Course introduction and administration.
Introduction to Embedded Systems.

Notes: Introduction

More on Embedded systems.
The synchronous model of reactive computation. Reactive components.

Notes:

• Introduction
• The Synchronous Model Part I

The Synchronous Model. Reactive components and their properties. Deterministic vs. non-deterministic, Combinational vs. stateful components. Event triggered components.
Dividing code reactions into tasks. Task graphs, await dependencies and schedules.
Parallel composition of components. Formal definitions.

• The Synchronous Model Part I
• The Synchronous Model Part II

Parallel composition of components.
Designing synchronous systems. Bottom-up vs. top-down design. Examples.
Synchronous networks.

• The Synchronous Model Part II
(revised)
• The Synchronous Model Part III

Safety Requirements. Transition systems. Safety properties and invariants. Verifying invariants. Inductive strengthening. Examples of inductive proofs. Requirement-based design. Complexity of automated invariant verification.

• Safety Requirements Part I (revised)
• Safety Requirements Part II
• Safety Requirements Part III

Introduction to the Asynchronous Model. Asynchronous processes. Input, output channels, states and tasks. Executions and interleaving semantics. Asynchronous parallel composition.
Safety and progress requirements. Asynchronous design primitives. Synchronization. Deadlocks. Shared memory. The mutual exclusion problem.

• The Asynchronous Model Part I (revised)
• The Asynchronous Model Part II

Fairness assumptions. Weak and strong fairness. Correctness under fairness assumptions.
Asynchronous coordination protocols. Leader election. Reliable transmission.

• The Asynchronous Model Part II
• The Asynchronous Model Part III

Midterm I

More on asynchronous coordination protocols. The alternating bit protocol. Wait-free consensus.
Specifying liveness requirements. Introduction to Linear Temporal Logic. Syntax and semantics.

• The Asynchronous Model Part III (revised)
• Liveness Requirements Part I

Derived LTL operators. Specifying system requirements in LTL. Examples. LTL equivalences. LTL specifications. Encoding fairness assumptions in LTL. Examples. Correspondence between LTL formulas and Büchi automata. Examples. Checking LTL properties of reactive systems by reduction to Büchi automata.

• Liveness Requirements Part I
• Liveness Requirements Part II (revised)

Extended spring break

The timed model. Clocks. Motivation and examples. Formal definition. Parallel composition. Modeling imperfect clocks. Timed based protocols. Examples.

• Timed Model Part I (revised)
• Timed Model Part II(revised)

Introduction to dynamical systems. General concepts and motivation. Feedback control loops. Examples of continuous-time components. Brief recap of derivatives and differential equations. Continuous-time components: definition and examples. Sufficient conditions for the existence and uniqueness of executions.

• Dynamical Systems Part I (revised)

More on dynamical systems. The pendulum example. Equilibria and Stability. Lyapunov and input-output stability. Linear systems. Solving linear differential equations.

• Dynamical Systems Part II (revised)
• Dynamical Systems Part III (revised)
• Linear Algebra by Jim Hefferon, 2014.

Designing controllers. Open- and closed-loop controllers. Stabilizing controllers. Gain matrix and controllability for linear systems. PID controllers.

Introduction to hybrid systems. Hybrid dynamical models. Motivation and examples. Formal definition of hybrid systems. Executions. Composition of hybrid processes. Examples.
Zeno behavior. Examples.

• Dynamical Systems Part IV (revised)
• Hybrid Systems Part I (revised)

Midterm II

Zeno executions, states and processes. Zeno processes and reachability. Stability of hybrid systems.
Designing Hybrid Systems. Examples.

• Hybrid Systems Part I
• Hybrid Systems Part II (revised)

Modeling and checking reactive systems with the Kind 2 model checker. Modeling examples from the textbook in Kind 2.

• Kind 2 examples: Miscellaneous, Railroad Controller, Car Cruise Controller