Recent Advances in Parameteridentification Techniques for O.D.E.

On estimation algorithms for ordinary differential equations

“…The Bock iteration [1] is the method of choice in the simultaneous method. Here the Newton iteration is modified by setting the constraint second derivatives to 0 in (11).…”

“…Methods for solving the optimization problem (4) fall into two general classes called here embedding [3], and simultaneous [1,6]. The embedding method provides a formal link between the problem and the closely related regression problem, but this connection involves some arbitrary choices that affects performance.…”

Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

“…There are also good reasons why collocation and multiple shooting, both dating back to the early eighties, [6,8,3], are most often superior to the single shooting approach. However, all further algorithms and reformulations yet to be presented can be equally applied to any one of the three.…”

Estimación del error en cierta clase de métodos numéricos combinados de estrategia recorrectora

“…Con la idea de validar una "familia" de métodos que se requerían fueran eficientes o al menos competitivos al abordar la resolución numérica de este tipo de problemas, se utilizó una estrategia compatible con la tendencia actual que emplea modelos con funciones objetivos mínimo-cuadradas para el ajuste de curvas y usa métodos de optimización sin y con restricciones (ver [3], [4], [7] por ejemplo), entre los que se destacan los de la familia de Newton, los quasi-Newton, el de matrices poco densas, los de tipo Broyden, entre otros para resolver un problema discretizado por un esquema numérico que puede ser implícito, semi-implícito o explícito.…”