Modified quasilinearization algorithm for optimal control problems with nondifferential constraints and general boundary conditions (Q1062009)

This paper considers the numerical solution of the problem of minimizing a functional I, subject to differential constraints, nondifferential constraints, and general boundary conditions. It consists of finding the state x(t), the control u(t), and the parameter \(\pi\) so that the functional I is minimized while the constraints are satisfied to a predetermined accuracy. The modified quasilinearization algorithm (MQA) is extended, so that it can be applied to the solution of optimal control problems with general boundary conditions, where the state is not explicitly given at the initial point. The algorithm presented here preserves the MQA descent property on the cumulative error. This error is comprised by the error in the optimality conditions and the error in the constraints. Three numerical examples are presented in order to illustrate the performance of the algorithm. The numerical results are discussed to show the feasibility as well as the convergence characteristics of the algorithm.