Funnel Control With Saturation: Linear MIMO Systems

Abstract

Tracking-by the system output-of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of linear <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -input, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -output systems subject to input saturation. The system is assumed to have strict relative degree one with stable zero dynamics. Prespecified is a performance funnel, within which the tracking error is required to evolve: transient and asymptotic behavior of the tracking error is influenced through choice of parameter values which define the funnel. The control structure is a saturating error feedback with a gain function designed to evolve so as to preclude contact with the funnel boundary. A feasibility condition (formulated in terms of the system data, the saturation bounds, the funnel data, bounds on the reference signal, and the initial state) is presented under which the tracking objective is achieved, whilst maintaining boundedness of all signals.