Discrete-time data-driven control with Hölder-continuous real-time learning

This work provides a framework for data-driven control of discrete-time systems with unknown dynamics and outputs controllable by the inputs. This framework leads to stable and robust real-time control such that a feasible output trajectory can be tracked. This is made possible by Hölder-continuous real-time stable learning schemes that act as discrete-time stable uncertainty observers. These observers learn from prior input-output history and ensure finite-time stable convergence of estimation errors to a bounded neighborhood of the zero vector if the system is Lipschitz-continuous with respect to time, outputs, inputs, internal parameters and states. In combination with nonlinearly stable controllers, this makes the proposed framework nonlinearly stable and robust to disturbances, model uncertainties, and unknown measurement noise. Nonlinear stability and robustness analyses of the observer and controller designs are carried out using discrete Lyapunov analysis. A numerical experiment on a second-order system demonstrates the performance of this nonlinear model-free control framework.