Gradient methods for identification of distributed parameter systems

Abstract

Parameter-dependence properties are developed in the context of a linear abstract Cauchy problem governed by a parameter-dependent operator. Of particular interest are problems in which the parameter induces an unbounded perturbation of the evolution operator. Conditions are stated under which the derivative of the state with respect to the parameter possesses certain smoothness properties. These properties lead to local convergence results for a gradient-based estimation algorithm based on quasi-linearization. Numerical results concerning a delay-differential equation indicate the effect of a forcing function on parameter sensitivity.