Adaptive systems and closed-loop reference models

Summary form only given. An integral part of adaptive control is the selection of a reference model that provides a desired target error that adaptive laws are designed to minimize. The classical approach towards this selection is to choose a corresponding desired output for the adaptive system as the output of linear time-invariant system with desired performance characteristics. A distinct departure from this approach has been suggested of late, in an attempt to improve the transient characteristics of the adaptive system. Here, the reference model is derived through a closed-loop where a tracking error is fed back. The challenge then is to determine this feedback loop so as to meet specifications of stability, transient performance, and learning, and ensure that any trade-offs that may be present are efficiently dealt with. This tutorial will provide the fundamentals of the design of closed-loop reference models, their role in adaptive systems where (i) states are accessible, (ii) multiple-inputs are present, and (iii) multi time-scales are present, and derive their properties of stability and transient performance.