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SUMMARY:Feedback stabilization of Autonomous Systems via Deep Neural Netwo
 rk Approximation - Karl Kunisch  (University of Graz\, Austrian Academy of
  Sciences)
DTSTART:20211119T140000Z
DTEND:20211119T143000Z
UID:TALK165460@talks.cam.ac.uk
DESCRIPTION:Optimal feedback stabilization of nonlinear systems&nbsp\; req
 uires&nbsp\; knowledge of the gradient of the solution to an Hamilton-Jaco
 bi-Bellman (HJB)&nbsp\; equation.&nbsp\; This is a computationally challen
 ging topic\, typically plagued by the high dimension of the underlying dyn
 amical system. In our contribution we do not address the solution of the H
 JB equation directly.Rather we propose a framework&nbsp\; for computing ap
 proximating&nbsp\; optimal feedback gains based on a learning approach usi
 ng neural networks. The approach rests on two main ingredients. First\, an
  optimal control (learning) formulation involving an ensemble of trajector
 ies with 'control' variables given by the feedback gain functions. Second\
 , an approximation to the feedback functions&nbsp\; by neural networks.&nb
 sp\; Existence and convergence of optimal stabilizing neural network feedb
 ack controllers is proven. Numerical examples illustrate the performance i
 n practice.This is joint work with Daniel Walter\, Radon Institute\, Linz.
 &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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