Robustness of funnel control in the gap metric

For m-input, m-output, finite-dimensional, linear systems satisfying the classical assumptions of adaptive control (i.e., (i) minimum phase, (ii) relative degree one and (iii) positive high-frequency gain), the well known funnel controller k(t) = (t) 1-(t) e(t) , u(t) = -k(t)e(t) achieves output regulation in the following sense: all states of the closed-loop system are bounded and, most importantly, transient behaviour of the tracking error e = y - yref is ensured such that the evolution of e(t) remains in a performance funnel with prespecified boundary (t)-1 , where yref denotes a reference signal bounded with essentially bounded derivative. As opposed to classical adaptive high-gain output feedback, system identification or internal model is not invoked and the gain k(

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Achim Ilchmann, Markus Mueller
• Keywords: CDC 2010, Control Systems, Essentially Bounded, Funnel Controller, Performance Funnel