HyDDRA- Hybrid Dynamics - Deconstruction and Aggregation
Abstract
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 paradigmof 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. There are no intrinsic reasons for that. Hybrid systems forma highly syncretic area, situated at a point where several branches of mathematics, control theory and theoretical computer science come together. Conceptually, the area is rife for the deployment of the most advanced tools mathematics has to offer. The attempts to do so were initiated over the past decade, but in a patchwork way, without the benefit of a coherent unifying program- each new approach came with the built-in overhead of fitting it into the context of the existing techniques and methods. This project aims at changing that. We will start with assembling existing approaches into a unified mosaic using the canvas of topology and algebra (using as our central tools category theory and algebraic topology), and proceed to forge a computationally effective theory for the specification and synthesis of hybrid system behaviors. 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 fromthem, rendering the distinction between open and closed systems as secondary, and simplifyingmany 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. While the primary goals of the project are theoretical and algorithmic, we expect interactions with and rapid impact on several domains of relevance to the DoD and AF in particular. Thus, we aim at applications in multi-agent systems (including the problem of safe coordination of swarms of manned and unmanned vehicles, and the problem of assured coverage. Robotic systems, a rich source of hybrid models, will benefit from efficient formalisms developedin this project, and innovative data-driven approaches bypassing explicit modeling. Material science and biological systems form a class of hybrid dynamical systems in an intellectually compelling and technologically rich domain heretofore barely touched upon. Ultimately, this project aims to transform synergetically the research paradigm of hybrid, and, more generally, control dynamical system, leading to a new generation of tools (algorithmic pipes and libraries) that engineers across DoD relevant industries would adopt.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310337
Entities
People
- Juliy Baryshnikov
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Illinois Urbana–Champaign