Funnel control for nonlinear systems with arbitrary relative degree using high-gain observers

We propose a new algorithm for controlling the transient behavior of the tracking error for nonlinear systems with arbitrary relative degree. In tracking problems, the transient behavior of the error is more important than the behavior of its derivatives. We introduce a concept of virtual output, which converts an arbitrary relative degree system into a relative degree one system. The virtual output is chosen in such a way that the difference between the virtual output and the tracking error can be made arbitrarily small all the time. Assuming that the state derivatives are not available for feedback we use a high-gain observer to estimate the derivatives and construct the virtual output. (C) 2019 Elsevier Ltd. All rights reserved.