Algebraic approach to sensitivity analysis in optimal feedback control system design

This paper is concerned with the sensitivity analysis of optimal feedback control system design with respect to design parameters that may be determined based on various requirements other than control. Once such parameters are fixed, there are established computational tools to accomplish optimal control design. Nevertheless it is usually unclear how optimal control design is affected in case the values of design parameters are changed. In particular, the problem becomes more complicated in the presence of another type of parameters, i.e., tuning parameters, that can (and will) be tuned for the best possible control performance. Such a case requires analysis of the effect of the change in design parameters on the best choice of the values of tuning parameters. The approach presented in this paper utilizes a recently developed algebraic approach to polynomial spectral factorization that employs the Sum of Roots to acquire an explicit relationship between parameters and the optimal performance level, and analyzes optimal design in the presence of design parameters. More specifically, algebraic approaches to the sensitivity analysis of the optimal feedback control performance with respect to design parameters, the optimal choice of tuning parameter values, and the relationship among parameters in optimal design are presented.