Publication
Probability-guaranteed set-membership state estimation for polynomially uncertain linear time-invariant systems
Conference Article
Conference
IEEE Conference on Decision and Control (CDC)
Edition
57th
Pages
2291-2296
Doc link
https://doi.org/10.1109/CDC.2018.8619698
File
Authors
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Wan, Yiming
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Puig Cayuela, Vicenç
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Ocampo Martínez, Carlos A.
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Wang, Ye
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Braatz, Richard
Abstract
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.
Categories
automation, control theory.
Author keywords
estimation, time-invariant systems, set membership estimation
Scientific reference
Y. Wan, V. Puig, C. Ocampo-Martínez, Y. Wang and R. Braatz. Probability-guaranteed set-membership state estimation for polynomially uncertain linear time-invariant systems, 57th IEEE Conference on Decision and Control, 2018, Miami, pp. 2291-2296.
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