Optimal control of distributed parameter systems via orthogonal polynomials

Abstract

In this thesis, orthogonal polynomials are employed successfully to solve optimal control problem of distributed parameter systems. Three types of orthogonal polynomials are described and used to give approximate solutions, mainly, Legendre polynomials, Chebyshev polynomials and Bernstein polynomials. By the use of the particular properties of these orthogonal polynomials, the optimal control problem is simplified into the optimal control of a linear time invariant lumped-parameter system. Next, a directly computational formulation for evaluating the optimal control and trajectory of a linear distributed- parameter system is developed, unlike the variational iteration method, which allows iteratively to approximate the solution where the problems are initially approximated with possible unknowns. By means of orthogonal polynomials the solutions of optimal control problems are obtained, comparison with the variational method is made. Examples are applied to verify the convergence results and to illustrate the efficiency and the reliability of each method.