


Embedded systems ecec 356 fall 2014 cat 268

Eric Wait

LEVER 3-D

  • Credentials

  • "Visualization and Correction of Automated Segmentation, Tracking and Lineaging from 5-D Stem Cell Image Sequences." BMC Bioinformatics 2014

  • “Segmentation of Occluded Hematopoietic Stem Cells from Tracking.” EMBC 2014

  • "Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing." Nat. Protocols 2011

  • BS,MS in CS UW-Milwaukee

  • Professional Photographer

  • Passions

  • Images (2-D & 3-D)

  • Cross discipline presentation

  • High Performance Computing

  • Computer Building

  • Teaching

  • Future

  • PhD in EE Drexel

  • Research in Image Processing


Montage

Montage


Fsm notation

FSM Notation

  • state

  • initial state

  • transition

  • self loop


Examples of guards for pure signals

Examples of Guards for Pure Signals


Examples of guards for signals with numerical values

Examples of Guards for Signals with Numerical Values


Example thermostat

Example: Thermostat

  • Exercise: From this picture, construct the formal mathematical model.


More notation default transitions

More Notation: Default Transitions

  • A default transition is enabled if no non-default transition is enabled and it either has no guard or the guard evaluates to true. When is the above default transition enabled?


Extended state machines

Extended State Machines


Traffic light controller

Traffic Light Controller


Definitions

Definitions

  • Stuttering transition: Implicit default transition that is enabled when inputs are absent and that produces absent outputs.

  • Receptiveness: For any input values, some transition is enabled. Our structure together with the implicit default transition ensures that our FSMs are receptive.

  • Determinism: In every state, for all input values, exactly one (possibly implicit) transition is enabled.


Example nondeterminate fsm

Example: Nondeterminate FSM

  • Nondeterminate model of pedestrians arriving at a crosswalk:

  • Formally, the update function is replaced by a function


Behaviors and traces

Behaviors and Traces

  • FSM behavior is a sequence of (non-stuttering) steps.

  • A trace is the record of inputs, states, and outputs in a behavior.

  • A computation tree is a graphicalrepresentation of all possible traces.

  • FSMs are suitable for formalanalysis. For example, safetyanalysis might show that some unsafestate is not reachable.


Uses of nondeterminism

Uses of nondeterminism

  • Modeling unknown aspects of the environment or system

    • Such as: how the environment changes the iRobot’s orientation

  • Hiding detail in a specification of the system

    • We will see an example of this later (see notes)

  • Any other reasons why nondeterministic FSMs might be preferred over deterministic FSMs?


Size matters

Size Matters

  • Non-deterministic FSMs are more compact than deterministic FSMs

    • ND FSM  D FSM: Exponential blow-up in #states in worst case


Non deterministic behavior tree of computations

Non-deterministic Behavior: Tree of Computations

  • For a fixed input sequence:

  • A deterministic system exhibits a single behavior

  • A non-deterministic system exhibits a set of behaviors

  • Deterministic FSM behavior for a particular input sequence:

  • . . .

  • Non-deterministic FSM behavior for an input sequence:

  • . . .

  • . . .

  • . . .

  • . . .


Related points

Related points

  • What does receptiveness mean for non-deterministic state machines?

  • Non-deterministic  Probabilistic


Example from industry engine control

Example from Industry: Engine Control

  • Source:

  • Delphi Automotive Systems (2001)


Elements of a modal model fsm

Elements of a Modal Model (FSM)

  • initial state

  • state

  • input

  • output

  • transition

  • Source:

  • Delphi Automotive Systems (2001)


Embedded systems ecec 356 fall 2014 cat 268

It is sometimes useful to even model continuous systems as FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber


Actor model of an fsm

Actor Model of an FSM

  • This model enables composition of state machines.


What we will be able to do with fsms

What we will be able to do with FSMs

  • FSMs provide:

  • A way to represent the system for:

    • Mathematical analysis

    • So that a computer program can manipulate it

  • A way to model the environment of a system.

  • A way to represent what the system must do and must not do – its specification.

  • A way to check whether the system satisfies its specification in its operating environment.

  • Understanding states, transitions, inputs and outputs is a key preliminary step to developing a working system!


Chapter 4 esm and hybrid automata

Chapter 4 – ESM and hybrid automata


Homework 3

Homework 3

  • HW 3 – due beginning of class 10/14

  • Read Chapter 4 of Lee & Seshia

  • L&S problems 3.5, 4.1,4.5

  • Review Appendix A

  • Exam 1 – 10/16!


Instructor contact information

Instructor Contact Information

Andrew R. Cohen

Associate Prof.

Department of Electrical and Computer Engineering

Drexel University

3120 – 40 Market St., Suite 110

Philadelphia, PA 19104

office phone: (215) 571 – 4358

http://bioimage.coe.drexel.edu/courses

[email protected]


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