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Summary: This article is devoted to the global practical tracking for a class of uncertain nonlinear systems. Notably, the input powers of the system are unknown and not required to be upper bounded by known constants. This means the presence of new type of serious uncertainties, which makes the problem under investigation largely challenging and urges us to develop a new powerful adaptive control scheme, particularly the compensation strategy to overcome the negative influence caused by the uncertainties. For this, a dual high‐gain‐based adaptive control design scheme is proposed, in which a dynamic high gain and a high gain function are jointly introduced to compensate the serious system uncertainties. Under the designed controller, all the signals of the resulting closed‐loop system are bounded and furthermore the tracking error remains any prescribed small after a finite time. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the global stabilization and practical tracking for a class of uncertain nonlinear systems. The presence of unknown powers and serious parameter unknowns makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and adding a power integrator, two novel adaptive state-feedback controllers are successfully designed to achieve global stabilization and practical tracking, respectively. Remarkably, the typical feature of the two controllers lies in the introduction of the adaptive dynamic and the terms of lower and higher powers (with respect to the unknown system powers), which makes the controller powerful enough to compensate the serious parameter unknowns and the unknown powers of the system. Finally, simulation examples are provided to illustrate the effectiveness of the designed controllers. [ABSTRACT FROM AUTHOR]