ABSTRACT
The optimal control of closed-loop systems requires the solution of a set of nonlinear differential equations. Since orthogonal functions (OF) are used, in the approach all that needs to be solved is a set of linear/non-linear algebraic equations, and the accuracy of the solution can be improved to the desired degree by increasing the number of OFs. The hierarchical control problem of large scale systems has also been studied via block-pulse functions (BPF). An attempt has been made to solve this problem using shifted Legendre polynomials (SLP) but failed. It is observed that solving this problem via SLPs, in a manner similar to BPF approachs, is not easy because SLPs lack disjoint property. The approach makes use of differentiation operational matrix of BPFs. Since BPFs are constant disjoint functions their differentiation operational matrix can’t be found by direct differentiation of BPFs.
