Feedback stabilization of Autonomous Systems via Deep Neural Network Approximation

Duration: 35 mins 43 secs

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Description:	Professor Karl Kunisch (University of Graz) 19th November 2021 \| 14:00 - 14:30


Created:	2021-11-22 13:35
Collection:	Modelling Behaviour to Inform Policy for Pandemics
Publisher:	Isaac Newton Institute for Mathematical Sciences
Copyright:	Professor Karl Kunisch
Language:	eng (English)


Abstract:	Optimal feedback stabilization of nonlinear systems requires knowledge of the gradient of the solution to an Hamilton-Jacobi-Bellman (HJB) equation. This is a computationally challenging topic, typically plagued by the high dimension of the underlying dynamical system. In our contribution we do not address the solution of the HJB equation directly. Rather we propose a framework for computing approximating optimal feedback gains based on a learning approach using neural networks. The approach rests on two main ingredients. First, an optimal control (learning) formulation involving an ensemble of trajectories with 'control' variables given by the feedback gain functions. Second, an approximation to the feedback functions by neural networks. Existence and convergence of optimal stabilizing neural network feedback controllers is proven. Numerical examples illustrate the performance in practice. This is joint work with Daniel Walter, Radon Institute, Linz.

Abstract:

Optimal feedback stabilization of nonlinear systems requires knowledge of the gradient of the solution to an Hamilton-Jacobi-Bellman (HJB) equation. This is a computationally challenging topic, typically plagued by the high dimension of the underlying dynamical system. In our contribution we do not address the solution of the HJB equation directly.
Rather we propose a framework for computing approximating optimal feedback gains
based on a learning approach using neural networks. The approach rests on two main ingredients.
First, an optimal control (learning) formulation involving an ensemble of trajectories with 'control' variables given by the feedback gain functions. Second, an approximation to the feedback functions by neural networks.
Existence and convergence of optimal stabilizing neural network feedback controllers is proven. Numerical examples illustrate the performance in practice.

This is joint work with Daniel Walter, Radon Institute, Linz.

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