Abstract
Confidence sets are constructed for the phase state of a multistep nonlinear system, the description of whose dynamics contains both random perturbations with given distributions and uncertain perturbations with information defined by their value domains. The design of optimal confidence sets is reduced to optimization of a quantile function. Its solution is based on the information sets of a perturbed deterministic system. For linear multistep systems with Gaussian perturbations, the optimal confidence sets are determined by nonlinear estimation methods unlike in the case of complete statistical information. An example is given to illustrate that nonlinear estimation methods are far better in certain cases than the linear estimation methods.
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Timofeeva, G.A. Nonlinear Confidence Estimates for Statistically Uncertain Systems. Automation and Remote Control 64, 1724–1733 (2003). https://doi.org/10.1023/A:1027374128737
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DOI: https://doi.org/10.1023/A:1027374128737