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...

In this paper, we prove the existence of a random common fixed point of two continuous contractive random operators on a separable Banach space. We introduce the random modified Ishikawa iteration scheme and use our existence result to study weak and strong convergence of this scheme to a unique random common fixed point of two random asymptotically quasi-nonexpansive operator. Our work extends...

in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

Robust dynamic programming (robust DP) mitigates the effects of ambiguity in transition probabilities on the solutions of Markov decision problems. We consider the computation of robust DP solutions for discrete-stage, infinite-horizon, discounted problems with finite state and action spaces. We present robust modified policy iteration (RMPI) and demonstrate its convergence. RMPI encompasses bo...

Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three implementations of approximate MPI (AMPI) that are exten...