ABSTRACT
Using the nonlinear operational matrix derived and other relevant operational properties of The Legendre polynomials (LP) and block-pulse functions (BPF), an approximate solution for a nonlinear optimal control problem with quadratic performance index is given. Looking at the historical developments on solving optimal control problem of nonlinear systems via the orthogonal functions approach, we find that not much work has been reported. Lee and Chang appear to be the first to study the optimal control problem of nonlinear systems using general orthogonal polynomials (GOP). For this, they introduced a nonlinear operational matrix of GOPs. Though their work is fundamental and significant, it is not attractive computationally, as it involves the Kronecker product operation. Chebyshev polynomials were used for solving the nonlinear optimal control problem. In a general framework for the nonlinear optimal control problem was developed by employing BPFs. This chapter describes BPFs and LPs for computing the optimal control law of nonlinear systems.
