Adaptive output feedback control of nonlinear systems using neural networks

A direct adaptive output feedback control design procedure is developed for highly uncertain nonlinear systems, that do not rely on state estimation. The approach is also applicable to systems of unknown, but bounded dimension. In particular, we consider single-input/single-output nonlinear systems, whose output has known, but otherwise arbitrary relative degree. This includes systems with both unstructured parameter uncertainty and unstructured unmodeled dynamics. This result is achieved by extending the universal function approximation property of linearly parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weights and the tracking errors are bounded. Numerical simulations of an output feedback controlled Van der Pol oscillator, coupled with a linear oscillator, is used to illustrate the practical potential of the theoretical results.