The term cyber-physical systems (CPS) refers to the integration of computation and networking with physical processes. CPS is firmly established as a buzzword du jour. Yet many of its elements are familiar and not altogether new. Is CPS just a rehash of old problems designed to attract new funding? In this talk, I will argue that quite to the contrary, CPS is pushing hard at the frontiers of engineering knowledge, putting severe stress on the abstractions and techniques that have proven so effective in the separate spaces of cyber systems (information and computing technology) and physical systems (the rest of engineering). My argument will center on the role of models, and I will show that questions about semantics of models become extremely challenging when the models are required to conjoin the cyber and the physical worlds.

A key challenge is that the notion of dynamics differs in the engineering abstractions used for the cyber and physical sides of the problem. On the physical side, dynamics refers to the change of state of a system over time, where time plays a central role. Many of the core abstractions used in the engineering of such systems explicitly refer to time. For example, ordinary differential equations (ODEs) are frequently used to describe the motion of mechanical parts and the dynamics of electrical circuits. In contrast, on the cyber side, the notions of computation dating back to Turing and Church make no reference to time, modeling dynamics as sequences of discrete state changes. These abstractions are fundamentally algorithmic, step-by-step operations, where the time it takes to perform a step is irrelevant.

The engineering abstractions used in both the cyber and physical spaces are key enablers of the high-tech revolution of the 20th century. On the cyber side, the ability to execute algorithms repeatedly, quickly, and essentially flawlessly underlies much of the information technology revolution. On the physical side, the ability to design stable and robust control systems accounts for the extraordinary reliability and efficiency of vehicles and transportation systems.

A central feature of these abstractions is determinism, where, once the inputs are defined, the behavior of a model of the system is unique and well-defined. Exactly one behavior is correct. Such determinism makes these models very powerful, because analyses of the models acquire the strength of mathematical theorems. Moreover, the models correspond well with the actual behavior of physical realizations. For example, a modern microprocessor can correctly execute a program with extremely high reliability. A mechanical feedback coupling can closely emulate the ODEs used to model it. The combination of expressiveness of the models, the fidelity of the models to the physical realization, and determinism is extremely powerful.

But when cyber and physical abstractions are combined, with today's abstractions, we lose determinism. The interaction between an algorithm and a physical dynamics is not well defined, because the modeling semantics of the algorithms eschews time, whereas the modeling semantics of the ODE embraces time. So instead of building models with deterministic abstractions, engineers today build cyber-physical systems by separately designing the cyber and physical parts, and then discovering the dynamics when they put the two realizations together.

To solve this problem, we can endow the cyber parts with physical abstractions (cyberizing the physical), for example by introducing time in the semantics. Or we can endow the physical parts with cyber abstractions (physicalizing the cyber), for example by enabling database queries over sensor networks. Both approaches have value and are necessary for the full realization of the vision of cyber-physical systems.

Edward A. Lee is the Robert S. Pepper Distinguished Professor in the Electrical Engineering and Computer Sciences (EECS) department at U.C. Berkeley. His research interests center on design, modeling, and analysis of embedded, real-time computational systems. He is the director of the nine-university TerraSwarm Research Center, a director of Chess, the Berkeley Center for Hybrid and Embedded Software Systems, and the director of the Berkeley Ptolemy project. From 2005-2008, he served as chair of the EE Division and then chair of the EECS Department at UC Berkeley. He is co-author of nine books (counting second and third editions) and numerous papers. He has led the development of several influential open-source software packages, notably Ptolemy and its various spinoffs. He received the B.S. degree in Computer Science from Yale University, New Haven, CT, in 1979, the S.M. degree in EECS from the Massachusetts Institute of Technology (MIT), Cambridge, in 1981, and the Ph.D. degree in EECS from the University of California Berkeley, Berkeley, in 1986. From 1979 to 1982 he was a member of technical staff at Bell Telephone Laboratories in Holmdel, New Jersey, in the Advanced Data Communications Laboratory. He is a co-founder of BDTI, Inc., where he is currently a Senior Technical Advisor, and has consulted for a number of other companies. He is a Fellow of the IEEE, was an NSF Presidential Young Investigator, and won the 1997 Frederick Emmons Terman Award for Engineering Education.