New iterative method to solve optimal control problems with terminal constraints

Abstract

Introduction T HE objective of this work is to present a new iterative method for solving optimal control problems with terminal constraints. The main idea in this work is to use a linear approximation to the state equations and a quadratic approximation to the cost functional, so that at each iteration efficient algorithms to solve linear quadratic (LQ) problems can be used to compute incremental corrections to the control signal, to make the terminal state approach the prescribed value. Many works on iterative techniques using second variations to solve optimal control problems can be found in the literature, including Refs. 1-3. The proposed scheme, however, differs from the neighboring extremal method because here the exact solution to an approximation is used in an iterative way, whereas Refs. 1-3 concern approximate solutions to the original nonlinear nonquadratic problem. The performance of the proposed method was studied in a number of examples, including a problem of atmospheric re-entry of Shuttle vehicles.