COMPARISON OF 2 METHODS FOR THE CALCULATION OF THE GRADIENT AND OF THE HESSIAN OF COST-FUNCTIONS ASSOCIATED WITH DIFFERENTIAL-SYSTEMS

Identification and control problems associated with lumped and distributed systems are studied. The problems are set in terms of minimization of a cost function and two methods for the calculation of the gradient and of the Hessian of the cost function are considered: the first method is based on the classical Lagrangian approach using an adjoint state and an adjoint equation, while the second method involves a direct differentiation of the state equation. The paper is devoted to a comparison between the number of elementary calculations required by each method. The Lagrangian method turns out to be more advantageous.