This note shows that the number of arithmetic operations required by any member of a broad class of optimistic policy iteration algorithms to solve a deterministic discounted dynamic programming problem with three states and four actions may grow arbitrarily. Therefore any such algorithm is not strongly polynomial. In particular, the modified policy iteration and λ-policy iteration algorithms a...

A modified version of the first-order logic of probability presented in (Halpern 1990) – with probability on possible worlds – makes it possible to formulate an alternative characterisation of fuzzy sets. In this approach, fuzzy sets are no longer seen as primitive entities with an intuitive justification, but rather as structured entities emerging in a suitable logical framework. Some fuzzy te...

This note proposes ILC for discrete-time affine nonlinear systemswith randomly iteration varying lengths. No prior information on the probability distribution of random iteration length is required prior for controller design. The conventional P-type update law is used with a modified tracking error because of randomly iteration varying lengths. A novel technical lemma is proposed for the stric...