Use of the Companion Transformation in Parameter Optimization and Adaptive Control

摘要

The transformation to companion canonic form for single-input, linear, time-invariant systems is shown to have important applications in the sensitivity analysis of control systems as well as in parameter optimization and model reference adaptive control problems. Two previously unknown properties of a system in companion form are demonstrated. These are the Total Symmetry Property of the sensitivity matrix of a system in companion form and the Complete Simultaneity Property. The latter states that all the sensitivity functions of the states of a companion form system can be generated by linear combinations of the signals on one sensitivity model of the system and the system states. (Author)