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Gradient-augmented supervised learning of feedback control laws for high-dimensional nonlinear dynamics

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MDLW03 - Deep learning and partial differential equations

High-dimensional Hamilton-Jacobi-Bellman PDEs naturally arise in feedback control synthesis for high-dimensional dynamics, and their numerical solution must be sought outside the framework provided by grid-based discretizations. In this talk, we discuss the construction of optimal feedback laws for high-dimensional nonlinear dynamics circumventing the direct numerical approximation of the HJB PDE . Our feedback law recovery is cast in a supervised learning framework, through the generation of a synthetic dataset from samples of the HJB solution and its gradient. This gradient-augmented formulation scales efficiently with respect to the dimension of the control system, and is complemented with sparse optimization to recover a feedback law of reduced complexity. We present different architectures for feedback recovery, including polynomial approximation, tensor decompositions, and deep neural networks. This talk is based on joint works with G. Albi, B. Azmi, S. Bicego, S. Dolgov, K. Kunisch and L. Saluzzi.

This talk is part of the Isaac Newton Institute Seminar Series series.

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