CLOT norm minimization for continuous hands-off control

Nagahara, Masaaki and Chatterjee, Debasish and Vidyasagar, Mathukumalli and et al, . (2020) CLOT norm minimization for continuous hands-off control. Automatica, 113. pp. 1-7. ISSN 0005-1098 (In Press)

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Abstract

In this paper, we propose optimal control that is both sparse and continuous, unlike previously proposed alternatives to maximum hands-off control. The maximum hands-off control is the L0-optimal (or sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. The proposed control is obtained via minimization of the CLOT (Combined L-One and Two) norm of the control input along with the constraints on the state variable. The constraints on the state variable ensures that the states are not blown up while achieving the optimal control. By using the non-smooth maximum principle, we prove that the CLOT-norm optimal control is unique, and it is continuous in the time variable. We show by numerical simulations that the CLOT control is continuous unlike L0-optimal control (or maximum hands-off control) and much sparser (i.e. has longer time duration on which the control equals 0) than the conventional EN (elastic net) control, which is a convex combination of L1 and squared L2 norms.

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IITH Creators:
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Item Type: Article
Additional Information: The research of MN was supported in part by JSPS, Japan KAKENHI Grant Numbers JP15H02668 and JP16KK0134 , and the Ministry of Internal Affairs and Communications of Japan under the Strategic Information and Communications R&D Promotion Programme, 2017–2019, No. 3620 . The research of MV and NC was supported by the US National Science Foundation, USA under Award No. ECCS-1306630 , the Cancer Prevention and Research Institute of Texas (CPRIT), USA under award No. RP140517 , and a grant from the Department of Science and Technology, Government of India . Appendix A
Uncontrolled Keywords: Bang-off-bang control, Convex optimization, Maximum hands-off control, Optimal control, Sparsity, Indexed in Scopus
Subjects: Electrical Engineering
Divisions: Department of Electrical Engineering
Depositing User: Team Library
Date Deposited: 02 Dec 2019 06:36
Last Modified: 27 Oct 2022 09:46
URI: http://raiith.iith.ac.in/id/eprint/7080
Publisher URL: http://doi.org/10.1016/j.automatica.2019.108679
OA policy: https://v2.sherpa.ac.uk/id/publication/4278
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