A compositional approach for performance certification of large-scale engineering systems
A major problem for safety-critical engineering systems is to certify the required stability and performance properties using analytical and computational models of the physical system. The existing methods for such certification are severely limited in their ability to cope with the number of physical components and the complexity of their interactions in today's large-scale systems. The project addresses this problem with a compositional approach that derives system-level guarantees from key structural properties of the subsystems and their interactions, rather than tackle the system model as a whole. The first objective is to develop tools that automatically detect useful properties of the subsystems and their interconnection, and to exploit these properties to simplify the task of performance certification. To select important subsystem properties, recently developed techniques for large-scale optimization are employed. Likewise, efficient algorithms from graph theory and computational algebra are leveraged to detect symmetries in the interconnection of the components, leading to further simplification. The second objective is to advance the aforementioned compositional approach to "hybrid" systems in which a supervisory control algorithm is able to switch from one mode of operation to another. The task is then to develop switching strategies to prevent the system from reaching states that are deemed "unsafe". One of the educational contributions of the project is the development of a desktop robotic system that mimics the logrolling game in which two players aim to stay on a floating log while attempting to cause the competitor to lose balance. This system embodies fundamental problems that are of great interest across a wide range of application areas and provides a test bed for new control algorithms, such as switching strategies between several modes (defensive, aggressive, short-term survival, etc.). A further educational contribution is a graduate course on the theme of this project that is being developed by the principal investigators.
The lack of scalable tools for verification is a major problem for safety-critical engineering systems in which the number of physical components and the complexity of their interactions are continuously increasing. This project addresses this problem with a compositional approach that exploits key structural properties of the subsystems and their interconnection topology, rather than tackle the system model as a whole. The first objective is to develop tools that automatically detect critical properties of the subsystems and their interconnection. This will be accomplished by exploiting symmetries in the interconnection topology to reduce the size of the numerical problem for performance certification and by employing large-scale optimization tools, such as the Alternating Direction Method of Multipliers (ADMM), to select the most important subsystem properties. The second objective is to advance the aforementioned compositional approach beyond traditional performance criteria and system models. The new tasks include safety verification where the goal is to ensure that no trajectory enters an undesirable set, and designing switching strategies for hybrid systems to maintain safety. The combination of the proposed compositional approach and modern computational tools predicated on semidefinite programming offer great potential to overcome the existing dimensional barriers for these problems. The PIs are developing a graduate course on the theme of this project. A further educational contribution is the development of a desktop robotic system that mimics the logrolling game in which two players aim to stay on a floating log while attempting to cause the competitor to lose balance. This system embodies fundamental distributed control problems that are of great interest across a wide range of application areas and provides a testbed for new algorithms, including those resulting from the proposed research.
