Optimal control of linear time-delay systems via general orthogonal polynomials

A Padé approximation is introduced to transform the delay differential equation into an ordinary equation. The optimal control of a linear time delay system with quadratic performance index is then derived via general orthogonal polynomials. The adjoint equation is also extracted using a maximum principle. The state and adjoint equations can be solved by using the general orthogonal polynomials and the difficulty encountered when using a two-point boundary condition is circumvented. Examples are given to demonstrate the usefulness of the proposed method.