Convex Optimization to solve Mixed time/frequency Robust Identification problems

PABLO PARRILO; RICARDO S. SÁNCHEZ PEÑA

Santiago

Seminario; Second Latin American Seminar on Advanced Control (LASAC95); 1995

Colegio de Ingenieros de Chile

The combination of both frequency and timeresponse experiments in a robust identification frameworkis presented. Necessary and sufficient conditions forconsistency are proved in terms of a convex constrainedoptimization problem. The latter is based on a generalizedinterpolation theory which takes the Caratheodory-Fejerand Nevanlinna-Pick problems as particular cases. Itssolution may be computed as a LMI or as a semidefiniteprogram. The identification procedure interpolates thefrequency and time domain data while restricting theidentified system to be in the a priori classes. This interpolationalgorithm produces a nominal model consistentwith both sources of experimental data. As a consequenceit is optimal up to a factor of 2 (with respect to centralalgorithms) and convergent. A state space realization ofthe nominal is provided.