<p>In this article, the issue of adaptive fuzzy asymptotic tracking control for odd-rational-powers high-order nonlinear systems with quantitative indices is investigated. By “quantitative indices,” we mean that convergence time, steady-state accuracy, overshoot, and maximum deviation, which are broadly required in practical application. On account of the coupling of multiple index constraints, the standard prescribed performance control schemes of “two-side” exponentially decaying are invalid. The matter will be fairly challenging and complex if the odd-rational-powers high-order nonlinear systems are taken into consideration. By introducing a pair of monotone tube boundary functions and designing the error transformation, along with the approximate capability of fuzzy logic systems, a quantitative adaptive fuzzy control algorithm is developed. A distinctive trait of the developed controller is that tracking error can satisfy the quantitative indices and ultimately converge to zero asymptotically, where these quantitative indices can be directly specified by users. In addition, the proposed algorithm contributes to suppress the jitter of the tracking error before the systems reach steady state. Two simulation results are offered to confirm the effectiveness of the theoretical findings.</p>