LQ control of unknown discrete‐time linear systems—A novel approach and a comparison study
dc.contributor.author | Li, Nan | |
dc.contributor.author | Kolmanovsky, Ilya | |
dc.contributor.author | Girard, Anouck | |
dc.date.accessioned | 2019-03-11T15:35:47Z | |
dc.date.available | 2020-05-01T18:03:26Z | en |
dc.date.issued | 2019-03 | |
dc.identifier.citation | Li, Nan; Kolmanovsky, Ilya; Girard, Anouck (2019). "LQ control of unknown discrete‐time linear systems—A novel approach and a comparison study." Optimal Control Applications and Methods 40(2): 265-291. | |
dc.identifier.issn | 0143-2087 | |
dc.identifier.issn | 1099-1514 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/148255 | |
dc.publisher | Routledge | |
dc.publisher | Wiley Periodicals, Inc. | |
dc.subject.other | unknown system | |
dc.subject.other | optimal control | |
dc.subject.other | LQ control | |
dc.title | LQ control of unknown discrete‐time linear systems—A novel approach and a comparison study | |
dc.type | Article | |
dc.rights.robots | IndexNoFollow | |
dc.subject.hlbsecondlevel | Industrial and Operations Engineering | |
dc.subject.hlbtoplevel | Engineering | |
dc.description.peerreviewed | Peer Reviewed | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/148255/1/oca2477.pdf | |
dc.description.bitstreamurl | https://deepblue.lib.umich.edu/bitstream/2027.42/148255/2/oca2477_am.pdf | |
dc.identifier.doi | 10.1002/oca.2477 | |
dc.identifier.source | Optimal Control Applications and Methods | |
dc.identifier.citedreference | Rosenbrock HH. An automatic method for finding the greatest or least value of a function. Comput J. 1960; 3 ( 3 ): 175 ‐ 184. | |
dc.identifier.citedreference | Liu S‐J, Krstić M, Başar T. Batch‐to‐batch finite‐horizon LQ control for unknown discrete‐time linear systems via stochastic extremum seeking. IEEE Trans Autom Control. 2017; 62 ( 8 ): 4116 ‐ 4123. | |
dc.identifier.citedreference | Dean S, Mania H, Matni N, Recht B, Tu S. On the sample complexity of the linear quadratic regulator. arXiv preprint arXiv:1710.01688. 2017. | |
dc.identifier.citedreference | Dean S, Mania H, Matni N, Recht B, Tu S. Regret bounds for robust adaptive control of the linear quadratic regulator. arXiv preprint arXiv:1805.09388. 2018. | |
dc.identifier.citedreference | Bernstein DS. Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Princeton, NJ: Princeton University Press; 2005. | |
dc.identifier.citedreference | Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: Society for Industrial and Applied Mathematics; 1994. | |
dc.identifier.citedreference | Anderson BDO, Johnson CR. Exponential convergence of adaptive identification and control algorithms. Automatica. 1982; 18 ( 1 ): 1 ‐ 13. | |
dc.identifier.citedreference | Drygas H. Weak and strong consistency of the least squares estimators in regression models. Zeitschrift Wahrscheinlichkeitstheorie Verwandte Gebiete. 1976; 34 ( 2 ): 119 ‐ 127. | |
dc.identifier.citedreference | Anderson B. Exponential stability of linear equations arising in adaptive identification. IEEE Trans Autom Control. 1977; 22 ( 1 ): 83 ‐ 88. | |
dc.identifier.citedreference | Bonvin D, Srinivasan B, Hunkeler D. Control and optimization of batch processes. IEEE Control Syst Mag. 2006; 26 ( 6 ): 34 ‐ 45. | |
dc.identifier.citedreference | Hawkins WM, Fisher TG. Batch Control Systems: Design, Application, and Implementation. Research Triangle Park, NC: ISA; 2006. | |
dc.identifier.citedreference | Sobel KM, Shapiro EY. A design methodology for pitch pointing flight control systems. J Guid Control Dyn. 1985; 8 ( 2 ): 181 ‐ 187. | |
dc.identifier.citedreference | McDonough K, Kolmanovsky I. Fast computable recoverable sets their use for aircraft loss‐of‐control handling. J Guid Control Dyn. 2017; 40 ( 4 ): 934 ‐ 947. | |
dc.identifier.citedreference | Andrade JPP, Campos VAF. Robust control of a dynamic model of an F‐16 aircraft with improved damping through linear matrix inequalities. Int J Comput Electr Autom Control Inf Eng. 2017; 11 ( 2 ): 230 ‐ 236. | |
dc.identifier.citedreference | Russell RS. Non‐linear F‐16 Simulation Using Simulink and Matlab. Technical Paper. Minneapolis, MN: University of Minnesota; 2003. | |
dc.identifier.citedreference | Garza FR, Morelli EA. A Collection of Nonlinear Aircraft Simulations in Matlab. Technical Report. Hampton, VA: NASA Langley Research Center; 2003. | |
dc.identifier.citedreference | Hueschen RM. Development of the Transport Class Model (TCM) Aircraft Simulation From a Sub‐Scale Generic Transport Model (GTM) Simulation. Technical Report. Hampton, VA: NASA Langley Research Center; 2011. | |
dc.identifier.citedreference | Grauer JA, Morelli EA. Generic global aerodynamic model for aircraft. J Aircr. 2015; 52 ( 1 ): 13 ‐ 20. | |
dc.identifier.citedreference | Dussart G, Portapas V, Pontillo A, Lone M. Flight dynamic modelling and simulation of large flexible aircraft. In: Flight Physics: Models, Techniques and Technologies. London, UK: IntechOpen Limited; 2018: 247. | |
dc.identifier.citedreference | MathWorks Inc. c2d: convert model from continuous to discrete time. https://www.mathworks.com/help/control/ref/c2d.html. Accessed July 25, 2018. | |
dc.identifier.citedreference | Bryson AE, Ho Y‐C. Applied Optimal Control: Optimization, Estimation and Control. New York, NY: Routledge; 2018. | |
dc.identifier.citedreference | Ljung L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice‐hall; 1987. | |
dc.identifier.citedreference | Ioannou PA, Sun J. Robust Adaptive Control. Upper Saddle River, NJ: Prentice‐Hall; 1996. | |
dc.identifier.citedreference | Boltyansky VG. Robust maximum principle in minimax control. Int J Control. 1999; 72 ( 4 ): 305 ‐ 314. | |
dc.identifier.citedreference | Poznyak AS, Duncan TE, Pasik‐Duncan B, Boltyanski VG. Robust maximum principle for multi‐model LQ‐problem. Int J Control. 2002; 75 ( 15 ): 1170 ‐ 1177. | |
dc.identifier.citedreference | Bemporad A, Borrelli F, Morari M. Min‐max control of constrained uncertain discrete‐time linear systems. IEEE Trans Autom Control. 2003; 48 ( 9 ): 1600 ‐ 1606. | |
dc.identifier.citedreference | Walton C, Phelps C, Gong Q, Kaminer I. A numerical algorithm for optimal control of systems with parameter uncertainty. IFAC‐Pap. 2016; 49 ( 18 ): 468 ‐ 475. | |
dc.identifier.citedreference | Dierks T, Thumati BT, Jagannathan TS. Optimal control of unknown affine nonlinear discrete‐time systems using offline‐trained neural networks with proof of convergence. Neural Netw. 2009; 22 ( 5‐6 ): 851 ‐ 860. | |
dc.identifier.citedreference | Lewis FL, Vamvoudakis KG. Reinforcement learning for partially observable dynamic processes: adaptive dynamic programming using measured output data. IEEE Trans Syst Man Cybern B Cybern. 2011; 41 ( 1 ): 14 ‐ 25. | |
dc.identifier.citedreference | Wang D, Liu D, Wei Q, Zhao D, Jin N. Optimal control of unknown nonaffine nonlinear discrete‐time systems based on adaptive dynamic programming. Automatica. 2012; 48 ( 8 ): 1825 ‐ 1832. | |
dc.identifier.citedreference | Lewis FL, Vrabie D. Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits Syst Mag. 2009; 9 ( 3 ): 32 ‐ 50. | |
dc.identifier.citedreference | Recht B. A tour of reinforcement learning: the view from continuous control. arXiv preprint arXiv:1806.09460. 2018. | |
dc.identifier.citedreference | Bellman R. Dynamic Programming. Chelmsford, MA: Courier Corporation; 2013. | |
dc.identifier.citedreference | Hudson J, Gupta R, Li N, Kolmanovsky I. Iterative model and trajectory refinement for orbital trajectory optimization. Optim Control Appl Methods. 2017; 38 ( 6 ): 1132 ‐ 1147. | |
dc.identifier.citedreference | Li N, Kolmanovsky I, Girard A. Model‐free optimal control based automotive control system falsification. Paper presented at: 2017 American Control Conference (ACC); 2017; Seattle, WA. | |
dc.identifier.citedreference | Li N, Girard A, Kolmanovsky I. Optimal control based falsification of unknown systems with time delays: a gasoline engine A/F ratio control case study. Paper presented at: 5th IFAC Conference on Engine and Powertrain Control, Simulation and Modeling (E‐CoSM); 2018; Changchun, China. | |
dc.identifier.citedreference | Anderson BDO, Moore JB. Optimal Control: Linear Quadratic Methods. Chelmsford, MA: Courier Corporation; 2007. | |
dc.identifier.citedreference | Bradtke SJ. Reinforcement learning applied to linear quadratic regulation. In: Advances in Neural Information Processing Systems 5. San Francisco, CA: Morgan Kaufmann Publishers; 1993: 295 ‐ 302. | |
dc.identifier.citedreference | Kawamura Y, Nakano M, Yamamoto H. Model‐free recursive LQ controller design (learning LQ control). Int J Adapt Control Signal Process. 2004; 18 ( 7 ): 551 ‐ 570. | |
dc.identifier.citedreference | Jiang Y, Jiang Z‐P. Computational adaptive optimal control for continuous‐time linear systems with completely unknown dynamics. Automatica. 2012; 48 ( 10 ): 2699 ‐ 2704. | |
dc.identifier.citedreference | Ouyang Y, Gagrani M, Jain R. Learning‐based control of unknown linear systems with Thompson sampling. arXiv preprint arXiv:1709.04047. 2017. | |
dc.identifier.citedreference | Abbasi‐Yadkori Y, Lazic N, Szepesvari C. The return of ε ‐greedy: sublinear regret for model‐free linear quadratic control. arXiv preprint arXiv:1804.06021. 2018. | |
dc.identifier.citedreference | Fazel M, Ge R, Kakade S, Mesbahi M. Global convergence of policy gradient methods for the linear quadratic regulator. In: Proceedings of the 35th International Conference on Machine Learning (ICML); 2018; Stockholm, Sweden. | |
dc.identifier.citedreference | Zhao Q, Xu H, Sarangapani J. Finite‐horizon near optimal adaptive control of uncertain linear discrete‐time systems. Optim Control Appl Methods. 2015; 36 ( 6 ): 853 ‐ 872. | |
dc.identifier.citedreference | Fong J, Tan Y, Crocher V, Oetomo D, Mareels I. Dual‐loop iterative optimal control for the finite horizon LQR problem with unknown dynamics. Syst Control Lett. 2018; 111: 49 ‐ 57. | |
dc.identifier.citedreference | Ariyur KB, Krstić M. Real‐Time Optimization by Extremum‐Seeking Control. Hoboken, NJ: John Wiley & Sons; 2003. | |
dc.identifier.citedreference | Frihauf P, Krstić M, Başar T. Finite‐horizon LQ control for unknown discrete‐time linear systems via extremum seeking. Eur J Control. 2013; 19 ( 5 ): 399 ‐ 407. | |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.