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 mult-input multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop system's relative degree as well as a bound on the first nonzero Markov parameter. Notably, the controller does not require knowledge of the command or the disturbance spectrum as long as the command and disturbance signals are generated by a Lyapunov-stable linear system. Thus, the command and disturbance signals are combinations of discrete-time sinusoids and steps. In addition, the Markov-parameter-based adaptive controller uses feedback action only, and thus does not require a direct measurement of the command or disturbance signals. Using a logarithmic Lyapunov function, we prove global asymptotic convergence for command following and disturbance rejection as well as Lyapunov stability of the adaptive system when the open-loop system is asymptotically stable.