Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign

In this paper, an adaptive dynamic surface control (DSC) for a class of nonlinear systems with unknown high-frequency gain (HFG) sign is proposed. The novelty of our scheme is that we separate the first virtual control signal from the HFG, which enables us to estimate the HFG directly. As a result, the traditional Nussbaum function (NF) approach is abandoned. By using the proposed DSC, the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated, which greatly reduces the computational burden. In particular, based on an initialisation technique, we prove that the ℒ∞performance of the system tracking error can be guaranteed even when the HFG sign is unknown. It is shown that all signals of the closed-loop system are semi-globally uniformly bounded. Simulation results illustrate that the proposed scheme is more applicable than that of the NF-based backstepping control.