Low-Complexity Tracking Control for p-Normal Form Systems Using a Novel Nussbaum Function

This article proposes a low-complexity control design for a class of nonlinear systems in p-normal form whose control directions are completely unknown. The novel contributions, as opposed to the state-of-the-art, of this study lie in the following twofold: to relax the conditional inequality regarding the derivative of Lyapunov function, a novel Nussbaum function with changing frequency is constructed, based on which an improved Nussbaum gain technical lemma is first designed such that closed-loop boundedness can be established for all time, rather than the forward completeness property (boundedness up to any finite time); to further handle nonaffine terms, the concept named separable characteristic is put forward, making the controlled systems more compatible with several general frameworks derived from backstepping-like technique. Thanks to abovementioned benefits, a prescribed performance control methodology is presented without involving any approximation techniques. Theoretical results are demonstrated via numerical simulation.