Large-scale cyber-physical systems (CPS) have transformed many aspects of our lives--from engine control in automobiles and airplanes, to robotic swarms, building management, and integrated medical devices. Embedded control software plays a significant role in CPS by controlling physical variables--for instance, pressure or velocity--through multiple sensors and actuators, and by communicating with other systems or with computing cloud servers. Spatially distributed CPS interact tightly with distributed computational components. Existing design techniques for such systems and with respect to high-level temporal logic requirements (e.g. those expressed as linear temporal logic formulae or by omega-regular languages) are inadequate. This is because (i) the algorithmic complexity of existing design schemes for these types of requirements is exponential in the number of dimensions of systems, and (ii) the centralized view that such design schemes assume is hard to implement because it requires all the subsystems to exchange their state information with each other. Current design approaches are thus based on ad-hoc solutions which result in error-prone control software with very high post-facto verification and validation costs. As a result, classical approaches are unlikely to meet the correctness and reliability requirements of autonomous vehicles and other modern safety-critical applications.
This ERC project developed a scalable correct-by-construction design scheme, in which embedded controllers are synthesized for large-scale CPS from high-level temporal logic requirements. In order to reduce the design costs of embedded control software and guarantee its correctness at the same time, this project proposed a divide and conquer strategy to scale automated synthesis of control software by leveraging compositional techniques from formal methods in computer science (e.g. assume-guarantee rules) with those from control theory (e.g. small-gain theorems). To tackle the design complexity, the project leveraged the natural structure present in the system to break the design problem into semi-independent ones (a.k.a. decomposition) and aggregate states or components to eliminate unnecessary details (a.k.a. abstraction).
By introducing a correct-by-construction methodology, this project enabled fast and reliable design of many safety-critical applications, including air traffic, power, transportation, and water networks. This project will have additional economic impact since certain CPS applications cannot be deployed without a rigorous controller design. Legal and safety issues are the main barriers when rolling out a safety-critical technology. In almost all new standards for safety and reliability of embedded control software (e.g. new autonomous driving standard ISO/PAS 21448), formal methods are introduced to achieve rigorous verification objectives. In general, this project--with its seamless process on scalable, formal synthesis--will help to apply formal methods techniques to future, large-scale CPS.
In conclusion, this project has significantly expanded the applicability of symbolic control techniques to systems of orders of magnitude larger than those previously addressed. With the findings presented herein, the design of correct-by-construction controllers capable of enforcing intricate temporal logic properties over complex Cyber-Physical Systems (CPS) becomes feasible. Moreover, the introduction of open-source software tools as part of this project ensures the accessibility and usability of the theoretical results among both academic and industrial communities, further enhancing their impact and practical relevance.
