Abstract
A continuation method is discussed in this paper for solving a large class of optimal control problems with general boundary conditions and nondifferential constraints. The method converts the optimal control problems into initialvalue problems of finite-dimensional ordinary differential equations that can be solved with existing algorithms for numerical integration. The present continuation method is stabilized in the sense that stabilization techniques are introduced to avoid accumulation of error in the integration process of the differential equations. It is shown that the stabilization of the continuation method is equivalent to control of linear systems, and several stabilizing techniques are considered. Furthermore, the multiplier method (augmented Lagrangian method) of continuous type is developed for the continuation method to solve optimal control problems with boundary constraints. The effectiveness of the present method is demonstrated for an example with initial and terminal constraints.
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