In March 2023 the AFOSR approved our proposal, HyDDRA as a Multi University Research Initiative. This site contains open information on the research funded by this grant.
Here’s what we try to achieve:
Hybrid control systems are a theoretical construct that emerged over the past several decades as the result of broad adoption of computerized, digital systems in control practice on one hand, and thanks to the recognition of the necessity to formalize the role which discrete, semantically driven events play in the process execution, on the other.
While hybrid systems are becoming an indispensable tool for analysis and design in modern engineering, the development of their theory was closely following the established research paradigm of classical nonlinear control, and was underutilizing some of the more sophisticated tools that became available to applied mathematicians and engineers, especially those stemming from the domains of algebraic and differential topology, model theory, category theory.
We are relying on several guiding principles. Tameness postulates that most if not all aspects of the theory can be seen through an algebraic lens: all objects of hybrid control systems are located within some o-minimal structure. Focus on Path Spaces implies they should be considered as one of the key primitives of the hybrid systems, and most if not all constructions could be derived from them, rendering the distinction between open and closed systems as secondary, and simplifying many problems of compositionality. Categorification means an upfront investment into the underlying topological and combinatorial structures, most naturally formalized in terms of topological categories: while the resulting constructions become more abstract, they also become easier to formalize and to compose.