In this project, we aim to establish a framework for learning problems in nonlinear dynamical systems theory. This is a collaborative project with mathematicians and computer scientists, where the development of new tools that can harness data obtained from unknown, “black-box,” and partially known, “gray-box,” dynamical systems is sought, in a manner that is robust to both noise and uncertainties. Subsequently, we will evaluate these tools through applications to unmanned aerial and land vehicles. The merit of the work is in the development of kernelized methods for dynamical systems. Occupation kernels represent a nontrivial generalization of the concept of occupation measures that are currently being leveraged to answer questions in optimal control theory by exploiting the Banach space duality between continuous functions and signed measures. By adjusting the function space to be that of reproducing kernel Hilbert spaces changes the duality, and thus makes available many tools from function theory that were hitherto unavailable to occupation measures. These tools in turn allow the embedding of trajectory information into reproducing kernel Hilbert spaces in a way that engenders a wide range of applications in dynamical systems theory.


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