Adaptive Tracking for Linear Plants under Fixed Feedback

This paper examines a control structure with two degrees of freedom, where the feedback is kept fixed while the prefilter contains adaptive features. Proofs of stability and error convergence under idealized assumptions are provided for the discrete-time case using a proposed algorithm, where parameter projection into a “stable” parameter set is utilized. Under model-mismatch assumptions, conditions for boundedness are also listed. Two challenging control problems from the literature are then considered to illustrate a pragmatic design method. The resulting controllers are compared with alternative suggested structures for adaptive tracking with fixed feedback, and differences are pointed out through simple interpretations of the respective schemes.