Periodic Reporting for period 4 - AutoCPS (Automated Synthesis of Cyber-Physical Systems: A Compositional Approach)
Berichtszeitraum: 2023-08-01 bis 2024-01-31
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.
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.
The project has achieved significant progress in pioneering novel methodologies and interdisciplinary advancements, fostering knowledge and technology dissemination.
A notable achievement is the development of control policies synthesis for discrete-time stochastic control systems, ensuring a minimum probability of satisfying complex temporal properties. By decomposing specifications into simpler tasks and employing control barrier certificates, a hybrid control policy is formulated, surpassing conventional discretization methods and proving efficacy in practical settings.
Another breakthrough involves a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. Through stochastic storage functions and simulation functions, the framework enables analysis and synthesis over abstract interconnected systems, with results applicable to concrete systems. Demonstrated on systems of significant dimensions, its scalability and utility in managing complex architectures are evident.
The project introduces a small-gain theorem for networks with a countably infinite number of finite-dimensional subsystems, ensuring exponential input-to-state stability. Illustrated through examples like nonlinear spatially invariant systems and road traffic networks, the theorem proves effective in ensuring stability for large-scale interconnected systems, with implications across diverse domains.
Additionally, a compositional approach for constructing both infinite and finite abstractions of large-scale interconnected discrete-time stochastic systems has been developed. Utilizing stochastic simulation functions and small-gain-type conditions, the framework enables the creation of finite abstractions with guaranteed error bounds, demonstrated on interconnected networks. This scalable approach facilitates technology transfer by providing solutions for policy synthesis in complex systems.
In essence, the project's publications showcase the integration of novel methodologies from control theory and computer science. These advancements promote knowledge and technology dissemination by addressing real-world challenges, demonstrating scalability, efficacy, and relevance across various domains.
A notable achievement is the development of control policies synthesis for discrete-time stochastic control systems, ensuring a minimum probability of satisfying complex temporal properties. By decomposing specifications into simpler tasks and employing control barrier certificates, a hybrid control policy is formulated, surpassing conventional discretization methods and proving efficacy in practical settings.
Another breakthrough involves a compositional approach for constructing infinite abstractions of interconnected discrete-time stochastic control systems. Through stochastic storage functions and simulation functions, the framework enables analysis and synthesis over abstract interconnected systems, with results applicable to concrete systems. Demonstrated on systems of significant dimensions, its scalability and utility in managing complex architectures are evident.
The project introduces a small-gain theorem for networks with a countably infinite number of finite-dimensional subsystems, ensuring exponential input-to-state stability. Illustrated through examples like nonlinear spatially invariant systems and road traffic networks, the theorem proves effective in ensuring stability for large-scale interconnected systems, with implications across diverse domains.
Additionally, a compositional approach for constructing both infinite and finite abstractions of large-scale interconnected discrete-time stochastic systems has been developed. Utilizing stochastic simulation functions and small-gain-type conditions, the framework enables the creation of finite abstractions with guaranteed error bounds, demonstrated on interconnected networks. This scalable approach facilitates technology transfer by providing solutions for policy synthesis in complex systems.
In essence, the project's publications showcase the integration of novel methodologies from control theory and computer science. These advancements promote knowledge and technology dissemination by addressing real-world challenges, demonstrating scalability, efficacy, and relevance across various domains.
The paramount achievement of this project lies in pioneering correct-by-construction techniques tailored for large-scale systems, a significant leap beyond the capabilities of existing methodologies. To accomplish this feat, we harmonized compositional techniques from disparate domains of control theory and formal methods within computer science. The introduction of open-source tools, exemplified by SCOTS with over 200 citations, underscores the project's impact in facilitating the utilization of theoretical techniques within symbolic control by academia and industry alike.
Moreover, in the project's final phase, we surpassed the initial scope outlined in the proposal by introducing groundbreaking methodologies for correct-by-construction in Cyber-Physical Systems (CPS), eliminating the need for closed-form mathematical models. Notably, we achieved this feat by leveraging raw data collected directly from the system's input-output interactions to construct controllers, circumventing the requirement for model construction entirely.
Moreover, in the project's final phase, we surpassed the initial scope outlined in the proposal by introducing groundbreaking methodologies for correct-by-construction in Cyber-Physical Systems (CPS), eliminating the need for closed-form mathematical models. Notably, we achieved this feat by leveraging raw data collected directly from the system's input-output interactions to construct controllers, circumventing the requirement for model construction entirely.