Asymptotic adaptive control of nonlinear systems with elimination of overparametrization in a Nussbaum-like design

Making a trade-off between the control accuracy and computational reduction is a problem frequently encountered in the system control design. This is especially difficult when one designs adaptive fuzzy (or neural network) controls for nonlinear systems, in which fuzzy controls have to consume many computational resources to tune a sufficiently large number of adaptive parameters, meanwhile nonlinear uncertainties block the high demanding control accuracy. Current works usually face a dilemma that, either the computation is reduced but the control accuracy is degraded due to the use of the norm estimation, or the asymptotic control is resulted but the computation is increased due to the extra compensation controls. To address such dilemma, we propose an asymptotic adaptive fuzzy tracking control algorithm, whose main feature is that only two adaptive laws are needed throughout the control scheme. In particular, we allocate one adaptive law to achieve adaptive fuzzy backstepping control for nonlinear systems with a focus on stabilizing the closed-loop system. We then allocate the other adaptive law not only to asymptotically drive the stabilization error to the zero, but also to achieve the elimination of overparametrization in a Nussbaum-like design, which is inspired by the tuning function-based approach.