Finite-Time Adaptive Control for Uncertain High-Order Stochastic Nonlinear Systems With Unknown Time-Varying Control Coefficients

This research article considers the subject of finite-time control for a set of uncertain high-order stochastic nonlinear systems (HOSNSs) with unknown time-varying control coefficients. The growth conditions for the uncertain nonlinearities are more inclusive compared to those found in most previous studies. The exponents of high-order systems can take arbitrary rational numbers, which can be represented by two positive odd integers, and they are not all exactly larger than 1. Based on the conventional backstepping idea, the method of adding a power integrator is adopted to design an adaptive controller that renders the closed-loop system stochastically finite-time stable (SFTS). Due to the general nonlinearities, high-order exponents, and stochastic characteristics, the design process requires more effort, so domination instead of cancellation techniques is used. A simulation example demonstrates the correctness of the theoretical results.