Sensitivity shaping with degree constraint by nonlinear least-squares optimization

This paper presents a new approach to shaping of the frequency response of the sensitivity function. In this approach, a desired frequency response is assumed to be specified at a finite number of frequency points. A sensitivity shaping problem is formulated as an approximation problem to the desired frequency response with a function in a class of sensitivity functions with a degree bound. The sensitivity shaping problem is reduced to a finite dimensional constrained nonlinear least-squares optimization problem. The reduction process involves the diffeomorphism from the set of all denominators for strictly positive-real functions with degree constraint to the set of Schur polynomials, firstly proven by Byrnes et al. To solve the optimization problem numerically, standard algorithms for an unconstrained version of nonlinear least-squares problems are modified to incorporate the constraint. Since the optimization problem is nonconvex, sensible selection of the initial point for the alg...

• Type: Journal
• Year: 2005
• Where: AUTOMATICA
• Authors: Ryozo Nagamune, Anders Blomqvist
• Keywords: AUTOMATICA 2005, Frequency Response, Optimization Problem, Sensitivity Function