Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm
Switched systems, or systems whose control parameters include a continuous-valued input and a discrete-valued input which corresponds to the mode of the system that is active at a particular instance in time, have shown to be highly effective in modeling a variety of physical phenomena. Unfortunatel...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/86125 |
| _version_ | 1826189964246777856 |
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| author | Vasudevan, Ramanarayan Gonzalez, Humberto Bajcsy, Ruzena Sastry, S. Shankar Vasudevan, Ram |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Vasudevan, Ramanarayan Gonzalez, Humberto Bajcsy, Ruzena Sastry, S. Shankar Vasudevan, Ram |
| author_sort | Vasudevan, Ramanarayan |
| collection | MIT |
| description | Switched systems, or systems whose control parameters include a continuous-valued input and a discrete-valued input which corresponds to the mode of the system that is active at a particular instance in time, have shown to be highly effective in modeling a variety of physical phenomena. Unfortunately, the construction of an optimal control algorithm for such systems has proved difficult since it demands some form of optimal mode scheduling. In a pair of papers, we construct a first order optimization algorithm to address this problem. Our approach, which we prove in this paper converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical chattering lemma that we formalize. In the second part of this pair of papers, we describe how this conceptual algorithm can be recast in order to devise an implementable algorithm that constructs a sequence of points by recursive application that converge to local minimizers of the optimal control problem for switched systems. |
| first_indexed | 2024-09-23T08:32:39Z |
| format | Article |
| id | mit-1721.1/86125 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:32:39Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/861252022-09-23T12:48:50Z Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm Vasudevan, Ramanarayan Gonzalez, Humberto Bajcsy, Ruzena Sastry, S. Shankar Vasudevan, Ram Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Vasudevan, Ram Switched systems, or systems whose control parameters include a continuous-valued input and a discrete-valued input which corresponds to the mode of the system that is active at a particular instance in time, have shown to be highly effective in modeling a variety of physical phenomena. Unfortunately, the construction of an optimal control algorithm for such systems has proved difficult since it demands some form of optimal mode scheduling. In a pair of papers, we construct a first order optimization algorithm to address this problem. Our approach, which we prove in this paper converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical chattering lemma that we formalize. In the second part of this pair of papers, we describe how this conceptual algorithm can be recast in order to devise an implementable algorithm that constructs a sequence of points by recursive application that converge to local minimizers of the optimal control problem for switched systems. National Science Foundation (U.S.) (Award ECCS-0931437) 2014-04-11T19:00:43Z 2014-04-11T19:00:43Z 2013-12 2013-09 Article http://purl.org/eprint/type/JournalArticle 0363-0129 1095-7138 http://hdl.handle.net/1721.1/86125 Vasudevan, Ramanarayan, Humberto Gonzalez, Ruzena Bajcsy, and S. Shankar Sastry. “Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm.” SIAM J. Control Optim. 51, no. 6 (January 2013): 4463–4483. © 2013, Society for Industrial and Applied Mathematics en_US http://dx.doi.org/10.1137/120901490 SIAM Journal on Control and Optimization Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Vasudevan, Ramanarayan Gonzalez, Humberto Bajcsy, Ruzena Sastry, S. Shankar Vasudevan, Ram Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title | Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title_full | Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title_fullStr | Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title_full_unstemmed | Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title_short | Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 1: A Conceptual Algorithm |
| title_sort | consistent approximations for the optimal control of constrained switched systems part 1 a conceptual algorithm |
| url | http://hdl.handle.net/1721.1/86125 |
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