Title: CPS: Breakthrough: Compositional Modeling of Cyberphysical Systems This project is devoted to the discovery of new mathematical modeling techniques for Cyber-Physical Systems. In particular, the research involves devising novel conceptual methods for assembling systems from subsystems, and for reasoning about the behavior of systems in terms of the behavior of their subsystems, which may be computational or physical. The results enable scientists and engineers to develop more realistic models of the systems they are designing, and to obtain greater insights into their eventual behavior, without having to build costly prototypes. The intellectual merits are the new notions of system behavior being developed that unify the computational and the physical, and the mathematical operators and laws governing the relationships between systems and subsystems. The project's broader significance and importance lie in the increased pace of innovation within Cyber-Physical System design that the new modeling techniques make possible, and the curricular enhancements that the novel conceptual frameworks under development support. The specific research program of this project involves the development of a novel modeling paradigm, Generalized Synchronization Trees (GSTs), into a rich framework for both describing Cyber-Physical Systems (CPSs) and studying their behavior under interconnection. GSTs are inspired by Milner's use of Synchronization Trees (STs) to model interconnected computing processes, but GSTs generalize the mathematical structure of their forebears in such a way as to encompass systems with discrete ("Cyber") as well as continuous ("Physical") dynamics. As Milner did with STs, the PIs are developing an algebraic theory of composition for GSTs. Such theories have a particular advantage over non-algebraic ones: because the composition of two (or more) objects results in an object of the same type, composition operators can be nested to build large structures out of smaller ones. Thus, the theory of GSTs is inherently compositional. The development of the theory involves five distinct but complementary endeavors. Standard models for cyber-physical systems are being encoded as GSTs in a semantically robust way; meaningful notions of composition and congruence for CPSs are being described and studied algebraically; the interplay between behavioral equivalence and the preservation of system properties is being investigated; a notion of real-time (or clock time) is under consideration for GSTs; and GSTs are being assessed as modeling tools for practical design scenarios.

Title: CPS: Breakthrough: A Mathematical Theory of Cyber-Physical Systems The fundamental challenge in cyber-physical systems is the confluence of distinct scientific and engineering models, methods, and tools for cyber and physical systems. Cyber systems are primarily about processing information. Physical systems are primarily about structure and dynamics, the evolution of state in time. This project develops a mathematical theory of cyber-physical systems that provides a formal interface between the cyber and the physical. The intellectual merits of the project are a solid basis for the modeling and design as well as the implementation and verification of cyber-physical systems, and a fruitful connection of the nascent discipline of cyber-physical-systems engineering with standard mathematical practice. The project's broader significance and importance are providing a sound foundation by which cyber-physical system technologies can be assessed, and enabling the discipline of cyber-physical-system engineering to evolve into a mature and durable field of study. The project builds on the theory of generalized ultrametric semilattices and the fixed-point theory of strictly contracting functions on generalized ultrametric semilattices to develop a cyber-physical domain theory, providing a firm mathematical footing for arbitrary composition and higher-order behavior, formulating the right notion of convergence and continuity for cyber-physical computation, and developing a notion of approximation and effectiveness that allows for a two-way connection between the abstractions of the theory and the realizations of practice. It further applies the theory to a wide range of classic problems of modeling and simulating mixed discrete and continuous phenomena, and extends it to embrace the discrete interventions of a cyber subsystem on its physical counterpart in a cyber-physical system. It also investigates the practical implications of the theory for the implementation and verification of cyber-physical systems by reexamining currently used timed models of computation through the prism of the theory, exploring the extension of programming languages with temporal constructs that are complete over the theoretical abstractions, and integrating the theory in automated and interactive theorem provers to supplement existing model-checking methods that might succumb to the scale of cyber-physical systems.

Accurate and reliable knowledge of time is fundamental to cyber-physical systems for sensing, control, performance, and energy efficient integration of computing and communications. This statement underlies the proposal. Emerging CPS applications depend on precise knowledge of time to infer location and control communication. There is a diversity of semantics used to describe time, and quality of time varies as we move up and down the system stack. System designs tend to overcompensate for these uncertainties and the result is systems that may be over designed, inefficient, and fragile. The intellectual merit derives from the new and fundamental concept of time and the holistic measure of quality of time (QoT) that captures metrics including resolution, accuracy, and stability. The proposal builds a system stack ("ROSELINE") that enables new ways for clock hardware, operating system, network services, and applications to learn, maintain and exchange information about time, influence component behavior, and robustly adapt to dynamic QoT requirements, as well as to benign and adversarial changes in operating conditions. Application areas that will benefit from Quality of Time will include: smart grad, networked and coordinated control of aerospace systems, underwater sensing, and industrial automation. The broader impact of the proposal is due to the foundational nature of the work which builds a robust and tunable quality of time that can be applied across a broad spectrum of applications that pervade modern life. The proposal will also provide valuable opportunities to integrate research and education in graduate, undergraduate, and K-12 classrooms. There will be extensive outreach through publications, open sourcing of software, and participation in activities such as the Los Angeles Computing Circle for pre-college students.

Accurate and reliable knowledge of time is fundamental to cyber-physical systems for sensing, control, performance, and energy efficient integration of computing and communications. This statement underlies the proposal. Emerging CPS applications depend on precise knowledge of time to infer location and control communication. There is a diversity of semantics used to describe time, and quality of time varies as we move up and down the system stack. System designs tend to overcompensate for these uncertainties and the result is systems that may be over designed, inefficient, and fragile. The intellectual merit derives from the new and fundamental concept of time and the holistic measure of quality of time (QoT) that captures metrics including resolution, accuracy, and stability. The proposal builds a system stack ("ROSELINE") that enables new ways for clock hardware, operating system, network services, and applications to learn, maintain and exchange information about time, influence component behavior, and robustly adapt to dynamic QoT requirements, as well as to benign and adversarial changes in operating conditions. Application areas that will benefit from Quality of Time will include: smart grad, networked and coordinated control of aerospace systems, underwater sensing, and industrial automation. The broader impact of the proposal is due to the foundational nature of the work which builds a robust and tunable quality of time that can be applied across a broad spectrum of applications that pervade modern life. The proposal will also provide valuable opportunities to integrate research and education in graduate, undergraduate, and K-12 classrooms. There will be extensive outreach through publications, open sourcing of software, and participation in activities such as the Los Angeles Computing Circle for pre-college students.

Accurate and reliable knowledge of time is fundamental to cyber-physical systems for sensing, control, performance, and energy efficient integration of computing and communications. This statement underlies the proposal. Emerging CPS applications depend on precise knowledge of time to infer location and control communication. There is a diversity of semantics used to describe time, and quality of time varies as we move up and down the system stack. System designs tend to overcompensate for these uncertainties and the result is systems that may be over designed, inefficient, and fragile. The intellectual merit derives from the new and fundamental concept of time and the holistic measure of quality of time (QoT) that captures metrics including resolution, accuracy, and stability. The proposal builds a system stack ("ROSELINE") that enables new ways for clock hardware, operating system, network services, and applications to learn, maintain and exchange information about time, influence component behavior, and robustly adapt to dynamic QoT requirements, as well as to benign and adversarial changes in operating conditions. Application areas that will benefit from Quality of Time will include: smart grad, networked and coordinated control of aerospace systems, underwater sensing, and industrial automation. The broader impact of the proposal is due to the foundational nature of the work which builds a robust and tunable quality of time that can be applied across a broad spectrum of applications that pervade modern life. The proposal will also provide valuable opportunities to integrate research and education in graduate, undergraduate, and K-12 classrooms. There will be extensive outreach through publications, open sourcing of software, and participation in activities such as the Los Angeles Computing Circle for pre-college students.

The aim of this project is to lay down the foundations of a novel approach to real-time control of networked cyber-physical systems (CPS) that leverages their cooperative nature. Most networked controllers are not implementable over embedded digital computer systems because they rely on continuous time or synchronous executions that are costly to enforce. These assumptions are unrealistic when faced with the cyber-physical world, where the interaction between computational and physical components is multiplex, information acquisition is subject to error and delay, and agent schedules are asynchronous. Even without implementation obstacles, the periodic availability of information leads to a wasteful use of resources. Tuning controller execution to the task at hand offers the potential for great savings in communication, sensing, and actuation. The goal of this project is to bring this opportunity to fruition by combining event- and self-triggered control ideas into a unified approach that inherits the best of both models. The key conceptual novelty is for agents to make promises to one another about their future states and warn each other if they later decide to break them. The information provided by promises allows agents to autonomously determine when fresh information is needed, resulting in an efficient network performance. Networked cyber-physical systems are transforming the way society interacts with the physical world. Advances in this field are extending the range of human capabilities in an increasing number of areas with high societal and economic impact, such as smart energy, intelligent transportation, advanced manufacturing, health technology, and the environment. This project contributes to the science and technology of cyber-physical systems by developing a novel principled approach for networked systems to operate efficiently and cope with the sources of uncertainty present in real-word applications. The potential benefits are real-time operation in a wide range of application domains of cooperative cyber-physical systems with a superior level of efficiency and robustness than currently possible. The project promises to contribute to the training of a new generation of engineering students at UC San Diego with the skills necessary to deal with this type of multi-faceted systems and applications. The plan includes undergraduate student involvement in research, graduate supervision and curriculum development, outreach to high-school students, retention of minorities in STEM disciplines, and broad dissemination activities.

The objective of this research is to address issues related to the platform revolution leading to a third generation of networked control systems. The approach is to address four fundamental issues: (i) How to provide delay guarantees over communication networks to support networked control? (ii) How to synchronize clocks over networks so as to enable consistent and timely control actions? (iii) What is an appropriate architecture to support mechanisms for reliable yet flexible control system design? (iv) How to provide cross-domains proofs of proper performance in both cyber and physical domains? Intellectual Merit: Currently neither theory nor networking protocols provide solutions for communication with delay constraints. Coordination by time is fundamental to the next generation of event-cum-time-driven systems that cyber-physical systems constitute. Managing delays and timing in architecture is fundamental for cyberphysical systems. Broader Impact: Process, aerospace, and automotive industries rely critically on feedback control loops. Any platform revolution will have major consequences. Enabling control over networks will give rise to new large scale applications, e.g., the grand challenge of developing zero-fatality highway systems, by networking cars traveling on a highway. This research will train graduate students on this new technology of networked control. The Convergence Lab (i) has employed minority undergraduate students, including a Ron McNair Scholar, as well as other undergraduate and high school researchers, (ii) hosts hundreds of high/middle/elementary school students annually in Engineering Open House. The research results will be presented at conferences and published in open literature.