Physical Processes (Section II) CPS Design & Optimization (Section V & VI) Modeling CPS Workload (Sections III & IV) Nature Users        0 , , , , , , ,         t u x H G t u x H t t u x H b            t x P x g x t x P x f x d t t x P b , , 2 2 ,              Aggregation Fusion Sensing Communication volume Queue occupancy Inter-event times Node-to-node latency Efficient, Dependable, Safe, Reliable, Secure Cost functions + constraints Master Equation Fractal Derivative Physical Processes (Section II) CPS Design & Optimization (Section V & VI) Modeling CPS Workload (Sections III & IV) Nature Users        0 , , , , , , ,         t u x H G t u x H t t u x H b            t x P x g x t x P x f x d t t x P b , , 2 2 ,              Aggregation Fusion Sensing Communication volume Queue occupancy Inter-event times Node-to-node latency Efficient, Dependable, Safe, Reliable, Secure Cost functions + constraints Master Equation Fractal Derivative Figure 1. CPS pyramid: The pyramid foundation summarizes the large set of physical processes of interest to the CPS community. Insights about physical processes gained through sensing, information fusion and aggregation lead to complex heterogeneous CPS workload. Accurate modeling of workloads enables the design of optimal CPS architectures that may improve our life. Similarly, to statistical physics which has been successful in explaining nature, the CPS workloads are modeled via master equations which later are used in defining various optimization problems of interest to the end users. Towards a Science of Cyber-Physical Systems Design Paul Bogdan Carnegie Mellon University Pittsburgh, PA 15213-3890, USA pbogdan@ece.cmu.edu Radu Marculescu Carnegie Mellon University Pittsburgh, PA 15213-3890, USA radum@ece.cmu.edu Abstract— Cyber-physical systems (CPS) represent the information technology quest of the 21-st century for a better, cleaner, safer life which integrates computation, communication, and control with physical processes. Physical processes are predominantly non-stationary and require time- dependent models for modeling and understanding their behavior. In contrast, in most current computing platforms, their workloads and design methodologies lack proper models for the time component and mostly assume stationary (i.e., time independent) behavior. In this paper, we use empirical data to identify the main characteristics (e.g., self-similarity, nonstationarity) of the communication workload of real CPS. Then, starting from the complex characteristics of CPS workloads, we present a novel statistical physics inspired model which is used to define a new optimal control problem that not only accounts for the observed self-similarity and nonstationarity properties of the CPS workload, but also allows for accurate predictions on CPS dynamical trajectories during the optimization process. This opens new venues for CPS design and optimization for real life applications. Keywords - cyber-physical systems, statistical physics, fractional calculus, nonlinear control, multi-fractal behavior. I. INTRODUCTION AND PRIOR WORK There is an increasing concern for bringing computation and communication together in order to design efficient cyber physical systems (CPS) [21][25][29]. These systems consist of networks of embedded computation and communication devices [7], as well as sensors [1][13][28], which are used to monitor and measure various physical processes taking place on electrical power grids, transportation and traffic roads, communication and financial networks, medical devices, smart buildings. Hence, CPS need to be dependable, safe, reliable, efficient, real-time, yet secure [15][25][27]. We expect that future CPS will help us define new communication and interaction protocols that will provide better control over physical processes. For instance, several research efforts focusing on how cell phone technology can be used to harness social tracking and knowledge fusion are now well under way [13][19][20]. The principles of community sensing through privately held sensors (e.g., GPS devices, embedded cell phones) are eloquently described in [13], together with several privacy issues. Such community sensing networks can be adequately used for road traffic monitoring. A more concrete incarnation of CPS for traffic optimization is presented in [20], which describes how smart-phones could be employed to sense the environment and transmit information about it to various traffic decision centers. Besides sensing infrastructure, a congestion control protocol has been proposed in [1] which reduces communication traffic based on the importance of collected data and desired estimation error. From a different perspective, it is crucial to design highly reliable and powerful defense systems that are fault-tolerant to both natural disasters and terrorist attacks. The analysis of CPS features can optimize the design of power grids and oil/gas transportation pipes [25]. Last but not least, CPS have the goal not only to help us design and build environmental friendly and energy efficient (smart) buildings [10], but also to cater for the changing needs of contemporary society at a time when we are increasingly concerned about dwindling natural resources. Building such CPS requires a new science of characterizing and controlling dynamic processes across heterogeneous networks of sensors and computational devices. This science needs to bridge the gap between real- time computing and signal processing techniques with distributed and/or self-organizing control of heterogeneous wireless sensor networks and embedded systems. Nevertheless, such a new science cannot rely solely on 2011 International Conference on Cyber-Physical Systems 978-0-7695-4361-1/11 $26.00 © 2011 IEEE DOI 10.1109/ICCPS.2011.14 99 2011 IEEE/ACM Second International Conference on Cyber-Physical Systems 978-0-7695-4361-1/11 $26.00 © 2011 IEEE DOI 10.1109/ICCPS.2011.14 99