Funnel control of higher relative degree systems

We propose a new algorithm for controlling the transient behavior of the tracking error for higher relative degree systems. When considering problems of tracking, controlling the transient behavior of the error is more important when compared to 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 tracking error approaches it from the initial time and the difference between the virtual output and the tracking error can be made arbitrarily small. 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. By designing a performance funnel for the virtual output we are able to make the error evolve within the funnel.