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Abstract 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. [ABSTRACT FROM AUTHOR]

Multivariable adaptive control is an important and challenging research area, where it usually requires designing adaptive laws to estimate a number of unknown parameters. Hence, this process may excessively consume limitedly available computational resources and large amount of computational time, which may degrade system performances, particularly for the case of online updating of parameter estimates. Thus reducing the number of parameters to be estimated is a promising way to solve the problem. The state-of-the-art result in the area is to update just one adaptive parameter. However, the tracking errors are only ensured bounded and thus the resulting closed-loop system is not asymptotically stable. Hence, a question that arises is whether such a result of non-zero tracking errors is the price paid for reducing the number of updating parameters. Up to now, there is still no answer to this question. In this paper, we address such an issue and realize asymptotic stability with online estimation of just one parameter. To achieve such a goal, a novel dynamic loop gain function based approach is proposed to incorporate with the backstepping control design procedure, which enables us to solve the algebraic loop problem caused by all the existing traditional Nussbaum function based approaches and thus establish system stability. A bound for the tracking error is explicitly established in terms of L 2 norm, which helps improve the transient performance by selecting the control parameters. Moreover, guaranteed by the Barbalat’s Lemma, the tracking error is further ensured to approach zero asymptotically. Finally, simulation examples are conducted to testify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]