TY - GEN
T1 - Control-Oriented Learning of Lagrangian and Hamiltonian Systems
AU - Ahmadi, Mohamadreza
AU - Topcu, Ufuk
AU - Rowley, Clarence
N1 - Funding Information:
M. Ahmadi and U. Topcu are with the Department of Aerospace Engineering and Engineering Mechanics, and the Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, 201 E 24th St, Austin, TX 78712. C. Rowley is with the Department of Mechanical Engineering and Aerospace Engineering, Princeton University, Princeton, NJ 08544, e-mail: ({mrahmadi, utopcu}@utexas.edu, {cwrowley}@princeton.edu). This work was supported by grants NSF 1646522, DARPA FA8750-17-C-0087, DARPA W911NF-16-1-0001, AFRL FA8650-15-C-2546.
PY - 2018/8/9
Y1 - 2018/8/9
N2 - We propose a method based on quadratic programming for learning control-oriented models of physical systems for which limited data from only one trajectory is available. To this end, we take advantage of the principle of least action from physics. We propose two methods based on quadratic programming to approximate either the Lagrangian or the Hamiltonian of the system from the data. We show how the learning methods based on convex optimization can accommodate symmetries about the underlying system if they are known a priori. Furthermore, we incorporate the error in the approximation to build a data-driven differential inclusion, that is suitable for control purposes. We illustrate the results by an example.
AB - We propose a method based on quadratic programming for learning control-oriented models of physical systems for which limited data from only one trajectory is available. To this end, we take advantage of the principle of least action from physics. We propose two methods based on quadratic programming to approximate either the Lagrangian or the Hamiltonian of the system from the data. We show how the learning methods based on convex optimization can accommodate symmetries about the underlying system if they are known a priori. Furthermore, we incorporate the error in the approximation to build a data-driven differential inclusion, that is suitable for control purposes. We illustrate the results by an example.
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U2 - 10.23919/ACC.2018.8431726
DO - 10.23919/ACC.2018.8431726
M3 - Conference contribution
AN - SCOPUS:85052594855
SN - 9781538654286
T3 - Proceedings of the American Control Conference
SP - 520
EP - 525
BT - 2018 Annual American Control Conference, ACC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2018 Annual American Control Conference, ACC 2018
Y2 - 27 June 2018 through 29 June 2018
ER -