Optimal control of linear time-varying discrete systems via discrete legendre orthogonal polynomials

A method of finite series expansion using discrete Legendre orthogonal polynomials (DLOP's) is proposed for the finite-time optimal control of time-varying discrete systems with a quadratic performance index. Computational algorithms are derived for solving two-point boundary-value canonical state equations. The method has the distinct advantage that it reduces the two-point boundary-value difference equations into a set of algebraic equations which involves specified boundary conditions. Hence, the method is particularly amenable to computer programming and parallel processing.