This paper investigates the adaptive output tracking problem for a class of high-order stochastic nonlinear systems with unknown time-varying powers and nonlinear parameterized uncertainties. By using the parameter separation technique and adding a power integrator design method, an adaptive controller with upper and lower bounds of the unknown time-varying power is successfully designed to guarantee that all the states of the closed-loop system are bounded in probability and the output tracking error can be regulated into a small neighborhood of the origin in probability. Finally, a simulation example is provided to illustrate the effectiveness of the designed controllers.
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