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This article addresses the issue of iterative learning control for a specific category of discrete linear singular time-delay systems. A new iterative learning control algorithm based on the p-accelerated normal S-iteration method is proposed, and convergence analysis of the corresponding learning control algorithm is studied. With certain assumptions, the proposed algorithm guarantees that the output of the system converges to the desired output trajectory within a finite time interval. The theoretical analysis is supported by numerical examples. The results indicate that the p-accelerated normal S-iterative learning control algorithm outperforms both the first-order PD-type iterative learning control and second-order PD-type iterative learning control algorithms for discrete linear singular systems theoretically and numerically. [ABSTRACT FROM AUTHOR]

The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive-type operators that are linked with variational inequality problems. Our new convergence theory permits us to settle down the difficulty of unification of Korpelevich's extragradient method, Tseng's extragardient method, and subgardient extragardient method for solving variational inequality problems through an auxiliary algorithmic operator, which is associated with the seed operator. The paper establishes an interesting the fact that the relaxed inertial normal S-iterative extragradient methods do influence much more on convergence behaviour. Finally, the numerical experiments are carried out to illustrate that the relaxed inertial iterative methods; in particular, the relaxed inertial normal S-iterative extragradient methods may have a number of advantages over other methods in computing solutions to variational inequality problems in many cases. [ABSTRACT FROM AUTHOR]

The second-order ILC algorithm is studied for a class of linear discrete-time switched systems with model uncertainties, external noises and the time-delay for tracking reference trajectory by taking advantage of super-vector representation. This study is based on the assumption that the systems operate under finite intervals. A sufficient condition for convergence of the algorithms is deduced when the model uncertainties and external noises are absent. Then the convergence is analysed, when the model uncertainties are present but the external noises are absent and the robustness against the bounded external noises is discussed. The analysis manifests that the second-order ILC algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily present switching rules when they are imposed on the system. We have presented a simulation example to illustrate effectiveness of the proposed second-order ILC algorithm in the study of robustness of the considered SISO linear discrete time-invariant time delay switched system. [ABSTRACT FROM AUTHOR]

A large number of nonlinear and optimization problems can be reduced to altering point problems. This paper aims to introduce the parallel normal S-iteration technique and study its convergence rates for solving such problems in infinite-dimensional Hilbert spaces under practical assumptions. We place particular emphasis on the parallel splitting method for the sum of two maximal monotone operators and that can apply for solving a class of convex composite minimization problems. Moreover, we present applications of our iterative methods to some nonlinear problems, such as a system of variational inequalities and a system of inclusion problems. Finally, to demonstrate the applicability of the altering point technique, the performances of our proposed parallel normal S-iteration methods are presented through numerical experiments in signal recovery problems. [ABSTRACT FROM AUTHOR]