Mathematics Colloquium - Armin Pirastehzad PhD, University of Groningen

Title: Complexity Reduction in Verification and Synthesis of Linear Control Systems: An Abstraction-based Approach

Abstract:

Verification and synthesis of modern engineering systems, which often appear as interconnections of heterogeneous components, have become overly laborious as these systems have grown increasingly complex. Traditional methods of verification and (control) synthesis are not expressive in the sense that they fail to address sophisticated specifications that these complex systems demand. On the other hand, these methods are not computationally tractable as they do not scale well with growing system dimension. Moreover, many of these methods formalize verification (synthesis) in frameworks that make them incompatible with many effective analytic (synthetic) methods in control theory. Motivated by these challenges, we develop verification and synthesis frameworks that are expressive, computationally tractable, and compatible with effective methods of analysis and synthesis in control theory. To enable computationally tractable verification, we develop frameworks that are modular in the sense that they allow for the decomposition of a global verification problem into local ones which can be handled independently. To reduce computational complexities of synthesis, on the other hand, we develop frameworks that are hierarchical in the sense that they split a complex synthesis task into consecutive simple sub-tasks that require cheap computations. The kernel of our approach in developing such verification and synthesis frameworks is system abstraction, which allows us to abstract complex (high-dimensional) models into simple (low-dimensional) ones and accordingly conduct verification (synthesis) on the basis of these abstract models.