Built on

D. A. Pomerleau, ALVINN: An Autonomous Land Vehicle in a Neural Network . San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 1989, p. 305–313
1989
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H. Hu, M. Fazlyab, M. Morari, and G. J. Pappas, “Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming,” p. arXiv:2004.07876
Original
2004
Earlier work this paper cites.
P. Pauli, A. Koch, J. Berberich, and F. Allgöwer, “Training robust neural networks using Lipschitz bounds,” p. arXiv:2005.02929
Original
2005
Earlier work this paper cites.
H. Daumé, J. Langford, and D. Marcu, “Search-based structured prediction,” Machine learning , vol. 75, no. 3, pp. 297–325, 2009
2009
Earlier work this paper cites.
A. Chakraborty, P. Seiler, and G. J. Balas, “Nonlinear region of attraction analysis for flight control verification and validation,” Control Engineering Practice , vol. 19, no. 4, pp. 335–345, 2011
2011
Earlier work this paper cites.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014
Original
2014
Earlier work this paper cites.
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht, “Gradient descent only converges to minimizers,” in 29th Annual Conference on Learning Theory , vol. 49. PMLR, 23–26 Jun 2016, pp. 1246–1257
2016
Earlier work this paper cites.
W. Sun, A. Venkatraman, G. J. Gordon, B. Boots, and J. A. Bagnell, “Deeply aggrevated: Differentiable imitation learning for sequential prediction,” in International Conference on Machine Learning , 2017
2017
Earlier work this paper cites.
T. Osa, J. Pajarinen, G. Neumann, J. Bagnell, P. Abbeel, and J. Peters, “An algorithmic perspective on imitation learning,” Foundations and Trends in Robotics , vol. 7, no. 1-2, pp. 1–179, 2018
2018
Earlier work this paper cites.

Similar

M. Jin and J. Lavaei, “Stability-certified reinforcement learning: A control-theoretic perspective,” arXiv preprint arXiv:1810.11505 , 2018
Original
2018
Cited alongside, same era.
S. Chen, K. Saulnier, N. Atanasov, D. D. Lee, V. Kumar, G. J. Pappas, and M. Morari, “Approximating explicit model predictive control using constrained neural networks,” in 2018 Annual American Control Conference (ACC) , 2018, pp. 1520–1527
2018
Cited alongside, same era.
J. F. Fisac, A. K. Akametalu, M. N. Zeilinger, S. Kaynama, J. Gillula, and C. J. Tomlin, “A general safety framework for learning-based control in uncertain robotic systems,” IEEE Transactions on Automatic Control , vol. 64, no. 7, pp. 2737–2752, 2018
2018
Cited alongside, same era.
K. K. Kim, E. R. Patrón, and R. D. Braatz, “Standard representation and unified stability analysis for dynamic artificial neural network models,” Neural Networks , vol. 98, pp. 251–262, 2018
2018
Cited alongside, same era.

Then

Y. Wang, W. Yin, and J. Zeng, “Global convergence of ADMM in nonconvex nonsmooth optimization,” Journal of Scientific Computing , vol. 78, no. 1, pp. 29–63, 2019
2019
Later among the works it cites.
H. Yin, P. Seiler, and M. Arcak, “Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers,” p. arXiv:2006.07579, Jun. 2020
Original
2020
Closest in time.
P. Pauli, J. Köhler, J. Berberich, A. Koch, and F. Allgöwer, “Offset-free setpoint tracking using neural network controllers,” arXiv preprint arXiv:2011.14006 , 2020
Original
2020
Closest in time.
M. Revay, R. Wang, and I. R. Manchester, “Convex sets of robust recurrent neural networks,” arXiv preprint arXiv:2004.05290 , 2020
Original
2020
Closest in time.

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2020

Imitation Learning with Stability and Safety Guarantees

Yin, He, Seiler, Peter, Jin, Ming et al.

Understand

A method is presented to learn neural network (NN) controllers with stability and safety guarantees through imitation learning (IL).

Convex stability and safety conditions are derived for linear time-invariant plant dynamics with NN controllers by merging Lyapunov theory with local quadratic constraints to bound the nonlinear activation functions in the NN.
These conditions are incorporated in the IL process, which minimizes the IL loss, and maximizes the volume of the region of attraction associated with the NN controller simultaneously.
An alternating direction method of multipliers based algorithm is proposed to solve the IL problem.

Built on

D. A. Pomerleau, ALVINN: An Autonomous Land Vehicle in a Neural Network . San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 1989, p. 305–313
1989
Earlier work this paper cites.
H. Hu, M. Fazlyab, M. Morari, and G. J. Pappas, “Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming,” p. arXiv:2004.07876
Original
2004
Earlier work this paper cites.
P. Pauli, A. Koch, J. Berberich, and F. Allgöwer, “Training robust neural networks using Lipschitz bounds,” p. arXiv:2005.02929
Original
2005
Earlier work this paper cites.
H. Daumé, J. Langford, and D. Marcu, “Search-based structured prediction,” Machine learning , vol. 75, no. 3, pp. 297–325, 2009
2009
Earlier work this paper cites.
A. Chakraborty, P. Seiler, and G. J. Balas, “Nonlinear region of attraction analysis for flight control verification and validation,” Control Engineering Practice , vol. 19, no. 4, pp. 335–345, 2011
2011
Earlier work this paper cites.
D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 , 2014
Original
2014
Earlier work this paper cites.
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht, “Gradient descent only converges to minimizers,” in 29th Annual Conference on Learning Theory , vol. 49. PMLR, 23–26 Jun 2016, pp. 1246–1257
2016
Earlier work this paper cites.
W. Sun, A. Venkatraman, G. J. Gordon, B. Boots, and J. A. Bagnell, “Deeply aggrevated: Differentiable imitation learning for sequential prediction,” in International Conference on Machine Learning , 2017
2017
Earlier work this paper cites.
T. Osa, J. Pajarinen, G. Neumann, J. Bagnell, P. Abbeel, and J. Peters, “An algorithmic perspective on imitation learning,” Foundations and Trends in Robotics , vol. 7, no. 1-2, pp. 1–179, 2018
2018
Earlier work this paper cites.

Similar

M. Jin and J. Lavaei, “Stability-certified reinforcement learning: A control-theoretic perspective,” arXiv preprint arXiv:1810.11505 , 2018
Original
2018
Cited alongside, same era.
S. Chen, K. Saulnier, N. Atanasov, D. D. Lee, V. Kumar, G. J. Pappas, and M. Morari, “Approximating explicit model predictive control using constrained neural networks,” in 2018 Annual American Control Conference (ACC) , 2018, pp. 1520–1527
2018
Cited alongside, same era.
J. F. Fisac, A. K. Akametalu, M. N. Zeilinger, S. Kaynama, J. Gillula, and C. J. Tomlin, “A general safety framework for learning-based control in uncertain robotic systems,” IEEE Transactions on Automatic Control , vol. 64, no. 7, pp. 2737–2752, 2018
2018
Cited alongside, same era.
K. K. Kim, E. R. Patrón, and R. D. Braatz, “Standard representation and unified stability analysis for dynamic artificial neural network models,” Neural Networks , vol. 98, pp. 251–262, 2018
2018
Cited alongside, same era.

Then

Y. Wang, W. Yin, and J. Zeng, “Global convergence of ADMM in nonconvex nonsmooth optimization,” Journal of Scientific Computing , vol. 78, no. 1, pp. 29–63, 2019
2019
Later among the works it cites.
H. Yin, P. Seiler, and M. Arcak, “Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllers,” p. arXiv:2006.07579, Jun. 2020
Original
2020
Closest in time.
P. Pauli, J. Köhler, J. Berberich, A. Koch, and F. Allgöwer, “Offset-free setpoint tracking using neural network controllers,” arXiv preprint arXiv:2011.14006 , 2020
Original
2020
Closest in time.
M. Revay, R. Wang, and I. R. Manchester, “Convex sets of robust recurrent neural networks,” arXiv preprint arXiv:2004.05290 , 2020
Original
2020
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

S. Gowal, K. Dvijotham, R. Stanforth, R. Bunel, C. Qin, J. Uesato, R. Arandjelovic, T. Mann, and P. Kohli, “On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models,” p. arXiv:1810.12715, Oct. 2018

Original

2018

Cited alongside, same era.

M. Fazlyab, M. Morari, and G. J. Pappas, “Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming,” p. arXiv:1903.01287, Mar. 2019

Original

2019

Cited alongside, same era.

M. Fazlyab, A. Robey, H. Hassani, M. Morari, and G. Pappas, “Efficient and accurate estimation of Lipschitz constants for deep neural networks,” in Advances in Neural Information Processing Systems 32 . Curran Associates, Inc., 2019, pp. 11 427–11 438

2019

Cited alongside, same era.

X. Zhang, M. Bujarbaruah, and F. Borrelli, “Safe and near-optimal policy learning for model predictive control using primal-dual neural networks,” in 2019 American Control Conference (ACC) , 2019

2019

Cited alongside, same era.

B. Karg and S. Lucia, “Efficient representation and approximation of model predictive control laws via deep learning,” IEEE Transactions on Cybernetics , vol. 50, no. 9, pp. 3866–3878, 2020

2020

Closest in time.

A. J. Taylor, A. Singletary, Y. Yue, and A. D. Ames, “A control barrier perspective on episodic learning via projection-to-state safety,” arXiv preprint arXiv:2003.08028 , 2020

Original

2020

Closest in time.

L. Lindemann, H. Hu, A. Robey, H. Zhang, D. V. Dimarogonas, S. Tu, and N. Matni, “Learning hybrid control barrier functions from data,” arXiv preprint arXiv:2011.04112 , 2020

Original

2020

Closest in time.

P. L. Donti, M. Roderick, M. Fazlyab, and J. Z. Kolter, “Enforcing robust control guarantees within neural network policies,” arXiv preprint arXiv:2011.08105 , 2020

Original

2020

Closest in time.