Passivity, Small Feedback, and Synthesis of Non-affine Systems in the Upper Triangular Form

Wei Lin
Warren E. Rupp Assistant Professor
Dept. of Electrical Engineering and Computer Science
Case Western Reserve University

This talk will present some recent advances in global asymptotic stabilization (GAS) of a significant class of non-affine control systems in the upper-triangular form.

For an upper-triangular system which is locally exponentially stabilizable and encompasses the feedforward system and the challenging ball-and-beam model, we show how to construct a globally stabilizing, nested saturation controller with state-dependent saturation levels, using a novel design approach which combines the nested saturation scheme for marginally unstable linear systems subject to input saturation (Teel, 1992), with the passivity-based small feedback design technique (Lin, 1995 and 1996), developed for global asymptotic stabilization of general non-affine systems with marginally stable free dynamics.

For an upper-triangular system whose Jacobian linearization is not controllable, the nested saturation design does not work due to loss of the local exponential stabilizability. In this situation we propose, in contrast to the state-dependent nested saturation design, a Lyapunov-based control scheme which provides a bottom-up, step-by-step, recursive design procedure for the construction of a globally stabilizing controller whose magnitude is "small" in nature. The proposed approach relies crucially on an effective coupling of Mazenc-Praly's forwarding design (1996, 1997) and the passivity-based small control strategy (Lin, 1995 and 1996).