Logical Foundations of Cyber-Physical Systems Andr Platzer Andr - - PowerPoint PPT Presentation

▶
logical foundations of cyber physical systems
SMART_READER_LITE
LIVE PREVIEW

Logical Foundations of Cyber-Physical Systems Andr Platzer Andr - - PowerPoint PPT Presentation

Oct 25, 2023 433 likes •940 views

Logical Foundations of Cyber-Physical Systems 01: Cyber-Physical Systems: Overview Andr Platzer Logical Foundations of Cyber-Physical Systems Andr Platzer Andr Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28 Outline CPS:

slide-1
SLIDE 1

Logical Foundations of Cyber-Physical Systems

01: Cyber-Physical Systems: Overview

Logical Foundations of Cyber-Physical Systems

André Platzer

André Platzer

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28

slide-2
SLIDE 2

Outline

1

CPS: Introduction Hybrid Systems & Cyber-Physical Systems Applications Robot Labs

2

Course: Logical Foundations of Cyber-Physical Systems Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources

3

Summary

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28

slide-3
SLIDE 3

Outline

1

CPS: Introduction Hybrid Systems & Cyber-Physical Systems Applications Robot Labs

2

Course: Logical Foundations of Cyber-Physical Systems Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources

3

Summary

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28

slide-4
SLIDE 4

Cyber-Physical Systems Analysis: Aircraft Example

Which control decisions are safe for aircraft collision avoidance?

Cyber-Physical Systems

CPSs combine cyber capabilities with physical capabilities to solve problems that neither part could solve alone.

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 2 / 28

slide-5
SLIDE 5

CPSs Promise Transformative Impact!

Prospects: Safe & Efficient

Driver assistance Autonomous cars Pilot decision support Autopilots / UAVs Train protection Robots near humans

Prerequisite: CPSs need to be safe

How do we make sure CPSs make the world a better place?

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 3 / 28

slide-6
SLIDE 6

Can you trust a computer to control physics?

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 4 / 28

slide-7
SLIDE 7

Can you trust a computer to control physics?

1

Depends on how it has been programmed

2

And on what will happen if it malfunctions

Rationale

1

Safety guarantees require analytic foundations.

2

A common foundational core helps all application domains.

3

Foundations revolutionized digital computer science & our society.

4

Need even stronger foundations when software reaches out into our physical world.

CPSs deserve proofs as safety evidence!

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 4 / 28

slide-8
SLIDE 8

CPSs are Multi-Dynamical Systems

d i s c r e t e c

  • n

t i n u

  • u

s nondet stochastic a d v e r s a r i a l

CPS Dynamics

CPS are characterized by multiple facets of dynamical systems.

CPS Compositions

CPS combines multiple simple dynamical effects. Descriptive simplification

Tame Parts

Exploiting compositionality tames CPS complexity. Analytic simplification

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 5 / 28

slide-9
SLIDE 9

CPSs are Multi-Dynamical Systems

d i s c r e t e c

  • n

t i n u

  • u

s nondet stochastic a d v e r s a r i a l

hybrid systems

HS = discrete+ ODE

stochastic hybrid sys.

SHS = HS+ stochastics

5 10 15 20 0.3 0.2 0.1 0.1 0.2 0.3

hybrid games

HG = HS+ adversary

distributed hybrid sys.

DHS = HS+ distributed

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 6 / 28

slide-10
SLIDE 10

CPS Analysis

Challenge (CPS)

Fixed rule describing state evolution with both Discrete dynamics (control decisions) Continuous dynamics (differential equations)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.8 0.6 0.4 0.2 0.2

a

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0v 2 4 6 8 10 t 2 4 6 8

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 7 / 28

slide-11
SLIDE 11

CPS Analysis

Challenge (CPS)

Fixed rule describing state evolution with both Discrete dynamics (control decisions) Continuous dynamics (differential equations)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.8 0.6 0.4 0.2 0.2

a

2 4 6 8 10 t 1.0 0.5 0.5

Ω

2 4 6 8 10 t 0.5 0.5 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 7 / 28

slide-12
SLIDE 12

Hybrid Systems Versus Cyber-Physical Systems

Mathematical model for complex physical systems:

Definition (Hybrid Systems)

Systems with interacting discrete and continuous dynamics Technical characteristics:

Definition (Cyber-Physical Systems)

(Distributed networks of) computerized control for physical system Communication, computation, and control for physics

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 8 / 28

slide-13
SLIDE 13

What CPSs are around us? What CPSs will be around us in the future? Which CPSs do we trust with our lives?

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 9 / 28

slide-14
SLIDE 14

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify 2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-15
SLIDE 15

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify 2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-16
SLIDE 16

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify 4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-17
SLIDE 17

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify 4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-18
SLIDE 18

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-19
SLIDE 19

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2: Follow the Leader

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Design, model Verify

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-20
SLIDE 20

LFCPS Labs

1: Charging Station

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

3: Racetrack Design, model Verify 4: Obstacles

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

slide-21
SLIDE 21

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.3 0.2 0.1 0.1 0.2a 2 4 6 8 10 t 0.2 0.4 0.6 0.8

v

2 4 6 8 10 t 1 2 3 4 5

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 11 / 28

slide-22
SLIDE 22

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.3 0.2 0.1 0.1 0.2a 2 4 6 8 10 t 0.00002 0.00004 0.00006 0.00008

Ω

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 11 / 28

slide-23
SLIDE 23

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake / stop (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.20 0.15 0.10 0.05

a

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0 1.2v 2 4 6 8 10 t 0.5 1.0 1.5 2.0 2.5 3.0 3.5

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 12 / 28

slide-24
SLIDE 24

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake / stop (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.20 0.15 0.10 0.05

a

2 4 6 8 10 t 0.00002 0.00004 0.00006 0.00008 0.00010 0.00012

Ω

2 4 6 8 10 t 1.0 0.5 0.5 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 12 / 28

slide-25
SLIDE 25

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.3 0.2 0.1 0.1 0.2a 2 4 6 8 10 t 0.2 0.4 0.6 0.8

v

2 4 6 8 10 t 0.5 1.0 1.5 2.0 2.5

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 13 / 28

slide-26
SLIDE 26

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accelerate / brake (discrete dynamics) 1D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.3 0.2 0.1 0.1 0.2a 2 4 6 8 10 t 0.00002 0.00004 0.00006 0.00008

Ω

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 13 / 28

slide-27
SLIDE 27

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accel / brake / steer (discrete dynamics) 2D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.8 0.6 0.4 0.2 0.2

a

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0v 2 4 6 8 10 t 2 4 6 8

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 14 / 28

slide-28
SLIDE 28

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Accel / brake / steer (discrete dynamics) 2D motion (continuous dynamics)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.8 0.6 0.4 0.2 0.2

a

2 4 6 8 10 t 1.0 0.5 0.5

Ω

2 4 6 8 10 t 0.5 0.5 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 14 / 28

slide-29
SLIDE 29

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Dynamic obstacles (other agents) Avoid collisions (define safety)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 4 3 2 1

a

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0v 2 4 6 8 10 t 1 2 3 4

p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 15 / 28

slide-30
SLIDE 30

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Dynamic obstacles (other agents) Avoid collisions (define safety)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 4 3 2 1

a

2 4 6 8 10 t 1.0 0.5 0.5

Ω

2 4 6 8 10 t 0.5 0.5 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 15 / 28

slide-31
SLIDE 31

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Control robot (respect delays) Environment interaction (obstacles, agents, uncertainty)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.6 0.4 0.2 0.2 0.4

a

2 4 6 8 10 t 0.2 0.4 0.6 0.8 1.0 1.2v 2 4 6 8 10 t 1 2 3 4 5 6 7p

px py

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 16 / 28

slide-32
SLIDE 32

CPS Analysis & Design: Robot Lab

Challenge (Hybrid Systems)

Design & verify controller for a robot avoiding obstacles Control robot (respect delays) Environment interaction (obstacles, agents, uncertainty)

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 4 6 8 10 t 0.6 0.4 0.2 0.2 0.4

a

2 4 6 8 10 t 1.0 0.5 0.5

Ω

2 4 6 8 10 t 0.5 0.5 1.0

d

dx dy

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 16 / 28

slide-33
SLIDE 33

Outline

1

CPS: Introduction Hybrid Systems & Cyber-Physical Systems Applications Robot Labs

2

Course: Logical Foundations of Cyber-Physical Systems Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources

3

Summary

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 16 / 28

slide-34
SLIDE 34

Logical Foundations

  • f

Cyber-Physical Systems

Logic

Theorem Proving Proof Theory Modal Logic Model Checking

Algebra

Computer Algebra R Algebraic Geometry Differential Algebra Lie Algebra

Analysis

Differential Equations Carath´ edory Solutions Viscosity PDE Solutions Dynamical Systems

Stochastics

Doob’s Super- martingales Dynkin’s Infinitesimal Generators Differential Generators Stochastic Differential Equations

Numerics

Hermite Interpolation Weierstraß Approx- imation Error Analysis Numerical Integration

Algorithms

Decision Procedures Proof Search Procedures Fixpoints & Lattices Closure Ordinals

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 17 / 28

slide-35
SLIDE 35

How to Teach Cyber-Physical Systems?

Onion Model

1

Going outside in

2

Unpeel layer by layer

3

Progress when all prereqs are covered

4

First study CS ∧ math ∧ engineering

5

Talk about CPS in the big finale

Scenic Tour Model

1

Start at the heart: CPS

2

Go on scenic expeditions into various directions

3

Explore the world around us as we find the need

4

Stay on CPS the whole time

5

Leverage CPS as the guiding motivation for understanding more about connected areas

Logical Foundations
  • f
Cyber-Physical Systems Logic Theorem Proving Proof Theory Modal Logic Model Checking Algebra Computer Algebra R Algebraic Geometry Differential Algebra Lie Algebra Analysis Differential Equations Carath´ edory Solutions Viscosity PDE Solutions Dynamical Systems Stochastics Doob’s Super- martingales Dynkin’s Infinitesimal Generators Differential Generators Stochastic Differential Equations Numerics Hermite Interpolation Weierstraß Approx- imation Error Analysis Numerical Integration Algorithms Decision Procedures Proof Search Procedures Fixpoints & Lattices Closure Ordinals

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 18 / 28

slide-36
SLIDE 36

Computational Thinking for CPS

Logical scrutiny, formalization, and correctness proofs are critical for CPS!

1

CPSs are so easy to get wrong.

2

Retrofitting CPSs for safety is not possible.

3

These logical aspects are an integral part of CPS design.

4

Critical to your understanding of the intricate complexities of CPS.

5

Tame complexity by a simple programming language for core aspects.

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 19 / 28

slide-37
SLIDE 37

About Logical Foundations of Cyber-Physical Systems

Foundations! Modeling & Control

1

Understand the core principles behind CPSs.

2

Develop models and controls.

3

Identify the relevant dynamical aspects.

Computational Thinking

1

Identify safety specifications and critical properties of CPSs.

2

Understand abstraction in system design.

3

Express pre- and postconditions for CPS models.

4

Use design-by-invariant.

5

Reason rigorously about CPS models.

6

Verify CPS models of appropriate scale.

CPS Skills

1

Understand the semantics of a CPS model.

2

Develop an intuition for operational effects.

3

Identify control constraints.

4

Understand opportunities and challenges in CPS and verification.

Byproducts

1

Well-motivated exposure to numerous math and science areas in action.

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 20 / 28

slide-38
SLIDE 38

Learning Objectives

CT M&C CPS identify safety specifications for CPS rigorous reasoning about CPS understand abstraction & architectures programming languages for CPS verify CPS models at scale cyber+physics models core principles of CPS relate discrete+continuous semantics of CPS models

  • perational effects

identify control constraints

  • pportunities and challenges

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 21 / 28

slide-39
SLIDE 39

Textbook and Course Outline

I Part: Elementary Cyber-Physical Systems

  • 2. Differential Equations & Domains
  • 3. Choice & Control
  • 4. Safety & Contracts
  • 5. Dynamical Systems & Dynamic Axioms
  • 6. Truth & Proof
  • 7. Control Loops & Invariants
  • 8. Events & Responses
  • 9. Reactions & Delays

II Part: Differential Equations Analysis

  • 10. Differential Equations & Differential Invariants
  • 11. Differential Equations & Proofs
  • 12. Ghosts & Differential Ghosts
  • 13. Differential Invariants & Proof Theory

III Part: Adversarial Cyber-Physical Systems

  • 17. Hybrid Systems & Hybrid Games

IV Part: Comprehensive CPS Correctness

Logical Foundations of Cyber-Physical Systems

André Platzer

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 22 / 28

slide-40
SLIDE 40

1 Introduction 2 Differential Equations & Domains 3 Choice & Control 4 Safety & Contracts 5 Dynamical Systems & Dynamic Axioms 6 Truth & Proof 7 Control Loops & Invariants 8 Events 9 Reactions & Delays 10 Differential Invariants 14–17 Hybrid Games I Elementary CPS III Adversarial CPS 11 Differential Equations & Proofs 12 Differential Ghosts 13 Differential Proof Theory II Advanced CPS 18 Axioms & Uniform Subst. 19 Verified Models & Runtime Validation 20 Virtual Substitution & Real Equations 21 Virtual Substitution & Real Arithmetic IV Comprehensive CPS

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 23 / 28

slide-41
SLIDE 41

Robot Model Labs

1

Robot on Rails

a

Autobots, Roll Out

b

Charging Station

2

Robot on Highways: Follow the Leader

a

with event-triggered control

b

with time-triggered control

3

Robot on Racetracks

a

stay on the circular racetrack

b

slow down to avoid collisions

4

Robot in a Plane

a

with obstacle avoidance

b

Robot vs. Roguebot: don’t collide with moving obstacles

5

Robot in Star-lab: self-defined final project

6

Final project presented at CPS V&V Grand Prix

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1 2 3 4 0.0 0.5 1.0 1.5 2.0 2.5

1 2 3 4 5 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

CPS V&V Grand Prix André Platzer (CMU) LFCPS/01: Overview LFCPS/01 24 / 28

slide-42
SLIDE 42

CPS V&V Grand Prix: Course Competition

2016 CPS V&V Grand Prix Carnegie Mellon University May 5th, 2016

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 25 / 28

slide-43
SLIDE 43

Assessment

TODO: Read Course Policies

Syllabus

≈22% Theory homework

Due at midnight

≈51% Labs, including ≈22% final project

1

Betabot in first week Due at beginning of lecture

2

Veribot in second week Due at midnight

Whitepaper For final project Proposal For final project Term paper Due with final project CPS V&V Grand Prix presentation Tue Dec 11

≈11% Midterm

In class

≈11% Final

In class

≈5% Participation in class and in online comments

Partner allowed for labs only and only starting in lab 2 TODO: Theory 0 prep homework Due this week

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 26 / 28

slide-44
SLIDE 44

Resources

Prerequisites

15-122 Principles of Imperative Computation if-then-else 21-120 Differential and Integral Calculus x′ (21-241 Matrix algebra or 15-251 Great Theoretical Ideas in Computer Science or Math proofs 18-202 Mathematical Foundations of Electrical Engineering) Substitutes: 21-242 Matrix theory or 21-341 Linear algebra I for 21-241 You are expected to follow extra material in the textbook. Further reading and background material on the course web page Check course web page periodically http://lfcps.org/course/lfcps.html KeYmaera X: aXiomatic Tactical Theorem Prover for Hybrid Systems Piazza, Autolab, Ask!

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 27 / 28

slide-45
SLIDE 45

Outline

1

CPS: Introduction Hybrid Systems & Cyber-Physical Systems Applications Robot Labs

2

Course: Logical Foundations of Cyber-Physical Systems Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources

3

Summary

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 27 / 28

slide-46
SLIDE 46

Logical Foundations of Cyber-Physical Systems

Logical foundations make a big difference for CPS, and vice versa

differential dynamic logic

dL = DL+ HP [α]ϕ ϕ α Strong analytic foundations Practical reasoning advances Significant applications Catalyze many science areas

1

Multi-dynamical systems

2

Combine simple dynamics

3

Tame complexity

4

V&V cool challenges Numerous wonders remain to be discovered

d i s c r e t e c

  • n

t i n u

  • u

s nondet stochastic a d v e r s a r i a l

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 28 / 28

slide-47
SLIDE 47

Logical Foundations of Cyber-Physical Systems

Logical foundations make a big difference for CPS, and vice versa

differential dynamic logic

dL = DL+ HP [α]ϕ ϕ α Strong analytic foundations Practical reasoning advances Significant applications Catalyze many science areas KeYmaera X Numerous wonders remain to be discovered

d i s c r e t e c

  • n

t i n u

  • u

s nondet stochastic a d v e r s a r i a l

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 28 / 28

slide-48
SLIDE 48

André Platzer. Logical Foundations of Cyber-Physical Systems. Springer, Switzerland, 2018. URL: http://www.springer.com/978-3-319-63587-3,

doi:10.1007/978-3-319-63588-0.

André Platzer. Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer, Heidelberg, 2010.

doi:10.1007/978-3-642-14509-4.

André Platzer. Logics of dynamical systems. In LICS, pages 13–24, Los Alamitos, 2012. IEEE.

doi:10.1109/LICS.2012.13.

André Platzer. Differential dynamic logic for hybrid systems.

  • J. Autom. Reas., 41(2):143–189, 2008.

doi:10.1007/s10817-008-9103-8.

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 28 / 28

slide-49
SLIDE 49

André Platzer. A complete uniform substitution calculus for differential dynamic logic.

  • J. Autom. Reas., 59(2):219–265, 2017.

doi:10.1007/s10817-016-9385-1.

André Platzer. Logic & proofs for cyber-physical systems. In Nicola Olivetti and Ashish Tiwari, editors, IJCAR, volume 9706 of LNCS, pages 15–21, Berlin, 2016. Springer.

doi:10.1007/978-3-319-40229-1_3.

André Platzer. Differential game logic. ACM Trans. Comput. Log., 17(1):1:1–1:51, 2015.

doi:10.1145/2817824.

André Platzer. Differential hybrid games. ACM Trans. Comput. Log., 18(3):19:1–19:44, 2017.

doi:10.1145/3091123.

André Platzer (CMU) LFCPS/01: Overview LFCPS/01 28 / 28