Funnel Control With Saturation: Nonlinear SISO Systems

Tracking—by the system output—of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class of nonlinear, single-input, single-output systems modelled by functional differential equations and subject to input saturation. Prespecified is a parameterized performance funnel within which the tracking error is required to evolve; transient and asymptotic behaviour of the tracking error is influenced through choice of parameter values which define the funnel. The control structure is a saturating error feedback with time-varying nonmonotone gain designed to evolve in such a way as to preclude contact with the funnel boundary. A feasibility condition—formulated in bounds of the plant data, the saturation bound, the funnel data, the reference signal, and the initial data—is presented under which the tracking objective is achieved, whilst maintaining boundedness of the state and gain function.