Techniques in the identification of deterministic systems

The paper deals with the problem of identifying the constants in a system described by linear ordinary or partial differential equations on the basis of noise-free observations. The techniques presented are derived from the ideas of R. Bellman and include applications of quasi-linearization, differential approximation, and dynamic programming. From knowledge of available input-output data, a numerical procedure is presented to determine both the system parameters and the initial conditions to best fit the output data in the least squared sense. For systems containing parameters which are known to change at specific but unknown times, a technique of segmental differential approximation is used. In the case of partial differential equations, the problem of dealing with partial information is discussed.