A generalized Bernoulli wavelet operational matrix of derivative applications to optimal control problems

Abstract

In this research paper we present a new hybrid analytico-numerical scheme for solving linear quadratic optimal control problems. The method is based on a new Bernoulli wavelet matrix.  After presenting relevant properties of
the Bernoulli wavelet, we apply its connected operational matrix to derivatives. The solution is then obtained by reducing the optimal control problem under consideration to that of algebraic equations, using Lagrange multipliers. The new scheme simultaneous straightforward applicability and thourough validity balance is then demonstrated through illustrative examples.