Fetching the paper…
Reading the bibliography…
We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees.
1904
Earlier work this paper cites.
1906
Earlier work this paper cites.
S. Gros and M. Zanon, “Reinforcement learning based on mpc and the stochastic policy gradient method,” in 2021 American Control Conference (ACC) , 2021, pp. 1947–1952
1952
Earlier work this paper cites.
W. Hoeffding, “Probability inequalities for sums of bounded random variables,” Journal of the American Statistical Association , vol. 58, no. 301, pp. 13–30, 1963. [Online]. Available: https://www.tandfonline.com/doi/abs/10.1080/01621459.1963.10500830
1963
Earlier work this paper cites.
M. Malek-Shahmirzadi, “A characterization of certain classes of matrix norms,” Linear and Multilinear Algebra , vol. 13, no. 2, pp. 97–99, 1983. [Online]. Available: https://doi.org/10.1080/03081088308817508
1983
Earlier work this paper cites.
G. Puskorius and L. Feldkamp, “Truncated backpropagation through time and Kalman filter training for neurocontrol,” in Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN’94) , vol. 4. IEEE, 1994, pp. 2488–2493
1994
Earlier work this paper cites.
A. Zheng and M. Morari, “Stability of model predictive control with mixed constraints,” IEEE Transactions on Automatic Control , vol. 40, no. 10, pp. 1818–1823, 1995
1995
Earlier work this paper cites.
A. Bemporad and M. Morari, “Robust model predictive control: A survey,” in Robustness in identification and control , A. Garulli and A. Tesi, Eds. London: Springer London, 1999, pp. 207–226
1999
Earlier work this paper cites.
R. S. Sutton, D. McAllester, S. Singh, and Y. Mansour, “Policy gradient methods for reinforcement learning with function approximation,” in Advances in Neural Information Processing Systems , S. Solla, T. Leen, and K. Müller, Eds., vol. 12. MIT Press, 2000. [Online]. Available: https://proceedings.neurips.cc/paper/1999/file/464d828b85b0bed98e80ade0a5c43b0f-Paper.pdf
1999
Earlier work this paper cites.
E. Asarin, O. Bournez, T. Dang, and O. Maler, “Approximate reachability analysis of piecewise-linear dynamical systems,” in Hybrid Systems: Computation and Control , N. Lynch and B. H. Krogh, Eds. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000, pp. 20–31
2000
Earlier work this paper cites.
A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, “The explicit solution of model predictive control via multiparametric quadratic programming,” in Proceedings of the 2000 American Control Conference, Danvers, MA, USA , vol. 2, 2000, pp. 872–876
2000
Earlier work this paper cites.
A. Bemporad, F. Borrelli, and M. Morari, “Explicit solution of LP-based model predictive control,” in CDC , Sydney, Australia, Dec. 2000
2000
Earlier work this paper cites.
D. Mignone, G. Ferrari-Trecate, and M. Morari, “Stability and stabilization of piecewise affine and hybrid systems: an lmi approach,” in Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) , vol. 1, 2000, pp. 504–509 vol.1
2000
Earlier work this paper cites.
D. Mayne, J. Rawlings, C. Rao, and P. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica , vol. 36, no. 6, pp. 789–814, 2000. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109899002149
2000
Earlier work this paper cites.
J. Schuurmans and J. A. Rossiter, “Robust predicive control using tight sets of predicted states.” Control Theory and Applications , vol. 147, pp. 13–18, 2000
2000
Earlier work this paper cites.
M. Grötschel, S. O. Krumke, and J. Rambau, Eds., Introduction to Model Based Optimization of Chemical Processes on Moving Horizons . Berlin, Heidelberg: Springer Berlin Heidelberg, 2001, pp. 295–339
2001
Earlier work this paper cites.
P. Tøndel, T. A. Johansen, and A. Bemporad, “An Algorithm for Multi-Parametric Quadratic Programming and Explicit MPC Solutions,” aut , Nov. 2001, preprint submitted
2001
Earlier work this paper cites.
A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications , ser. MPS/SIAM Series on Optimization. SIAM, 2001
2001
Earlier work this paper cites.
J. M. Maciejowski, Predictive Control with Constraints . Prentice Hall, 2002
2002
Earlier work this paper cites.
A. Bemporad, M. M., V. Dua, and E. N. Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,” Automatica , vol. 38, no. 1, pp. 3 – 20, 2002
2002
Earlier work this paper cites.
J. Löfberg, “Minimax approaches to robust model predictive control,” 2003
2003
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, Convex Optimization . Cambridge University Press, 2004
2004
Earlier work this paper cites.
K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers . Princeton University Press, 2004. [Online]. Available: https://fbswiki.org/wiki/index.php/Main_Page
2004
Earlier work this paper cites.
J. Löfberg, “YALMIP : A Toolbox for Modeling and Optimization in MATLAB,” in Proc. of the CACSD Conference , Taipei, Taiwan, 2004, available from http://users.isy.liu.se/johanl/yalmip/
2004
Earlier work this paper cites.
S. V. Rakovic, E. C. Kerrigan, D. Q. Mayne, and J. Lygeros, “Reachability analysis of discrete-time systems with disturbances,” IEEE Transactions on Automatic Control , vol. 51, no. 4, pp. 546–561, April 2006
2006
Earlier work this paper cites.
L. Koci and M. Mateji, “Contractive affine transformations of complex plane and applications,” Facta Universitatis Series Mathematics and Informatics , vol. 21, pp. 65–75, 01 2006
2006
Earlier work this paper cites.
A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Mathematical Programming , vol. 106, pp. 25–57, 2006
2006
Earlier work this paper cites.
A. Bemporad, “Model predictive control design: New trends and tools,” in Proceedings of the 45th IEEE Conference on Decision and Control , 2006, pp. 6678–6683
2006
Earlier work this paper cites.
R. Cagienard, P. Grieder, E. Kerrigan, and M. Morari, “Move Blocking Strategies in Receding Horizon Control,” Journal of Process Control , vol. 17, no. 6, pp. 563–570, Jul. 2007
2007
Earlier work this paper cites.
S. Hovland and J. T. Gravdahl, “Complexity reduction in explicit mpc through model reduction,” IFAC Proceedings Volumes , vol. 41, no. 2, pp. 7711–7716, 2008, 17th IFAC World Congress. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S1474667016401874
2008
Earlier work this paper cites.
U. von Luxburg and B. Schoelkopf, “Statistical learning theory: Models, concepts, and results,” 2008
2008
Earlier work this paper cites.
A. Alessio and A. Bemporad, A Survey on Explicit Model Predictive Control, in Nonlinear Model Predictive Control: Towards New Challenging Applications . Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, pp. 345–369
2009
Earlier work this paper cites.
M. Kvasnica, Real-Time Model Predictive Control via Multi-Parametric Programming: Theory and Tools . VDM Verlag, Jan. 2009
2009
Earlier work this paper cites.
H. Lin and P. J. Antsaklis, “Stability and stabilizability of switched linear systems: A survey of recent results,” IEEE Transactions on Automatic Control , vol. 54, no. 2, pp. 308–322, 2009
2009
Earlier work this paper cites.
K. Kang and R. R. Bitmead, Model Predictive Control with Control Lyapunov Function Support . Berlin, Heidelberg: Springer Berlin Heidelberg, 2009, pp. 79–87. [Online]. Available: https://doi.org/10.1007/978-3-642-01094-1_6
2009
Cited alongside, same era.
A. Domahidi, M. N. Zeilinger, M. Morari, and C. N. Jones, “Learning a feasible and stabilizing explicit model predictive control law by robust optimization,” in 2011 50th IEEE Conference on Decision and Control and European Control Conference , 2011, pp. 513–519
2011
Cited alongside, same era.
A. Gupta, S. Bhartiya, and P. Nataraj, “A novel approach to multiparametric quadratic programming,” Automatica , vol. 47, no. 9, 2011
2011
Cited alongside, same era.
M. Kvasnica and M. Fikar, “Clipping-based complexity reduction in explicit mpc,” IEEE Transactions on Automatic Control , vol. 57, no. 7, pp. 1878–1883, 2012
2012
Cited alongside, same era.
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
A. Hill, A. Raffin, M. Ernestus, A. Gleave, A. Kanervisto, R. Traore, P. Dhariwal, C. Hesse, O. Klimov, A. Nichol, M. Plappert, A. Radford, J. Schulman, S. Sidor, and Y. Wu, “Stable baselines,” https://github.com/hill-a/stable-baselines , 2018
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Aswani, H. Gonzalez, S. S. Sastry, and C. Tomlin, “Provably safe and robust learning-based model predictive control,” Automatica , vol. 49, no. 5, pp. 1216 – 1226, 2013
2013
Cited alongside, same era.
M. Kvasnica, J. Hledík, I. Rauová, and M. Fikar, “Complexity reduction of explicit model predictive control via separation,” Automatica , vol. 49, no. 6, pp. 1776–1781, 2013. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109813001076
2013
Cited alongside, same era.
M. Herceg, M. Kvasnica, C. Jones, and M. Morari, “Multi-parametric toolbox 3.0,” in 2013 European Control Conference, Zurich, Switzerland , 2013, pp. 502–510
2013
Cited alongside, same era.
J. Drgoňa, M. Kvasnica, M. Klaučo, and M. Fikar, “Explicit Stochastic MPC Approach to Building Temperature Control,” in IEEE Conference on Decision and Control , Florence, Italy, 2013, pp. 6440–6445
2013
Cited alongside, same era.
G. Frison and J. B. Jørgensen, “A fast condensing method for solution of linear-quadratic control problems,” in 52nd IEEE Conference on Decision and Control , 2013, pp. 7715–7720
2013
Cited alongside, same era.
A. Aswani, P. Bouffard, X. Zhang, and C. Tomlin, “Practical comparison of optimization algorithms for learning-based mpc with linear models,” 2014
2014
Cited alongside, same era.
G. Montúfar, R. Pascanu, K. Cho, and Y. Bengio, “On the number of linear regions of deep neural networks,” 2014
2014
Cited alongside, same era.
M. Mahmood and P. Mhaskar, “Constrained control lyapunov function based model predictive control design,” International Journal of Robust and Nonlinear Control , vol. 24, no. 2, pp. 374–388, 2014. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.2896
2014
Cited alongside, same era.
E. T. Maddalena, C. G. da S. Moraes, G. Waltrich, and C. N. Jones, “A neural network architecture to learn explicit mpc controllers from data,” 2019
2019
Later among the works it cites.
2019
Later among the works it cites.
S. W. Chen, T. Wang, N. Atanasov, V. Kumar, and M. Morari, “Large scale model predictive control with neural networks and primal active sets,” 2019
2019
Later among the works it cites.
X. Zhang, M. Bujarbaruah, and F. Borrelli, “Safe and near-optimal policy learning for model predictive control using primal-dual neural networks,” 2019 American Control Conference (ACC) , pp. 354–359, 2019
2019
Later among the works it cites.
T. Yang, “Advancing non-convex and constrained learning: Challenges and opportunities,” AI Matters , vol. 5, no. 3, p. 29–39, Dec. 2019
2019
Later among the works it cites.
J. Z. Kolter and G. Manek, “Learning stable deep dynamics models,” in Advances in Neural Information Processing Systems 32 . Curran Associates, Inc., 2019, pp. 11 126–11 134
2019
Later among the works it cites.
2019
Later among the works it cites.
B. Chen, Z. Cai, and M. Bergés, “Gnu-rl: A precocial reinforcement learning solution for building hvac control using a differentiable mpc policy,” in Proceedings of the 6th ACM International Conference on Systems for Energy-Efficient Buildings, Cities, and Transportation , ser. BuildSys ’19. New York, NY, USA: Association for Computing Machinery, 2019, p. 316–325. [Online]. Available: https://doi.org/10.1145/3360322.3360849
2019
Later among the works it cites.
2019
Later among the works it cites.
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga et al. , “Pytorch: An imperative style, high-performance deep learning library,” in Advances in Neural Information Processing Systems , 2019, pp. 8024–8035
2019
Later among the works it cites.
Y. Zhou, J. Yang, H. Zhang, Y. Liang, and V. Tarokh, “Sgd converges to global minimum in deep learning via star-convex path,” 2019
2019
Later among the works it cites.
Z. Wu, F. Albalawi, Z. Zhang, J. Zhang, H. Durand, and P. D. Christofides, “Control lyapunov-barrier function-based model predictive control of nonlinear systems,” Automatica , vol. 109, p. 108508, 2019. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109819303693
2019
Later among the works it cites.
J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, “Casadi: a software framework for nonlinear optimization and optimal control,” Mathematical Programming Computation , vol. 11, no. 1, pp. 1–36, Mar 2019. [Online]. Available: https://doi.org/10.1007/s12532-018-0139-4
2019
Later among the works it cites.
L. Hewing, K. P. Wabersich, M. Menner, and M. N. Zeilinger, “Learning-based model predictive control: Toward safe learning in control,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 3, no. 1, p. null, 2020
2020
Closest in time.
M. Gulan, N. A. Nguyen, and G. Takács, “Convex lifting based inverse parametric optimization for implicit model predictive control: A case study,” in 2020 59th IEEE Conference on Decision and Control (CDC) , 2020, pp. 2501–2508
2020
Closest in time.
A. Raha, A. Chakrabarty, V. Raghunathan, and G. T. Buzzard, “Embedding approximate nonlinear model predictive control at ultrahigh speed and extremely low power,” IEEE Trans. Control. Syst. Technol. , vol. 28, no. 3, pp. 1092–1099, 2020
2020
Closest in time.
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.
J. Hendriks, C. Jidling, A. Wills, and T. Schön, “Linearly constrained neural networks,” Submitted to IEEE Transactions on Neural Networks and Learning Systems , 2020
2020
Closest in time.
H. Kervadec, J. Dolz, J. Yuan, C. Desrosiers, E. Granger, and I. Ben Ayed, “Constrained deep networks: Lagrangian optimization via log-barrier extensions,” 05 2020
2020
Closest in time.
2020
Closest in time.
P. Petsagkourakis, W. P. Heath, and C. Theodoropoulos, “Stability analysis of piecewise affine systems with multi-model predictive control,” Automatica , vol. 111, p. 108539, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0005109819304005
2020
Closest in time.
B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “OSQP: an operator splitting solver for quadratic programs,” Mathematical Programming Computation , vol. 12, no. 4, pp. 637–672, 2020. [Online]. Available: https://doi.org/10.1007/s12532-020-00179-2
2020
Closest in time.
2020
Closest in time.
R. van de Geijn and M. Myers, Advanced Linear Algebra: Foundations to Frontiers . Creative Commons NonCommercial (CC BY-NC), 2020
2020
Closest in time.
B. Karg and S. Lucia, “Approximate moving horizon estimation and robust nonlinear model predictive control via deep learning,” Computers & Chemical Engineering , vol. 148, p. 107266, 2021
2021
Closest in time.
A. Tuor, J. Drgona, and E. Skomski, “NeuroMANCER: Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations,” 2021. [Online]. Available: https://github.com/pnnl/neuromancer
2021
Closest in time.
B. Karg, T. Alamo, and S. Lucia, “Probabilistic performance validation of deep learning‐based robust nmpc controllers,” International Journal of Robust and Nonlinear Control , vol. 31, no. 18, p. 8855–8876, Jul 2021. [Online]. Available: http://dx.doi.org/10.1002/rnc.5696
2021
Closest in time.
J. Drgoňa, S. Mukherjee, J. Zhang, F. Liu, and M. Halappanavar, “On the stochastic stability of deep markov models,” in 35th Conference on Neural Information Processing Systems (NeurIPS 2021), Sydney, Australia , 2021
2021
Closest in time.
2021
Closest in time.
M. Fazlyab, M. Morari, and G. J. Pappas, “Safety verification and robustness analysis of neural networks via quadratic constraints and semidefinite programming,” IEEE Transactions on Automatic Control , vol. 67, no. 1, pp. 1–15, 2022
2022
Closest in time.