**CMPE142: Introduction to Cyber-physical Systems**

**GENERAL INFORMATION:****Lectures:** Tuesday and Thursday 4pm to 5:45pm (10/02/14 - 12/12/14), J. Baskin Engr 372

**Office hours:** T 6:00pm to 7:00 pm and Th 3:00pm to 4:00 pm (both at E2-321)

**COURSE DESCRIPTION**

Cyber-physical systems combine digital and analog devices, interfaces, networks, computer sys- tems, and the like with the natural and man-made physical world. The inherent interconnected and heterogeneous combination of behaviors in these systems makes their analysis and design a challenging task. Safety and reliability specifications imposed in cyber-physical applications, which are typically translated into stringent robustness standards, aggravate the matter. Unfortunately, state-of-the-art tools for system analysis and design cannot cope with the intrinsic complexity in cyber-physical systems. Tools suitable for analysis and design of cyber-physical systems must allow a combination of physical or continuous dynamics and the cyber or computational components, as well as handle a variety of types of perturbations, such as exogenous disturbances, time delays, and system failures.

This course provides an introduction to modeling and analysis of cyber-physical systems. After an introduction to the class of systems of interest via examples in engineering and science, several models of continuous-time systems and discrete-time systems are introduced. The main focus is on models in terms of differential equations for the modeling of physical process. Finite state machines and stateflow are introduced and combined with the physical models. Applications of the resulting models for modeling and analysis of embedded systems are discussed. With this basic background, the more advanced timed automata and hybrid automata models are introduced. Then, linear temporal logic, which is the main tool taught in this class, is introduced and applied to specify the desired system behavior. Tools for analytical study and numerical verification of the satisfaction of linear temporal logic formulae are presented and discussed in numerous applications.

**TOPICS:** This course will cover: Introduction to continuous-time systems; Modeling of physical processes; Linear time-invariant systems; Numerical simulation of differential equations; Introduction to discrete-time systems and return maps; Finite state machines; Event triggered systems; Stateflow; Timed automata; Hybrid automata; Concurrency; Invariants; Linear temporal logic; Introduction to verification.

**SYLLABUS:** The class syllabus is available here *(last update: 10/07/14)*

**CLASS MATERIAL: **class notes posted at our Google group

*Lecture 1* (10/02/14): Introduction to cyber-physical systems (slides).

*Lecture 2* (10/07/14): Models of physical systems.

*Lecture 3* (10/09/14): Simulation of physical systems and introduction to models of cyber components.

*Lecture 4* (10/14/14): Finite-state machines.

*Lecture 5* (10/16/14): Discrete systems.

*Lecture 6* (10/21/14): Models of interfaces.

*Lecture 7* (10/23/14): Cyber-physical systems models as interconnections.

*Lecture 8* (10/28/14): Executions.

*Lecture 9* (10/30/14): Summary of models.

*In-class Midterm*

*Lecture 10* (11/06/14): Invariants.

*Lecture 11* (11/08/14): Attractivity.

*Lecture 12* (11/18/14): Stability.

*Lecture 13* (11/20/14): Temporal logic (part 1).

*Lecture 14* (11/25/14): Temporal logic (part 2).

*Lecture 15* (12/02/14): Robustness.

*Lecture 16* (12/04/14): Verification.