Probability-Guaranteed Set-Membership State Estimation for Polynomially Uncertain Linear Time-Invariant Systems
Name
2114-Probability-Guaranteed-Set-Membership-State-Estimation-for-Polynomially-Uncertain-Linear-Time-Invariant-Systems.pdf
Description
Accepted version
Size
816.87 KB
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Unknown
Checksum (MD5)
f82976e9636d1b6c730497b30c8a042a
Author(s)
Wan, Yiming
Puig, Vicenc
Ocampo-Martinez, Carlos
Wang, Ye
Braatz, Richard D
Date Issued
December 2018
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
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."
Version
Author's final manuscript
Abstract
© 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.
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/cdc.2018.8619698
