Numerical Solutions for Nonlinear Two-Point Boundary-Value Problems

Abstract

Optimal control problems for linear systems with quadratic performance criteria involve the solution of linear two-point boundary-value problems. The numerical solutions of these problems were discussed in the previous chapter. For nonlinear optimal control problems, iterative methods must be used to obtain the numerical solutions of the nonlinear two-point boundary-value problems. Two iterative methods for the numerical solutions are discussed in this chapter, (i) the method of quasilinearization and (ii) the Newton-Raphson method. These methods can also be used for linear or nonlinear optimal control problems subject to integral constraints.