HYBRID APPROACH TO OPTIMAL CONTROL PROBLEMS WITH BOUNDED STATE - 1. THEORY.

This paper considers the numerical solution of optimal control problems involving a functional I subject to differential constraints, a state inequality constraint, and terminal constraints. The approach taken is a sequence of two-phase processes or cycles, each composed of a gradient phase and a restoration phase. The gradient involves a single iteration and is designed to decrease the functional, while the constraints are satisfied to first order. The restoration phase involves one or several iterations and is designed to restore the constraints to a predetermined accuracy, while the norm of the variations of the control and the parameter is minimized.