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

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

Outline CPS: Introduction 1 Hybrid Systems & Cyber-Physical Systems Applications Robot Labs Course: Logical Foundations of Cyber-Physical Systems 2 Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources Summary 3 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28

Outline CPS: Introduction 1 Hybrid Systems & Cyber-Physical Systems Applications Robot Labs Course: Logical Foundations of Cyber-Physical Systems 2 Educational Approach Objectives Outline Labs CPS V&V Grand Prix Assessment Resources Summary 3 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 1 / 28

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

CPSs Promise Transformative Impact! Prospects: Safe & Efficient Pilot decision support Driver assistance Train protection Autopilots / UAVs Autonomous cars 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

Can you trust a computer to control physics? André Platzer (CMU) LFCPS/01: Overview LFCPS/01 4 / 28

Can you trust a computer to control physics? Depends on how it has been programmed 1 And on what will happen if it malfunctions 2 Rationale Safety guarantees require analytic foundations. 1 A common foundational core helps all application domains. 2 Foundations revolutionized digital computer science & our society. 3 Need even stronger foundations when software reaches out into our 4 physical world. CPSs deserve proofs as safety evidence! André Platzer (CMU) LFCPS/01: Overview LFCPS/01 4 / 28

CPSs are Multi-Dynamical Systems CPS Dynamics CPS are characterized by multiple facets of dynamical systems. e o n c t t e i n r c u s o i u d s l a stochastic i r a s r nondet e v d a CPS Compositions Tame Parts Exploiting compositionality CPS combines multiple tames CPS complexity. simple dynamical effects. Analytic simplification Descriptive simplification André Platzer (CMU) LFCPS/01: Overview LFCPS/01 5 / 28

CPSs are Multi-Dynamical Systems hybrid systems HS = discrete + ODE e o n c t t e i n r c u s o i u d s hybrid games stochastic hybrid sys. HG = HS + adversary SHS = HS + stochastics l a stochastic i r a 0.3 s r nondet 0.2 e 0.1 v d 5 10 15 20 a � 0.1 � 0.2 � 0.3 distributed hybrid sys. DHS = HS + distributed André Platzer (CMU) LFCPS/01: Overview LFCPS/01 6 / 28

CPS Analysis Challenge (CPS) Fixed rule describing state 3.5 evolution with both 3.0 2.5 Discrete dynamics 2.0 (control decisions) 1.5 Continuous dynamics 1.0 0.5 (differential equations) 0.0 0 1 2 3 4 5 6 a 1.0 v p 0.2 8 0.8 10 t 2 4 6 8 6 0.6 � 0.2 p x 4 0.4 � 0.4 � 0.6 0.2 2 p y � 0.8 10 t 10 t 2 4 6 8 2 4 6 8 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 7 / 28

CPS Analysis Challenge (CPS) Fixed rule describing state 3.5 evolution with both 3.0 2.5 Discrete dynamics 2.0 (control decisions) 1.5 Continuous dynamics 1.0 0.5 (differential equations) 0.0 0 1 2 3 4 5 6 d a Ω 1.0 d x 0.2 0.5 10 t 0.5 2 4 6 8 10 t 2 4 6 8 � 0.2 � 0.5 10 t � 0.4 2 4 6 8 d y � 0.6 � 1.0 � 0.5 � 0.8 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 7 / 28

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

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

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 2: Follow the Leader 4: Obstacles 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.0 0.5 0.0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

LFCPS Labs 1: Charging Station 3: Racetrack 4: Obstacles 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0 1 2 3 4 5 6 0.0 0 1 2 3 4 6 5 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 0 1 2 3 4 6 5 0 1 2 3 4 5 6 � Design, model � Verify André Platzer (CMU) LFCPS/01: Overview LFCPS/01 10 / 28

CPS Analysis & Design: Robot Lab Challenge (Hybrid Systems) Design & verify controller for a 3.5 robot avoiding obstacles 3.0 2.5 Accelerate / brake 2.0 (discrete dynamics) 1.5 1.0 1D motion 0.5 (continuous dynamics) 0.0 0 1 2 3 4 6 5 0.2 a v p 5 0.8 0.1 4 0.6 10 t 2 4 6 8 3 0.4 � 0.1 p x 2 � 0.2 0.2 1 p y � 0.3 10 t 10 t 2 4 6 8 2 4 6 8 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 11 / 28

CPS Analysis & Design: Robot Lab Challenge (Hybrid Systems) Design & verify controller for a 3.5 robot avoiding obstacles 3.0 2.5 Accelerate / brake 2.0 (discrete dynamics) 1.5 1.0 1D motion 0.5 (continuous dynamics) 0.0 0 1 2 3 4 6 5 0.2 a d Ω 1.0 d x 0.00008 0.1 0.8 0.00006 10 t 0.6 2 4 6 8 0.00004 � 0.1 0.4 0.00002 � 0.2 0.2 10 t � 0.3 2 4 6 8 d y 10 t 2 4 6 8 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 11 / 28

CPS Analysis & Design: Robot Lab Challenge (Hybrid Systems) Design & verify controller for a 3.5 robot avoiding obstacles 3.0 2.5 Accelerate / brake / stop 2.0 (discrete dynamics) 1.5 1.0 1D motion 0.5 (continuous dynamics) 0.0 0 1 2 3 4 6 5 a 1.2 v p 10 t p x 3.5 2 4 6 8 1.0 3.0 � 0.05 2.5 0.8 2.0 � 0.10 0.6 1.5 0.4 � 0.15 1.0 p y 0.2 0.5 � 0.20 10 t 10 t 2 4 6 8 2 4 6 8 André Platzer (CMU) LFCPS/01: Overview LFCPS/01 12 / 28