Discrete-Time Adaptive Command Following and Disturbance Rejection with Unknown Exogenous Dynamics

We present an adaptive controller that requires limited model information for stabilization, command following, and disturbance rejection for multi-input, multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop system´s relative degree and a bound on the first nonzero Markov parameter. Notably, the controller does not require knowledge of the command or disturbance spectrum as long as the command and disturbance signals are generated by Lyapunov-stable linear systems. Thus, the command and disturbance signals are combinations of discrete-time sinusoids and steps. In addition, the controller uses feedback action only and thus does not require a direct measurement of the command or disturbance signals. We prove global asymptotic convergence for command following and disturbance rejection