Solution of two-point-boundary-value problems by generalized orthogonal polynomials and application to optimal control of lumped and distributed parameter systems

摘要: A set of generalized orthogonal polynomials (GOPs) that can represent all types polynomial and non-orthogonal Taylor series are first introduced to solve dynamic state equations with two-point-boundary conditions. The basic idea is any function be expressed as a power series, vice versa. operational matrix for the integration thus derived. Using special characteristics these polynomials, equation two-point-boundary-value problem reduced an initial-value problem. This effective approach applied optimal control lumped or distributed parameter system. computational algorithm, in conjunction recursive formula, much simpler easier than conventional individual polynomials.