Optimal control, MPC and MPC-like algorithms for wave energy systems: An overview

Numerical solution of linear Fredholm integral equation by using hybrid Taylor and Block-Pulse functions

Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions

The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.

A new set of orthogonal functions and its application to the analysis of dynamic systems

The multidimensional Ito-Volterra integral equations arise in many problems such as an exponential population growth model with several independent white noise sources. In this paper, we obtain a stochastic operational matrix of block pulse functions on interval [0,1) to solve m-dimensional stochastic Ito-Volterra integral equations. By using block pulse functions and their stochastic operational matrix of integration, m-dimensional stochastic Ito-Volterra integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. We prove that the rate of convergence is O(h). Furthermore, a 95% confidence interval of the errors' mean is made, the results shows that the approximate solutions have a credible degree of accuracy.

A numerical method for solving m-dimensional stochastic Itô-Volterra integral equations by stochastic operational matrix

Operations of block pulse series.- Block pulse operators.- Block pulse transforms.- Block pulse operational matrices for integrations.- Nonparametric representations of dynamic systems.- Input-output representations of dynamic systems.- State space representations of dynamic systems.- Practical aspects in using block pulse functions.

Z. Jiang

Papers

Block pulse functions and their applications in control systems