Neural approximation of PDE solutions
An application to reachability computations
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Date
2006
Publication Type
Conference Paper
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yes
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Abstract
We consider the problem of computing viability sets for nonlinear continuous systems. Our main goal is to deal with the "curse of dimensionality", the exponential growth of the computation in the dimension of the state space. The viability problem is formulated as an optimal control problem whose value function is known to be a viscosity solution to a particular type of Hamilton Jacob! partial differential equation. We propose a trial solution based on a Feed-Forward Neural Network for the Hamilton Jacobi equation with the given boundary conditions. We use random extractions from the state space to generate training points and then employ the r-algorithm for non smooth optimization to train the network. We illustrate the method on a 2 dimensional example from aerodynamic envelope protection. © 2006 IEEE.
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published
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Book title
Proceedings of the 45th IEEE Conference on Decision and Control : San Diego, CA, December 13-15, 2006
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Pages / Article No.
3034 - 3039
Publisher
IEEE
Event
45th IEEE Conference on Decision and Control
Edition / version
Methods
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03751 - Lygeros, John / Lygeros, John