Modified Quasilinearization Algorithm for Optimal Control Problems with Nondifferential Constraints and General Boundary Conditions. Part 1. Thory

摘要

The numerical solution of two classes of optimal control problems, Problem (P1) and Problem (P2), is considered. Problem (P1) involves a functional I, subject to differential constraints and general boundary conditions. It consists of finding the state, the control, and the parameter so that the functional I is minimized while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem (P2) extends Problem (P1) to include nondifferential constraints to be satisfied everywhere along the interval of integration. Algorithms are developed for both problems. Several numerical examples are presented to illustrate the performance of these algorithms. Results reveal the feasibility as well as the convergence characteristic of the algorithms.