セットメンバシップ同定への確率的アプローチ

—メンバシップ集合の大きさと収束性—

抄録

Probabilistic approach to set membership identification is presented. Especially, the size and convergence properties of the membership set are investigated in the presence of not only bounded disturbance but also bounded parameter uncertainty. The bounds of the disturbance and the parameter uncertainty are assumed to be tight in a probabilistic sense. Then, the following results are obtained. (i) The size of the membership set converges to zero with probability one as the number of samples tends to infinity. This means that the membership set converges to the true but unknown parameter. (ii) For a given number of samples, the size of the membership set can be estimated with a probabilistic confidence. This result also clarifies the necessary number of samples such that the distance between the true parameter and any parameter in the membership set is less than a specified upper bound with a specified probability.