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Robust filtering for a class of nonlinear stochastic systems with probability constraints

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Abstract

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.

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Correspondence to Lifeng Ma.

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Original Russian Text © Lifeng Ma, Zidong Wang, Hak-Keung Lam, Fuad E. Alsaadi, Xiaohui Liu, 2016, published in Avtomatika i Telemekhanika, 2016, No. 1, pp. 50–71.

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Ma, L., Wang, Z., Lam, HK. et al. Robust filtering for a class of nonlinear stochastic systems with probability constraints. Autom Remote Control 77, 37–54 (2016). https://doi.org/10.1134/S0005117916010033

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