  This work provides a framework for nonlinear model-free control of systems
with unknown input-output dynamics, but outputs that can be controlled by the
inputs. This framework leads to real-time control of the system such that a
feasible output trajectory can be tracked by the inputs. Unlike existing
model-free or data-driven control approaches, this framework guarantees
nonlinear stability. The controller and observer designs in the proposed
framework are nonlinearly stable and robust to the unknown dynamics as well as
unknown measurement noise. For ease of computer implementation, the framework
is developed in discrete time. Nonlinear stability analyses of the
discrete-time observers and controllers are carried out using discrete Lyapunov
analysis. The unknown input-output dynamics is learnt in real time using a
nonlinearly stable observer from prior input-output history. This observer
ensures finite-time stable convergence of model estimation errors to zero if
the unknown model is constant, and model estimation errors converge to a
bounded neighborhood of the zero vector if the model has bounded change in
discrete time. Measured outputs are filtered by a finite-time stable observer
before use in feedback tracking of a desired output trajectory. Finite-time
stable observer design in this framework also ensures that a nonlinear
separation principle is in effect for separate controller and observer design.
A model-free nonlinearly stable control scheme is then designed to ensure
convergence of observed outputs to a desired output trajectory. This control
scheme ensures nonlinear finite-time stable convergence of tracking errors to a
manifold where the tracking errors decay asymptotically. A numerical experiment
on a nonlinear second-order system demonstrates the performance of this
nonlinear model-free control framework.
