Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems
© 2018 IEEE. Conventional deterministic set-membership (SM) estimation is limited to unknown-but-bounded uncertainties. In order to exploit distributional information of probabilistic uncertainties, a probability-guaranteed SM state estimation approach is proposed for uncertain linear time-invariant...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/137989 |
| _version_ | 1826212132292657152 |
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| author | Wan, Yiming Puig, Vicenc Ocampo-Martinez, Carlos Wang, Ye Braatz, Richard D. |
| author_facet | Wan, Yiming Puig, Vicenc Ocampo-Martinez, Carlos Wang, Ye Braatz, Richard D. |
| author_sort | Wan, Yiming |
| collection | MIT |
| description | © 2018 IEEE. Conventional deterministic set-membership (SM) estimation is limited to unknown-but-bounded uncertainties. In order to exploit distributional information of probabilistic uncertainties, a probability-guaranteed SM state estimation approach is proposed for uncertain linear time-invariant systems. This approach takes into account polynomial dependence on probabilistic uncertain parameters as well as additive stochastic noises. The purpose is to compute, at each time instant, a bounded set that contains the actual state with a guaranteed probability. The proposed approach relies on the extended form of an observer representation over a sliding window. For the offline observer synthesis, a polynomial-chaos-based method is proposed to minimize the averaged H2 estimation performance with respect to probabilistic uncertain parameters. It explicitly accounts for the polynomial uncertainty structure, whilst most literature relies on conservative affine or polytopic overbounding. Online state estimation restructures the extended observer form, and constructs a Gaussian mixture model to approximate the state distribution. This enables computationally efficient ellipsoidal calculus to derive SM estimates with a predefined confidence level. The proposed approach preserves time invariance of the uncertain parameters and fully exploits the polynomial uncertainty structure, to achieve tighter SM bounds. This improvement is illustrated by a numerical example with a comparison to a deterministic zonotopic method. |
| first_indexed | 2024-09-23T15:16:53Z |
| format | Article |
| id | mit-1721.1/137989 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:16:53Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1379892021-11-10T03:08:12Z Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems Wan, Yiming Puig, Vicenc Ocampo-Martinez, Carlos Wang, Ye Braatz, Richard D. © 2018 IEEE. Conventional deterministic set-membership (SM) estimation is limited to unknown-but-bounded uncertainties. In order to exploit distributional information of probabilistic uncertainties, a probability-guaranteed SM state estimation approach is proposed for uncertain linear time-invariant systems. This approach takes into account polynomial dependence on probabilistic uncertain parameters as well as additive stochastic noises. The purpose is to compute, at each time instant, a bounded set that contains the actual state with a guaranteed probability. The proposed approach relies on the extended form of an observer representation over a sliding window. For the offline observer synthesis, a polynomial-chaos-based method is proposed to minimize the averaged H2 estimation performance with respect to probabilistic uncertain parameters. It explicitly accounts for the polynomial uncertainty structure, whilst most literature relies on conservative affine or polytopic overbounding. Online state estimation restructures the extended observer form, and constructs a Gaussian mixture model to approximate the state distribution. This enables computationally efficient ellipsoidal calculus to derive SM estimates with a predefined confidence level. The proposed approach preserves time invariance of the uncertain parameters and fully exploits the polynomial uncertainty structure, to achieve tighter SM bounds. This improvement is illustrated by a numerical example with a comparison to a deterministic zonotopic method. 2021-11-09T17:18:53Z 2021-11-09T17:18:53Z 2018-12 2019-08-14T18:42:10Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137989 Wan, Yiming, Puig, Vicenc, Ocampo-Martinez, Carlos, Wang, Ye and Braatz, Richard D. 2018. "Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems." en 10.1109/cdc.2018.8619698 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) other univ website |
| spellingShingle | Wan, Yiming Puig, Vicenc Ocampo-Martinez, Carlos Wang, Ye Braatz, Richard D. Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title | Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title_full | Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title_fullStr | Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title_full_unstemmed | Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title_short | Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems |
| title_sort | probability guaranteed set membership state estimation for polynomially uncertain linear time invariant systems |
| url | https://hdl.handle.net/1721.1/137989 |
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