Algorithms of data generation for deep learning and feedback design: A survey

Kang, Wei; Gong, Qi; Nakamura-Zimmerer, Tenavi; Fahroo, Fariba

doi:10.1016/j.physd.2021.132955

Cited by 17 publications

(10 citation statements)

References 30 publications

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“…Consequently, the computation does not require a grid. Demonstrated in several studies [21,22,26,27], causality-free algorithms are advantageous in data-driven computational methods for PDEs. They have perfect parallelism, a desirable property for generating a large amount of data.…”

Section: A Data-driven Methods Based On Deep Learningmentioning

confidence: 99%

Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation

Kang¹,

Sun²,

Li³

2021

Preprint

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This paper deals with a special type of Lyapunov functions, namely the solution of Zubov's equation. Such a function can be used to characterize the domain of attraction for systems of ordinary differential equations. In Theorem 2, we derive and prove an integral form solution to Zubov's equation. For numerical computation, we develop two data-driven methods. One is based on the integration of an augmented system of differential equations; and the other one is based on deep learning. The former is effective for systems with a relatively low state space dimension and the latter is developed for high dimensional problems. The deep learning method is applied to a New England 10-generator power system model. A feedforward neural network is trained to approximate the corresponding Zubov's equation solution. The network characterizes the system's domain of attraction. We prove that a neural network approximation exists for the Lyapunov function of power systems such that the approximation error is a cubic polynomial of the number of generators. The error convergence rate is O(n −1/2 ), where n is the number of neurons.

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Section: A Data-driven Methods Based On Deep Learningmentioning

confidence: 99%

Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation

Kang¹,

Sun²,

Li³

2021

Preprint

Self Cite

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“…Pseudospectral methods have the added benefit of the covector mapping theorem [35,10], which allows one to extract costate data from the solution of the discretized OCP. For further discussion on solving infinite horizon open loop OCPs and data generation approaches for supervised learning, we refer the reader to [10,17,30,32,13] and references therein.…”

Section: Data Generationmentioning

confidence: 99%

Neural Network Optimal Feedback Control with Guaranteed Local Stability

Nakamura-Zimmerer¹,

Gong²,

Kang³

2022

Preprint

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Recent research shows that deep learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In particular, some NNs with high test accuracy can fail to even locally stabilize the dynamic system. To address this challenge we propose several novel NN architectures, which we show guarantee local stability while retaining the semi-global approximation capacity to learn the optimal feedback policy. The proposed architectures are compared against standard NN feedback controllers through numerical simulations of two highdimensional nonlinear optimal control problems (OCPs): stabilization of an unstable Burgers-type partial differential equation (PDE), and altitude and course tracking for a six degree-of-freedom (6DoF) unmanned aerial vehicle (UAV). The simulations demonstrate that standard NNs can fail to stabilize the dynamics even when trained well, while the proposed architectures are always at least locally stable. Moreover, the proposed controllers are found to be near-optimal in testing.

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“…In this paper we put aside the details of how best to generate data, and assume that we can generate accurate data of the form (3.8) as we desire. For more detailed discussions on solving infinite-horizon open loop OCPs (2.1) and data generation methods in supervised learning, we refer the reader to [15,26,4,9] and references therein.…”

Section: Data Generationmentioning

confidence: 99%

Neural network optimal feedback control with enhanced closed loop stability

Nakamura-Zimmerer,

Gong,

Kang

2021

Preprint

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Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not well understood. In this paper we use numerical simulations to demonstrate that typical test accuracy metrics do not effectively capture the ability of an NN controller to stabilize a system. In particular, some NNs with high test accuracy can fail to stabilize the dynamics.To address this we propose two NN architectures which locally approximate a linear quadratic regulator (LQR). Numerical simulations confirm our intuition that the proposed architectures reliably produce stabilizing feedback controllers without sacrificing performance. In addition, we introduce a preliminary theoretical result describing some stability properties of such NN-controlled systems.

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Algorithms of data generation for deep learning and feedback design: A survey

Cited by 17 publications

References 30 publications

Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation

Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation

Neural Network Optimal Feedback Control with Guaranteed Local Stability

Neural network optimal feedback control with enhanced closed loop stability

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